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Jamie Black

TE 801 005

Project 2

Section 1: Big ideas :

A digit has a different value depending on its place in a number. Each coin holds a different monetary value, different combinations or sets of

coins will represent various monetary values Numbers can be composed or decomposed into larger or smaller units. For

example, the number 52 can be decomposed into 5 ten units and 2 one units, whereas 10 one units can be composed into 1 ten unit.

We measure using units; units are different depending on what we are measuring. For example, if we are measuring temperature we use degrees, if we are measuring money we are using cents and dollars.

Common Core Standards :

CCSS.2.OA.1: Represent and solve problems involving addition and subtractionUse addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

CCSS.2.NBT.1: Understand place valueUnderstand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:a. 100 can be thought of as a bundle of ten tens — called a “hundred.”b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

CCSS.2.NBT.2: Count within 1000; skip-count by 5s, 10s, and 100s.

CCSS.2.NBT.3: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

CCSS.2.NBT.4-Compare two three-digit numbers based on meanings of hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.

CCSS.2.MD.8: Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

Standards for mathematical practice (at beginning of CCSS document)

#1 Make sense of problems and persevere in solving them According to the Common Core State Standards for Mathematics, making sense of a problem and solving it involves being able to:

Consider analogous problems Rely on using concrete objects or pictures to help conceptualize and solve a problem Check their answers to problems using a different method, and they continually ask

themselves, “Does this make sense?” Understand the approaches of others to solving complex problems and identify

correspondences between different approaches. (CCSS)

I chose this standard for mathematical practice because I want my students to work toward becoming independent math problem solvers that persevere even when the work is challenging. In order to solve a problem, students must understand it, so I want them to look back to analogous problems and see what strategies were used previously and if they would work again. I plan to help support students work toward this by asking them to remember problems that we have done previously and have them help me re-solve the problem.

Relying on objects to help conceptualize a problem will be important throughout my unit because my students will be asked to count change which they will need some way to record their counting. For this, I will ask students to draw the coins they are counting by labeling them: P, N, D, and Q.

Also, I want students to be able to go back and check their answers and ask themselves, “Does this make sense?” When a student gives me an answer in class I plan to ask them to explain their answer to me and help them check to see if they answered the question properly. This may look like me asking “what is our unit in this problem?” or “can you count this back to me?” If the student doubts their answer I may ask: “would you like to change your answer?” Giving students the opportunity to look over their answer again will promote the sense of perseverance that is necessary when solving math problems. I never want students to get the impression that just because their answer was wrong that means that they are bad at math and should stop trying, I want them to see what they did wrong and help them work through the problem and persevere.

Lastly, I want students to understand how to solve problems in different ways. To support this skill I will ask students to show me their thinking to see if they agree with the answer that was given or not. For example, if I ask how much money is shown and I get the answer of 25 cents, I will tell students “show me a thumbs up if you agree with this or a sideways shaking thumb if you are thinking differently.” We already do this in class and it asks students to answer the question “does this make sense?” and “is this the same or different from my answer?” During my unit I will also try my best to walk around and monitor student’s answers so that I can see different ways students solved the problems and ask students to share these answers with the class. If a student is unsure of how to solve a problem, seeing someone else’s thinking may help them find a way they feel confident to answer a similar problem next time.

Learning targets:

Days one and two:

I can make change by counting up from the cost of an item, to the amount I paid for the item

I can count money to help me solve word problems

Lesson three:

I can count money to help me solve word problems I can make exact change I can make change by counting up from the cost of an item, to the amount I paid for the

item

Lesson four:

I can determine a total value of a group of coins I can count money to help me solve word problems I can count to 1,000 using 1s, 5s, 10s, and 100s I can make $1.00 using different combinations of coins

Lesson five:

I can make exact change

Lesson six:

I can identify the hundreds, tens, and ones digit of a number

Lesson seven:

I can compare two digit numbers using greater than, less than, and equal to

Lesson eight:

I can understand and use hundreds, tens, and ones to make two and three digit numbers using base tens blocks

I can read and write numbers to 1,000 in different ways (standard form, expanded form, number name, base 10 blocks)

Lesson nine:



Lesson ten:



I can explain my thinking and critique the thinking of others

The majority of this lesson is focused on working with money, which is a skill my students will need the rest of their lives. From day to day we need to know how to pay in exact change and we need to be able to count up change to see how much money we should be getting back. If one of my students were to buy something at the store, they would need to know the value of each coin and be able to determine the total value of a group of coins in order to give the cashier the correct amount. Counting in different intervals is also helpful to my students outside of school. When setting the table they must count how many people will be eating with them, which they would count by 1s. When ordering pizza that is five dollars, they could count by 5s to figure out how much money they would spend on several pizzas for a party.

In project 1 I observed a grocery store in the community where many of these skills would be beneficial. For instance, if my student wanted to buy a gumball for 25 cents, they would have to look at the machine and notice that it only accepts exact change and then determine the value of a group of coins used to pay for the gumball. When paying at the grocery store you could either pay in exact change or you would want to calculate the change back to make sure you are getting the correct amount back, so these are skills that my students can develop throughout my unit.

Section 2 A: Pre-assessment design

Pre-assessment

1) Miss Black has 3 dimes, 1 nickel and 2 pennies in her pocket. How much money does she have in her pocket?

_____________ ¢

I can determine a total value of a group of coins I can count money to help me solve word problems I can count to 1,000 using 1s, 5s, 10s, and 100s

2) Here is one way to make 25 cents:

Q

I can make exact change I can count money to help me solve word problems I can give coin equivalencies

Using P, N, D and Q show me another way to make 25 cents.

3) Ms. Van Hekken has 2 Quarters.

She wants to buy a pencil for 10 cents.

Using P, N, D and Q show how much money she will get back.

I can make change by counting up from the cost of an item, to the amount I paid for the item

4) Write the correct number of hundreds, tens, and ones in the number 234.

______ hundreds

______ tens

______ ones

Given a 3 digit number, I can write what number is in the ones, tens and hundreds place

5) Going from 23 to 24 is one hop. How many hops would it take to go from the number 24 to 28

on the number line below?

I can find a given number on the number line I can count to 1,000 using 1s, 5s, 10s, and 100s

6) The clock below shows the time that Miss Black goes to bed. Write what time she goes to bed.

I can record times shown on the Judy clock

Section 2B: Pre-Assessment ResultsWhat my students did well with:

Place value-working with a three digit number, most students were able to correctly identify the values of the ones, tens, and hundreds places.

Determining the value of a group of coins-most students were able to tell me there was 37 cents - many students used the “eyelash” strategy to count by 5s to count coins

Hops on the number line

23 24 25 26 27 28 29

1 hop

- Most students were able to locate their starting number on the number line and get to the ending number and record how many hops were in between.

Coin equivalencies- Most of my students were able to show me different ways to make 25 cents- Some students drew 25 pennies but most found simpler ways to show 25 cents

besides the quarter- I was surprised when a couple students wrote down two different ways to show 25

cents when I only asked for one. - (see performance chart- students that struggled typically got several wrong on the

assessment)

What my students struggled with:

Giving change back (problem 3)- This does not surprise me because it will be a new concept for students during this

unit. - Many students did not understand the problem so they just copied the coins that were

given Time

-18 out of 28 students were able to correctly identify the time was 10:00 and they wrote it in proper time notation- A couple students misunderstood the problem and gave responses that were not even related to the question (one gave a number model and one drew the clock again) - the most common mistake was mistaking the minute and hour hands, so my students recorded 12:50 as the time. - a few students also wrote 12:10 as the time, which suggests that they do not understand the clock hands and that the minutes are expressed by counting fives starting at 12 and continuing around the clock

What surprised me:

7 of my students were able to tell me the correct change that they should receive back when using two quarters to pay for a ten cent pencil. This was surprising because we have not taught this yet, so it suggests that these students might have prior experience with making change or were able to connect this to a subtraction problem of 50-10=40. To push these students further I will make them show their answers using the fewest amounts of coins possible.

Students got really creative with making 25 cents in other ways. I was initially thinking that I would myself draw two dimes and a nickel, but they used a variety of coins to show this.

Next steps:

Since making change is something students struggled with I want to teach students in my lesson to make a number model to help them solve this problem. For example, if the problem is: “I have two quarters. I want to buy a pencil for 10 cents. How much money will I get back?” I plan to model working through the problem thoroughly by asking them

“How much are two quarters worth?” Ok, so we have 50 cents, now we want to buy something for ten cents. So we are need to take away 10 cents. Our number model would be 50-10=_____. Our answer is how much change we will get back. So, how much change will we get back? What coins will we need to show that amount?” I feel like I really need to make this step explicit, and connect it to their previous knowledge (number model) as much as possible. Also, making this content authentic will help me engage the students, so I plan to make activities where we pretend to buy items that they would really buy outside of school.

A few students struggle with counting coins still, so I already plan to review practicing this skill and practicing skip counting by 5s, 10s, and 25s. For those who do not struggle, I will have them then start skip counting by a different number, so getting them to automatically switch between counting by 5s and then 10s.

My mentor teacher will be reviewing time with them, so this is something that I personally will not be covering, but I will take it into consideration when we near the end of our unit that will be shortly after I am done with guided lead teaching. Again, it will be a lot of explicit instruction of which one is the minute hand and hour hand and how we count by 5s for the minutes around the clock.

Since most students worked well on giving me coin equivalencies, I might challenge them more in some of my math messages within the lesson and have them share what they came up with. I know one of the big ideas of this unit is that the same amount of money can be represented in many different ways, so this will help cover that big idea.

Student performance chart- C= correct I= incorrect. This is a breakdown of individual student performance. I wrote notes on areas students did particularly well or areas they struggled with.

Student Question 1- counting coins

Question 2- showing how to make equivalent group of coins

Question 3- giving back change

(answer= 40 cents)

Question 4 – place value (1s, 10s, 100s places)

Question 5- number line

Question 6- telling time

1 C c c c c c2 c c- showed

numerous ways

I-15 cents c c Left blank

3 c c I-15 cents c c c4 c c I c c c- not

written in time notation. Written as: 10 O’clock

5 c c-used all pennies

I-25 cents. Tried to draw

c c I- wrote 12:50

it out with dots

instead of 10:00 (flip flopped hands)

6 c c-showed 2 ways

I-tried to show equivalencies

c c I-wrote 12:10. Trouble with hands and counting by fives for minute hand

7 c c-showed 2 ways

I-wrote 30 cents. He miscounted the dime as 20 cents.

c c c

8 c c-showed 25 pennies

I-no answer. Tried to draw coins.

c c I-wrote 12:50/ flip flopped hands

9 c I-showed 23 cents using all pennies

I-wrote 99 cents (with cent symbol backwards)

c c c

10 c c I-wrote 10 cents. Misunderstood problem

c I-did not answer

c

11 c c-showed all pennies.

c c c c

12 c c c c c c13 c c c c c c14 c c c c c I-no

answer15 I-14 cents I-drew 3 Q,

3P, 2DI-15 cents I-random

guessesI-went backwards on number line instead ofForwards

I-wrote number model, did not tell time

16 c c c-used least amount of coins

c c c

17 c c c c c c18 c I-drew 2

quarters and 3 nickels

I-drew 60 cents

I-for the number 234 he said there were 4 hundreds, 2 tens, 3 ones.

c c

20 c c c-used smallest amount of coins possible

c c I-flip flopped hands. Wrote 12:50

21 c c-drew 3 ways

c- drew 2 ways to solve

c c c

22 c c I-drew 10 cents

c c c

23 c c-used all pennies.

I-drew a nickel

c c c

24 c c I-drew a dime

c c I-wrote 12:10

26 I-20 cents instead of 37 cents

I-drew a quarter. I already gave a quarter

I-looks like she tried to do coin equivalencies instead of making change

c c I-no time in time notation, she re-drew the clock

27 I-wrote 42 cents

I I-28 cents, appears to be a random guess

I-appear to be random guesses.

c c

28 c c I-15 cents instead of 40

c I-5 hops instead of 4

c

Section 2C:

Formative Assessment

Assessment strategies:

1) Hand signals

What it is: My classroom already uses hand signals as a gesture used to express agreement or disagreement with math answers. A thumbs up is given if you agree with a previously shared answer or a sideways shaking thumb if you are not so sure about their answer and you would like to suggest a different answer.

How I will use it: During my unit teaching I plan to stop during math lessons and ask the whole class to show me hand signals after an answer is shared, this will help me see individual students and if they have the right answer or not. Of course I cannot ask this after every single problem we cover; therefore I may save it for questions that the answers are debatable or after a student shares an incorrect solution. I will make sure that I ask them to justify their opinion and always push further to ask for an explanation.

2) Whisper check What it is: After students are given time to come up with a solution, on the count of three they will all whisper their answer for the teacher to hear.

How I will use it: After I hae a question that is a one word answer I will ask students to think about it. Next, I will count to three, on three everyone will whisper their answer to me and I will listen for responses. If I hear an overwhelming response, then I will say something like “I hear… what do you think?” Then I will push for an explanation. If I hear an incorrect answer from a lot of students, then we will discuss it and it will let me know if I need to re-teach the material.

3) Math journalsWhat it is: Each student has their own math notebook in which to record their answers.

How I will use it: Everyday Math lessons start with mental math and math message activities, so I will ask students to write their solutions to these questions in their math journals. This is quicker and more efficient for my second graders rather than writing it on white boards. During the lesson I will walk around and monitor their answers. If needed, I can have students turn their journals in. Looking at the answers in their math journal will allow me to choose and sequence those students who I wish to share their answers.

The above ideas for formative assessment were suggestions made by the following source:

Formative (Informal) Assessment Strategies (2008). In American Federation of Teachers.

http://www.aft.org/pdfs/teachers/teach11materials/t11_providingh3.pdf

http://www.aft.org/pdfs/teachers/teach11materials/t11_providingh3.pdf

How I will track individual student growth:

I plan to use the math journals as a system that I can keep track of individual student growth. I will look at student responses to mental math and math message problems to assess student growth in the area of my learning targets. Each type of problem that is presented in Everyday Math is related to a learning goal that I cover throughout my unit, so I will be able to analyze student understanding of specific target areas based on looking at their answers to the various types of problems. I will check math journals during the lesson as I walk around and monitor answers, if a student has an incorrect solution I may ask them to share and see what other students think. However, I will not stop there, I will give students the chance to revise their solutions and explain their thought processes and change in thinking. Another formative assessment that I will use is a whisper response. I will ask students on the count of three to whisper their answer to me, this way I can quickly and easily check which students understand the concept or not.

Summative Assessment

The summative assessment of my unit will be a practice test in which I will analyze a handful of questions that relate to the concepts I taught during my unit. I will use student’s answers to these practice test questions and encourage discussion and sharing of strategies for each one. I will try to take notes on common misunderstandings that students make as I walk around and monitor. The following are the problems I will be looking at and learning targets that they align with:

1. What number does the picture show? (2.NBT.1 I can understand and use hundreds, tens, and ones)

What is another way to write this number? ______________________

2) What is another way to write 700+40+9 ((2.NBT.1 I can understand and use hundreds, tens, and ones)

A. 749 B. 479 C. 709 D. 794

3) What is another way to write 839? (2.NBT.1 I can understand and use hundreds, tens, and ones)

4) 684 Choose the correct number name: (2.NBT.1 I can understand and use hundreds, tens, and ones)A. Six hundred eighty-fourB. Six hundred forty-eightC. Six hundred sixty-four D. Eight hundred forty-six

5) 684. How do you write this number in expanded form? (2.NBT.1 I can understand and use hundreds, tens, and ones)

A. 600 + 40 + 4 B. 600 + 8 + 4 C. 600 + 80 + 4 D. 800 + 60 + 4 E. 600 + 40 + 8

6) Mary had 9 nickels. Then she found 7 pennies. How much money does Mary have? Label your answer. ______________ ( 2.MD.8 I can count money to help me solve word problems)

7) Anna used 2 quarters and 6 dimes to pay for a kite. How much money did she use? ( 2.MD.8 I can count money to help me solve word problems)

8) Jim used 3 quarters, 1 nickel, 3 pennies and $1 to buy a book. How much money did he use? (( 2.MD.8 I can count money to help me solve word problems)

9) 658= 60 + 50 +80

Is this statement true or false? Explain your thinking.

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

.

Section 3: Differentiation Strategies:

Strategies:

1) More higher level tasks and choice- I will be inventing new math messages and mental math activities for most of my lessons to allow for more higher level and open ended tasks that support discussion and sharing answers. I may try to incorporate more discussion with these problems by setting up a turn and talk. Personally, I feel more comfortable sharing my ideas with the whole group after I had time to talk it over with at least one other person, and I feel like many of my students might feel the same way (especially those who are shyer).

2) Using manipulatives- By using manipulatives my students will get to see math represented in a number of ways. As the Miller and Hudson article (2006) suggests, students should see math represented in different modes that start with concrete, to pictorial, to abstract. Hence, I want to start out with concrete examples, or manipulatives that my students can actually see and physically manipulate. The most common manipulative that we will be using throughout my unit will be coins. Each student will bring in a bag of real coins from home to manipulate, but also I will have access to large magnetic coins that I can use on the board for the whole class to see. Another manipulative that I plan to use is a hundreds chart. Every student has a small hundreds chart on their name tag along with a number line and addition chart which we will be using frequently. After my students become more comfortable with the manipulatives we can move onto other modes of representations such as pictorial (drawing out our coins) and then to more abstract methods. I would also love to try and find a smartboard lesson that I could use during my unit that would allow students to participate and interact with. I will encourage students to use the manipulatives that they are most comfortable with, for example if they would rather draw out the coins they may do so or if they would rather move they physical coins they may also do so. I will leave this open for students that do not need manipulatives, they may just be able to do it in their head.

3) Appeal to different learning styles- Throughout my teaching I want students to interact with me in a number of different ways so each student has at least one area in which they can excel. For example, I want to try to incorporate a smart board lesson or at least some lesson that can get students up and moving (which would appeal to my kinesthetic learners as well as visual learners). Another way to appeal to these types of learners would be using the manipulatives such as coins, because it would give students the opportunity to visualize the coin amounts and physically touch and move the coins. I also mentioned trying to do turn and talks which would allow my auditory learners to listen to other’s thinking and explanations. For my read-write learners I may try to incorporate problems that allow them to explain their thinking through writing.

Scaffolding and Support:

I plan to model a lot throughout my lessons, so I will use the document camera to display work pages that we are completing or I will use large magnetic coins up on the board. Along with modeling, I think it is extremely important to set clear expectations so that all students know exactly what to expect. Among my lessons I will seek opportunities to involve students in my modeling so that their peers can make that connection. For example, if I am explaining a game that requires partners I will ask a student to be my partner so that they get practice with the game, but also that their classmates can see that what I am asking them to do is manageable.

Also, I will try as much as possible to have gradual release throughout my lessons. We will work on a problem together as a class and do a couple that are similar, and then I will allow the students to help me on the next one, and last I will give them the opportunity to try one by themselves. Whenever possible, I will give students the opportunity to teach the rest of the class and share their answers. After getting to understand the format of the problem I will let students attempt them on their own and then share answers with the class. The turn and talk partner discussion will also allow students to show their own understanding before it is explicitly modeled in front of them. I will also pull sticks to make sure everyone participates.

I know that I have one student who has Asperger’s and he is very bright, but sometimes the social situations are a challenge for him. Not every student will be comfortable working with other students all the time, hence I will allow for individual problem solving activities alongside group or partner solving activities. This student also does well with a consistent schedule; therefore I will try to structure my lessons in a predictable format each time so that he and my other learners will have a good feel for what is expected from them next.

How I plan to use other adults in the room:

During most lessons there will be two other adults in the classroom. First, my mentor teacher will be there and second, there is a paraprofessional that works mostly one on one with a particular student. I plan that my mentor teacher will support my lesson in many ways. First, I expect that she will circulate the room with me and make sure that students are on task and she will help answer questions that students may have or areas they are struggling with. I also expect that my MT will be able to conference with me after I teach and let me know what observations she made during the lesson and areas that were challenging or areas that students excelled in. While I am teaching I hope that she is able to take notes on what strategies worked with my students so that I can build on those same strategies in the following lessons.

There is a paraprofessional that usually comes to work one on one with a female student in the class who needs extra support, so she will assist her with keeping up on notes that we take in class and working one on one with her to build needed skills for our lesson. My MT often gives the paraprofessional something extra for this student to practice that has relevance to the day’s lesson, therefore I may want to communicate ways she can help this student succeed, such as reviewing counting by 5s and 10s with her.

Connection back to project 1:

In project 1 I learned a lot about ways in which my students were “math smart.” The main conclusions that I came to were that my students learn math in different ways. Some students love to explain their thinking in words, while some like to draw or use manipulatives. Many of my students like to be challenged and solve problems, therefore, making my math message more open ended will allow for them to be more creative with their mathematical thinking.

In the second part of project one I looked at a grocery store in the community, which will have significance throughout my unit. I will be referring a lot in my unit about buying items at the store or buying items from a vending machine, which more than likely most if not all of my students have previous experience with. Whenever I am able to make the connection in my lesson that counting change is something they need to be able to do in everyday life, it will hopefully motivate students because they know it is a worthwhile skill to have.

Section 4: Projected Sequence of Lessons:

Date: Monday October 28, 2013 (Lesson 1)Lesson 3.7

CCSS(s):2.OA.1- Use addition and subtraction within 100 to solve one and two step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

2.NBT.1- Understand that the three digits of a three digit number represent the amounts of hundreds, tens, and ones: e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:a. 100 can be thought of as a bundle of ten tens- called a “hundred”b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

2.NBT.2- Count within 1000; skip count by 5s, 10s, and 100s

2.MD.8- Solve word problems, involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

Learning Target/Objectives: To make change by counting up from the cost of an item to the amount tendered. Students will be able to make change by counting up from the cost of an item to the

amount tendered.

Rationale: (connect to previous math lessons)

In previous lessons my students have practiced using coins to buy items, in this lesson they will explore what happens when they do not have the exact change to pay for that item. They already have a solid foundation about the values of each coin and some practice totaling a given amount of coins. In this lesson they will make connections to buying items at a grocery store, which most if not all of them have experience with outside of school. In project one I observed a local grocery store, so I can relate the lesson to that particular store.

Brief description/overview of lesson: In this lesson my students will be learning to make change1) Mental Math Review counting by 5s, 10s, 25’s (do this with coins under the document camera or

magnetic coins on the front board)2) Introduce turn and talk3) Math message & turn and talk- Draw coins that you would pay to buy a toy for 48 cents. Share student responses to math message Establish that any combination of coins that total 48 cents can be used to pay for that item4) Whole class activity: demonstrate how to make change by counting up Have students go to fruit and vegetable stand in journal pg 54 Pose problems to them to model giving change by counting up Write on board:

I bought I paid My change was:

Model several transactions for students and have them help determine the change5) Page 72 student math journals: acting as customer or clerk Do this together as a class under document camera

Problem #1- Model for themProblem #2- model with their helpProblem #3- give them a couple minutes to do it on their own, draw a stick for that student to share their response and record it in math journal under doc cam

Materials: Student math journal Document camera Real coins for mental math (pennies, nickels, dimes, quarters) Magnetic coins Pencils Class hundreds chart

Plans for formative assessment: Student responses to mental math and math message Student answers to 72 in math journal

Daily reflection: Overall, I felt this was a great first day for teaching my math unit! The students were really antsy because it was taught in the afternoon, so I had trouble with managing the class. In order to ease them into math I related math to going to a sports practice. I said “first we need to warm up.

Let’s warm up our bodies” (I modeled some simple stretching moves they could do while sitting down and had them do them with me). Next, I said that we needed to warm up our brains and we practiced counting coins under the doc cam. This was all kind of last minute planning because I noticed my students needed to get the extra energy out. Next, I did the math message with my students where they had to pay for the 48 cent toy. They wrote answers in their math journals and I called on two students to see how they would pay for it. One student said (Q, D, N, P, P, P) and another student said (Q, Q). I almost did not take the 2 quarters example because I was looking for exact change solutions, but then I realized that it transitioned well into today’s lesson of making change. I then used this and said “Could I still buy this toy with 50 cents? What would happen then?” Many students shouted “yes” that I can still buy the toy and one student offered that I would get money back. After this I modeled counting back change on the board and noticed that some students were already familiar with the concept while others, not so much. I modeled quite a few examples and asked for students to help me identify how much change I would get back. As we completed the worksheet I told students that we were going to go shopping together, so we recorded the date of our shopping trip and what time we went (we always do date and time in our math journals). I then asked students to picture where they shop and told them that they would get to shop today and buy something. I was surprised how many of them got excited about this, they kept asking when they would get to share what they wanted to buy. On this worksheet there was a challenge space where we were asked to buy 2 items and pay for them using a dollar. I wanted to start off simple so as to not confuse the students, so I chose a 30 cent and 40 cent item. One student responded with “Miss Black, you chose and easy one!” To which I asked if anyone else came up with a harder one. Then I wrote down a couple examples of “harder” problems (this was something that I did not originally plan to do, but some students really wanted to apply their knowledge and I loved to see them doing their own work and excited to share it). In the next lesson I will try to give my students the opportunity to do more by themselves and share their answers with the class and teach us how they did the problem. Since making change is new, I will also review this several times in my following lessons and give them multiple opportunities to practice.

Date: Tuesday October 29, 2013 (Lesson 2)Lesson 3.8 Coin Exchanges

CCSS(s):2.OA.1- Use addition and subtraction within 100 to solve one and two step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.


Learning Target/Objectives: Students will be able to solve multi step problems for amounts under $1.00 Students will practice making change using nickels, dimes, and quarters

Students will be able to pay for items using exact change

Rationale: We are going to review using coins to buy items and what happens when we need to pay in exact change or what happens when we don’t have exact change to pay for items. This will build heavily on the previous lessons and rely on student’s knowledge of coin values and totaling a group of coins. We will connect this idea to paying for items out of a vending machine, which most students will have experience with and this will make it authentic.

Brief description/overview of lesson:1) Mental math

Game on the computer “One dollar store”http://www.smartygames.com/igre/math/learnMoney.html

Show how you can pay for each item using N, D, Q (have all students record these in their math journal)

Do three items on here (must be exact change!) Call 3 sticks for students to share their answers.

2) Math message- turn and talkTalk about vending machine.

What is this? What coins or bills can you use in it? What happens if you don’t have exact change? Review concept of making change The buyer pays with coins or bills that add up to more than the cost of the item.

They get some money back (the difference)3) Discuss buying items with and without exact change (pg 76 math journal, buying from a

vending machine)4) Math journal page 77 “buying from a vending machine continued”

Materials: Student math journals Doc Cam Pencils Math masters page 58 Coin packets (one for each student)

Plans for formative assessment: Student answers in math journal and responses to math message and mental math Student responses during sharing of answers/discussion

Daily reflection: This was my second day teaching math for GLT and I was also being observed by my field instructor. Again, math is always taught in the afternoon, and it is right before Halloween, so we think the kids are getting really anxious and antsy. I recorded this lesson, but my computer died

http://www.smartygames.com/igre/math/learnMoney.html

and I lost the file. Since it was a Tuesday my students come from art and then have math for a little bit and then have recess for 20 minutes and continue with math after this second recess. Overall, my students behavior was very off, my MT had to tell three students to flip their cards and this made me embarrassed a little bit because I did not catch this inattentiveness, however this is something I am continually working on and have sought advice on from my MT. The timing of this lesson did not go as originally planned, I thought I would have time to get through my mental math and math message before recess, but was only able to get the mental math done. Instead of using the problem in the book, I used the smartboard for the first time. It is amazing how excited and cooperative kids get when they might have the chance to come show us on the smartboard! This game was called the “one dollar store” where every item was less than one dollar and the students had to pay for each item by dragging the coins into a box (they had to pay in exact change). I would count the coins once they placed them into the box and would ask them to check their response. I may want to use this game again in another lesson because the kids were really engaged and it reviewed counting change in a fun interactive way. After this we did a turn and talk about the “super-secret mystery object” (a vending machine) where I modeled how to do a turn and talk. I originally had a big scripted discussion plan for this turn and talk, but I abandoned it because my MT has already done some turn and talks with them, so I did not want to introduce a new routine and confuse them. Instead, I just very explicitly modeled what I expected them to do. For example, I said, can I turn to my partner and say: “last weekend I……” or “my favorite color is...?” To which they all said “no,” and I then asked a student to repeat what I asked them to discuss. The turn and talk went well, and I think they discussed a lot of good ideas, then I had two groups share with the class. If I were to do this lesson again, I am not sure I would spend as much time on this vending machine talk because I realized some of my students may not be able to relate as much to a vending machine. With credit cards, I feel like a vending machine might become a lost art. Last, I did two worksheets under the doc cam with the whole class. I had a lot more individual student work and then share out with the whole class than previous lessons. I was pleased that they could do work independently, but I think I jumped into it too soon; next time I think I need to model a little more and set clearer expectations. From observing the math journals I tracked student’s progress to see if they understood making change. For the most part my students are able to make exact change but making change is hard. Many students failed to understand that when making change we have to pay more money than the item costs. I had a student share out to the class and he said he would pay exact change (55 cents) when I wanted him to pay more so he would get money back. In the following lessons I want to review making change and see if there is a more explicit way I can teach this so my students know that in order to give change back we need to pay more than the item costs.Date: Wednesday October 30, 2013 (Lesson 3)Curriculum drive lesson (Ohio Department of Education part 1)

CCSS(s):

2.OA.1- Use addition and subtraction within 100 to solve one and two step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.



Learning Target/Objectives: Students will be able to determine a value of a collection of coins and dollar bills Students will be able to represent and write the value of money using the ¢ sign and in

decimal form when using the $ sign Students will be able to make change using coins for values up to one dollar Students will be able to count money and make change using coins and a dollar bill

Rationale:In this lesson we will review counting change and totaling a group of coins. We will make connections between writing amounts using ¢ and $ notation. We will also continue making change for amounts under $1.

Brief description/overview of lesson:1) Mental math: Practice skip counting (use computer program to total the different amounts

of coins) Have students total the amounts in their math journal and write it down Call student volunteers to come up to board and count the coins, enter their

answer in the correct field and check it. If it is wrong, have them count it and try again.

2) Math message: Beth has 60 cents in her pocket. What coins could she have? Make a T-chart on the board with 60 cents up top. Call two students at random to

draw how they made 60 cents.3) Coin jar worksheet

Display attachment D worksheet under doc cam and pass out copy to each student Time students for 30 seconds and ask them to circle jars that contain more than 60

cents Ask if any students were able to count all the coin jars

-students will most likely say no.-prompt students: without counting all the coins, what is one way we can figure out if the jar has more than 60 cents?-Review T chart again and say we know 60 cents looks like 2 quarters and a dime. Ask student: what does 60 cents look like? Ask another student: what does 60 cents look like? (emphasize that any jar with at least 2 quarters and a dime is 60 cents, 3 quarters would also be more than 60 cents because 3 quarters are 75 cents.

Time students again and see if they can quickly circle the jars that contain more than 60 cents

Discuss that if we know what 60 cents looks like we can quickly identify it without counting every single coin.

Ask students to count and total remaining jars

4) Discuss grouping like coins What is the easiest way to count these coins? Practice grouping like coins from largest to smallest amount and counting to total

themMaterials:

Coin jar worksheet (a copy for each student and 1 for teacher) Coin packets (1 per student and 1 for teacher)

Plans for formative assessment: Student responses during discussion, mental math and math message Coin jars worksheet

Daily reflection:Wow, was this lesson tough! The basis for this lesson was given to me off of the curriculum drive from my school and was created by the Ohio Department of Education. It was something new that my MT does not normally cover, but was required for this year. The lesson given to me was a four hour long lesson and seemed really unrealistic, especially knowing the students in my class. Therefore, I changed a lot of this lesson to make it more manageable for my students. However, when I made changes to the lesson I think I made it too easy for most of my students and that caused them to become disengaged. One suggested activity that was in this lesson plan was to give students time to look at a coin jars and figure out which ones had more than 60 cents in them. However, students were not to be given too much time to look at them, because we wanted to see if they could quickly analyze coins and know that 2 quarters and a dime is 60 cents, rather than having to count each coin. I timed my students and most of them just blindly circled all of the jars without even looking at them. Some students did look and picked up on this pattern right away, so it was not a learning moment like I anticipated. Overall, I was very frustrated at the end of this lesson and discussed it with my MT. I made the professional decision not to do part two of this lesson next week and instead will be scratching that lesson completely. She said that I did fine with what I was given, but I still feel like there is so much more I could have done. It simply frustrates me that I wasted time on a lesson that was not beneficial for my students, but was required because it was on the curriculum drive. My MT had to comment at the end of the lesson that many of the students were not paying attention and that Miss Black was trying to teach them something important, at this point I felt even worse and discouraged. Hopefully I have better success with my next lesson.

Date: Thursday October 31, 2013 (Math lesson is Halloween related)Date: Friday November 1, 2013 (5.3 lesson needed to be rescheduled due to a PBIS celebration- reward for students with good behavior all month)Date: Monday November 4 (No school records day)Date: Tuesday November 5 (No school records day)

Date: Wednesday November 6 (Lesson 4)Lesson 5.3 Exploring coins

CCSS(s):




Learning Target/Objectives: Students will be able to identify coin combinations equivalent to $1.00

Rationale:Again, we are reviewing our prior knowledge from other lessons and establishing that different coin combinations can be used to make the same amount.

Brief description/overview of lesson:1) Read Smart by Shel Silverstein and discuss

-read first- have students act out trades- turn and talk on rug:

Who was the real fool in the story? Why? How did the dad really feel at the end? Why? Did the son make a good trade? How do you know?2) Making a dollar

Name collection box- 4 ways to make $1 Have students draw four square in their math journals and come up with four

ways to make a dollar.-emphasize that these 4 ways to make $1 would be good trades that the son could have made in the smart poem

Call four students to come up to the board and draw what coins they used to make $1 using Q, N, D, P

Ask: how can we make $1 using the least amount of coins?3) Play dollar rummy

Model the game with a student partner Choose partner pairs to play the game together and assign them to a spot in the

room Play for about 10 minutes

Materials: Coin packets (1 for each student and 1 for teacher) Doc cam Pencils

Math masters page 87 (copy for teacher) Dollar rummy cards (math masters pages 48 and 49)

Plans for formative assessment: Student interactions when playing dollar rummy Responses to math message and mental math (check student math journals during the

lesson) Responses to class discussion

Daily reflection: The day before I taught this lesson I found the poem Smart by Shel Silverstein and really wanted to incorporate it into the lesson for a fun and engaging start. The first time I read it I asked students to give me a thumbs up if they think they understood the poem and why it was funny. I was surprised that about only half of my students gave me a thumbs up so I made it more clear the second time around. The second time around I had five kids be the five characters and they liked this a lot, I think it helped them visualize the trades. We then discussed it a little, I wanted everyone to participate so I had them do a turn and talk to their partner answering whether they think they boy got a good deal. I wish I would have listened in on the partner conversations instead of just discussing with one group. During the discussion I had a couple students share out and I focused on using my teacher talk moves to move discussion along. I remember that I asked a student to explain what another student already said and I was surprised with how well they were able to explain it and not just repeat word for word. After this I had students go back to their desk and explained how to play a game called dollar rummy. In this game the students play in partner pairs and draw cards and try to add amounts to one dollar. I used a student as my partner to model the game and showed the cards under a document camera. It was a lot harder to explain the game than I thought. I then paired my students up to play and sent them to various spots in the room. As I walked around to monitor I noticed that some were playing the game incorrectly and would have too many cards in their hands. I tried to correct and re-explain the rules when possible. I was recording video of this lesson on my computer and was able to record one of the partner pairs playing the game. This pair was playing the game correctly and they were both very verbal about making the dollar amounts, they would even say “cha-ching” when they made a dollar, which was really funny and cute to see.Date: Thursday November 7, 2013 (Lesson 5) Lesson 10.1 Money

CCSS(s):2.MD.8- Solve word problems, involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

Learning Target/Objectives: Students will be able to use cent and dollar notation properly when expressing an

amount of money Students will be able to give money equivalencies

Rationale: This lesson will build on my last lesson by getting students to total various coin amounts. It will also lead into the fact that we can use different coins to make the same amount of money. We will discuss coin equivalencies and establish that 5 pennies is the same amount as 1 nickel,

10 pennies is the same amount as a dime, etc. I will make this relevant to student’s lives by asking them to think about ways they can pay for an item they want to buy and also what coins they would like to receive as a gift (this will force them to think that they would like to receive the most money as possible, which will motivate them to total the amounts of money).

Brief description/overview of lesson: Math message – Miss Black wanted to buy a package of cookies that costs $3.25 cents.

So, I checked my wallet to see how much money I had. This is what money I had in my wallet:

Place the 2 dollar bills, 4 Q, 5 D, 5 N on under the doc cam- Do I have enough money to buy the cookies? How do you know?

Mental math- Miss Black wants to give her students some money for being such a good class. You can choose between getting four quarters or 10 dimes, which one would you choose and why? (show the four quarters and the 10 dimes under the document camera) along with the prompt: “I would choose ___________ because _____________.”

1) Assess understanding of values of coins and bills How many pennies in a nickel? In a dime? How many pennies in a quarter? In a half-dollar? How many pennies in a dollar? In 2 dollars? In 10 dollars?

2) Assess understanding of exchange values How many dimes in a dollar? In 60 cents? How many nickels in a quarter? How many quarters in a half dollar? In a dollar? In 10 dollars?

3) Making equivalent amounts with coins and bills4) Have students look at page 240 in their math journal “good buys poster”

Check that children know how to read prices of items5) Page 240 math journal6) Page 241 math journal (for review)

Materials: Coin packets (1 for each student and one for teacher) Student math journals Pencils Doc cam 2 dollar bills, 4 Q, 4 D, 2 N and wallet (for teacher)

Plans for formative assessment: Check answers to page 241 in math journal Student responses to discussion in class Walk around and look at student answers to math message and mental math

Daily reflection: I really liked the math message that I did with this lesson, but I am not sure that I liked how the discussion turned out. I was hoping for it to generate more of discussion, but looking back at

it I only called on one student to share their answer and then moved on. Maybe if I were to re-teach it I would do a turn and talk to have all students share their ideas. With the “good buys poster” in the math journal I tried something new in order to engage my students. This math journal page involved selecting an item to buy and then paying for it in two different ways, so I switched it up and I drew one way to pay for an item and made students find what item I was buying and then make another way to pay for that. I think this really excited them at first and they had fun counting the money that I drew and then finding the total cost and matching it to the item. I like to give my students some sort of ownership over the problems we do, so I also allowed students to buy an item of their choosing.Date: Monday November 11 (Lesson 6)“I spy a number”

CCSS(s):2.NBT.1- Understand that the three digits of a three digit number represent the amounts of hundreds, tens, and ones: e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:a. 100 can be thought of as a bundle of ten tens- called a “hundred”b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

2.NBT.3- Read and write numbers to 1000 using base-ten numerals, number names and expanded form.

Learning Target/Objectives: Students will be able to guess a mystery number 0-99 by correctly identifying its digits

and the value of its ones and tens places

Rationale:In this lesson we will play a game where students use what they know about place value (ones, tens, and hundreds places) to construct a number. It will be review of what my MT started to teach at the beginning of the unit. It will help them see that value of a number depends on where its digits are placed in a number, for example, 57 and 75 are made of the same two digits (5 and 7), but 75 is larger because it has more tens than the number 57.

Brief description/overview of lesson: Review ones, tens, and hundreds places of a three digit number Discuss digit vs. place. Digit is the number and place is where it is located (ones, tens,

hundreds spot) Model how to play I spy a number game

-Teacher chooses a mystery number- Students guess a number- Teacher will record it in the following chart:Guess Digits Correct Places correct

- Teacher will continue until number is identified

Keep playing I spy a number game as a class with different mystery numbers (record the chart on the board)

Play game in partner pairs if time permits

Materials: Chart paper and maker

Plans for formative assessment: Student responses and guesses to finding the mystery number If students play in partner pairs I can collect their charts to see their written answers

Daily reflection: Before teaching this lesson I was really nervous that students would have a hard time with this game, but once I started teaching it went better than I imagined it would. I made sure to distinguish between what a digit and place is and modeled this heavily. To play, I drew this a chart on the chart paper and had everyone sit on the rug, which I really like starting math out on the rug. When my students are on the rug I feel like they listen better and that they are easier for me to keep track of and hold accountable for their behavior. First I modeled a practice round of the game where I did a think aloud and showed my math strategies and reasoning. Next, I had them play a round with me where I helped a little. They were all really excited to guess my number. At first I tried writing my mystery number on a white board and flipping it over so they couldn’t see it, but they kept seeing my answer. I then had to tell them I would keep the number in my head which worked better. Sometimes it’s the small things that you do not think of while planning the lesson! I decided to play the game three times because students were doing so well with it. A couple days after I taught this lesson I had students asking me if they could play this game with partners, which made me excited that they enjoyed it!

Date: Monday November 11, 2013 (Lesson 7)Lesson 2.8 Fact Families (pan balance comparisons)

CCSS:

Learning targets/ Objectives: Students will be able to make weight comparisons between two different objects

Rationale: This lesson is building upon skills that my class has been learning all year. They have been practicing making comparisons of numbers using greater than, less than, and equal to, so this is an opportunity to apply it to real world contexts. Students will also use their place value knowledge to compare numbers to find out which one is greater.

Brief Description/ overview of the lesson: Explore weight using a pan balance-Present two items. Ask: which item do you think is heavier? How can we tell which item weighs more?-weigh items on balance. How do you know which item is heavier?- Things that weigh more will tip the scale farther down

Review greater than, less than, equal to Look at page 38 in math journal (these show items and their weight)- Discuss the need to convert pounds to ounces so you can compare all items using ounces

as the common unit of measurement Do page 39 in math journal- Model one example- Allow time for students to work individually on some and then share out with the class

Materials: Pan balance 2 objects to weigh Student math journals

Plans for formative assessment: Student responses to pan balance exploration and discussion Student answers in math journal

Daily Reflection: I know this lesson may seem out of sequence with my unit, and that’s because it is. My MT wanted me to go back and cover this one before we take the unit test. On the unit test there is a comparison problem using greater than, less than, or equal to so that is what I emphasized during this lesson. It worked well to mention that they have weighed items before, because I had just watched them do this in their e-lab science class. Being able to see the pan balance brought real life experience in this lesson and really helped visualize this concept instead of just looking at pan balances in their math journals. What was tricky with this lesson was that some items were measured in ounces while others were in pounds, therefore we had to convert them to the same unit of measurement which was hard for some students to understand. Once we worked on a couple problems together I let them do one on their own and share some ideas out with the class. Overall the class was pretty high energy and antsy this day, so I again struggled with classroom management. My MT suggested that if there are too many behavior issues to just have students put their heads down until you think they are ready to continue. I have not yet used this strategy, but I may have to in future lessons. I am still working on pacing of my lesson too. I know that my MT has students quickly do the pages in their math journals and I notice mine take longer. I am trying to cut any unnecessary words out of my teaching and making the pace appropriate so I do not stretch it out and lose some of my student’s attention.

Date: Tuesday November 12, 2013 (Lesson 8)Expanded form

CCSS:2.NBT.1- Understand that the three digits of a three digit number represent the amounts of hundreds, tens, and ones: e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:a. 100 can be thought of as a bundle of ten tens- called a “hundred”b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).


Learning target/ objectives: Given a number in standard form, students will be able to write the number in expanded

form

Rationale: In this lesson we will review place value and learn to write numbers in expanded form. This lesson will help greatly to prepare students for the upcoming unit test. Writing a number in expanded from reinforces the fact that the digits of a number represent the number of hundreds, tens and ones in the number.

Brief description/overview of lesson: Review place value and base 10s Ask how much a flat, long, and cube is worth (100, 10, 1) Have students show you a three digit number using base ten blocks Record the amount of hundreds, tens, and ones in each number on the caterpillar Record this number on the board in expanded form above the caterpillar Explain expanded form- it is making something bigger, stretching it out

Materials: Caterpillar page (1 per student) Base 10 blocks (9 flats, 9 longs, 9 cubes) Whiteboard and dry erase markers Student math journals

Plans for formative assessment: Student responses to discussion Student responses on caterpillar worksheet Whisper numbers (on the count of three students will whisper the number that I showed

in expanded form)

Daily reflection: This lesson went much better than I imagined it would! My students seemed to pick up expanded form really quickly. I liked using the caterpillar because I first recorded the number in standard form on his head, the number of hundreds on his first body piece, the number of tens on the middle body piece and the number of ones on the last body piece. I was most proud of the consistency of this lesson; I followed the same order so it was really easy for my students to follow. I did multiple problems with them before I expected them to produce anything by themselves; therefore I found that students were engaged because they knew exactly what was expected from them at each step. By the end of the lesson, given the standard form of the number, my students were able to write it in expanded form and vice versa. After I taught this lesson I reviewed it the next lesson and I was happy to see my students drawing the caterpillar in their math journals to help them write the number in expanded form.

Date: Tuesday November 12, 2013 (Lesson 9)Writing number names

CCSS: 2.NBT.3- Read and write numbers to 1000 using base-ten numerals, number names and expanded form.

Learning target/ objectives: Given a three digit number in standard form, students will be able to write the number

name Given the number name, students will be able to write the three digit number in standard

form

Rationale: Writing out a number will encourage students to use what they know about place value to write the number out in words. This lesson is beneficial because students need this exposure before expecting to do this on the upcoming unit test. This skill is also transferable to everyday contexts such as writing out a check.

Brief description/overview of lesson: Review the different ways we can write a number: standard form, base ten blocks,

expanded form Another way we can write numbers is by using words. Write 1 one hundred eighty five on board and have student read it. Discuss writing hundreds first, tens, then ones.- Hand out student sheet with number names- Practice writing number names- Have students record number name and numbers in their math journals

Write on board: 264

Two hundred sixty-four

Two hundred forty-six- Have students circle which one shows the correct number. Discuss that we need to look

closely at the hundreds, tens and ones place when reading a number.

Materials: White board and dry erase markers Doc cam Ways to write a number chart (1 for teacher) Number name chart (1 per student) Student math journals

Plans for formative assessment: Student discussion responses

Student whisper responses on count of three Student answers in math journals

Daily reflection: This was one of the most difficult lessons I had to teach during my unit! We normally follow everyday math curriculum and lessons, but the test on this unit is this week, and the test had items that everyday math did not cover. In one sense you hate to teach to the test, but on the other hand, you want students to have that experience and exposure to what is on the test so they can perform well and not become discouraged. On this assessment expanded form and writing a number in words or number name were two concepts that everyday math did not cover. Therefore, I was on my own for creating this lesson, I looked to a lot of outside resources, but did not find anything helpful for teaching this concept. I wrote two numbers out on the board and asked students to choose the correct one that read 264, looking back on this I think I could have allowed for some discussion about this one, I should have went around and asked various students how they knew which number name was correct rather than explaining it for them. I think at times I underestimate my student’s abilities and I try to make it more comprehensible, but sometimes it actually disengages them. As an area of improvement, I hope to work more on making my activities more open ended and challenging so I do not lose student’s focus, especially those who are strong with their math abilities. During this lesson I was being observed by my field instructor and I made a mistake in my teaching. I asked how many 10s were in the number 72, but then I started to draw flats or 100s using base ten blocks. I was embarrassed, but I caught my mistake before the students did. I joked it off saying that none of them corrected me, and that they were supposed to help me out, which they responded well too. I think it may have just been the nerves, but I am glad that I did not allow it to throw off my lesson.

Date: Tuesday November 12, 2013 (Lesson 10)Explaining our thinking through writing

CCSS:2.NBT.1- Understand that the three digits of a three digit number represent the amounts of hundreds, tens, and ones: e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:a. 100 can be thought of as a bundle of ten tens- called a “hundred”b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).


Learning targets/objectives: Students will be able to identify whether a given statement is true or false and explain

their thinking in writing

Rationale: A big push for my students throughout math and especially on the unit tests is being able to explain their thinking. Since they will be expected to do this on the unit test, I want to give them practice with the types of problems they will see. The problems we will use to practice

will also review place value, especially comparing a number in standard form with the same number written in expanded form.

Brief description/overview of lesson: Review standard vs. expanded form of a number Practice problems that require explaining our thinking- Model a problem with a correct answer and explain thinking

Ex. 458= 400+50+8This statement is true because there is a 4 in the hundreds place which equals 400. There is a 5 in the tens place which equals 50 and there is a 8 in the ones place which equals 8. When you put these together it makes the number 458.

- Model a couple more problems- Ask students a problem and have them answer individually and then share out with the

class

Materials: Explain your reasoning worksheet (1 per student) Doc cam White board and dry erase markers Student math journals

Plans for formative assessment: Student responses to discussion Student answers in math journal Student responses on explain your reasoning worksheet

Daily reflection: This is another lesson that is kind of teaching towards the test. During our last unit test we noticed that most of our class was not getting full points because they did not know how to explain their thinking. Obviously we ask them every day to discuss or tell us how they got a certain answer, but we hardly ever ask them to explain their thinking in writing. Therefore, when they come to writing it is hard for them to explain their thought process, so we wanted to take some time to help them put this in writing. I had my students first look at the expanded notation problem and give me a thumbs up if they thought it was correct or a sideways thumb if they thought it was wrong. Then I called on students to share their reasoning. At this point maybe I could have implemented a turn and talk to get every student sharing their ideas. Most of my students failed to recognize that this was testing them on place value, they would look at the problem and just add all the pieces and say they did not equal the target number. For example the problem was 872= 80 + 70 +20, to which one boy told me 80 plus 20 is one hundred and plus another 70 is 170. Given this response I tried to steer them back towards thinking about place value by saying: how many hundreds are in this number? Tens? Ones? Overall, I think my students could have benefited more from a turn and talk or even more practice with this type of problem. Tomorrow my MT will hold a review for the unit test and I am anxious to see if this lesson will help them answer the written one on the practice test.

Omitted lessons: (these are lessons I originally planned but did not teach because I had to rearrange lessons according to the needs of my students)

Capture the Caterpillar



2.NBT.4-Compare two three-digit numbers based on meanings of hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.

Learning Target/Objectives: Students will be able to identify the ones, tens, and hundreds digit of a number Students will be able to compare two three-digit numbers using >, =, and < symbols

Brief description/overview of lesson: Review ones, tens, hundreds place of a three digit number

Capture the caterpillar activity I will roll a dice three times to generate a target number (example: 534) I will model the activity I want students to complete Students will take turns rolling a dice three times each to get the digits for their three digit

number (they must record these 3 numbers on a piece of paper!) Students must order these three digits to get as close to target number as possible Students will complete the caterpillar worksheet displaying their number ( how many:

hundreds, tens, ones) Once every student has their caterpillar we will put them in a pile of greater than target

number, less than target number or equal to target number. (I will write this on the board and students will bring their caterpillar to me, I will read number and have students show thumbs up if it is greater than, less than or equal to target number)

Materials: Capture the caterpillar page (1 for teacher and 1 for each student) Dice (either computer generated dice or real dice that students can add two sides to get

numbers less than 9)

Plans for formative assessment: Caterpillar worksheet Students must show that they used their place value knowledge to get as close to target

number as possible.

Date: Monday November 11, 2013 (Day 7)Place Value lesson 2: Explorations dayCCSS(s):2.NBT.1- Understand that the three digits of a three digit number represent the amounts of hundreds, tens, and ones: e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:a. 100 can be thought of as a bundle of ten tens- called a “hundred”b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).



Learning Target/Objectives: Students will be able to locate a number on the number line Students will be able to add and subtract numbers within 100

Rationale:This will be a review from what my MT started to teach earlier in this unit. Students will need to use their knowledge of place value to find numbers on a number line. They will need to use place value to determine if they should advance forward on the number line (add) or go back on the number line subtract. I have changed this lesson so it is more relevant to place value. My MT and I will work together and each take a group of students to work on two different tasks that review place value.

Brief description/overview of lesson:Group 1:

Students will use base ten blocks (flats, longs, cubes) to build a structure (this will be done independently)

Next students will have to use what they know about place value and base ten blocks to estimate how many cubes makes up their structure.

Students will draw a picture of their structure and then write their estimate on a piece of paper (I will collect this to assess their understanding)

Group 2: This group will play “where am I on the number line?” but this time skip count by 10s My MT and I noticed students need to work on adding in increments of 10, so we will

use a hundreds chart that starts at 110 and counts by 10s to get to 1,000. This time the spinner will have moves such as: +10, -10, +20, -20, etc.

Materials: 110-1,000 hundreds chart (1 per student and 1 for teacher) Spinner used for skip counting (1 for whole class or 1 per partner group if time to play

game in pairs) A coin for each student to use as a place marker

Plans for formative assessment: Have students answer the following questions verbally: If you are on the number________, what number would you land on next if your spinner

landed on _________? What number is 10 less than (10 more than, 20 more/less than, 30 more/less than, etc) What numbers are next door neighbors of ________?

Curriculum Drive Place Value lesson 1: “Where am I on the Number Line?”




Learning Target/Objectives: Students will be able to locate a number on the number line Students will be able to add and subtract numbers within 100

Rationale:This will be a review from what my MT started to teach earlier in this unit. Students will need to use their knowledge of place value to find numbers on a number line. They will need to use place value to determine how to add larger amounts such as 10, 30, 50 and 100, to given number.Brief description/overview of lesson:

Introduce students to hundreds chart Pass out hundreds chart to each student Teach students to play “where am I on the number line?” game- Model as a class how to play- Have class play against each other (teacher led)

Materials: 1-100 number lines (1 per student and 1 for teacher) Spinner used for number line 0-100 Coin as a place marker for each student

Plans for formative assessment: Have students answer the following questions verbally:- If you are on the number________, what number would you land on next if your spinner

landed on _________?

- What number is 10 less than (10 more than, 5 more, 5 less than …, etc.) ______?- What numbers are next door neighbors of ________?

Curriculum Drive Lesson (Ohio Department of Education part 2)CCSS(s):2.OA.1- Use addition and subtraction within 100 to solve one and two step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.



Learning Target/Objectives: Students will be able to determine a value of a collection of coins and dollar bills

(amounts over $1 but under $5) Students will be able to represent and write the value of money using the ¢ sign and in

decimal form when using the $ sign Students will be able to make change using coins for values up to one dollar

Rationale: In this lesson we will review counting change and totaling a group of coins. We will make connections between writing amounts using ¢ and $ notation. We will also continue making change for amounts under $1.

Brief description/overview of lesson:1) Counting amounts over $1 and review grouping coins from largest to smallest value

2) Practice making dollar and cent amounts discuss $ and ¢ notation$1.32

Decimal point Number in front of decimal point is the number of dollars we have Number behind decimal point is the number of cents we have Practice making amounts over $1 using a T-chart

Dollars Cents

3) Practice story problems counting amounts over $1 Kadin used 2 quarters and 6 dimes to pay for a toy car. How much money did he use?

($1.10) Ashleigh used 3 quarters and 5 dimes to buy a notebook. How much money did she

use? ($1.25)

4) Review and practice making change for amounts under $1 (possibly computer game with interactive white board: http://justkidsgames.com/play.php?MakingChange)

Section 5: Three Daily Plans:

Day 1: 10/28/13

Overall lesson topic/title3.7 Making Change by Counting Up

CCSS(s):


2.NBT.1- Understand that the three digits of a three digit number represent the amounts of hundreds, tens, and ones: e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:a. 100 can be thought of as a bundle of ten tens- called a “hundred”b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).



Learning Target(s)/Objective(s): Students will be able to make change by counting up from the cost of an item to the

amount tendered.

RationaleIn previous lessons my students have practiced using coins to buy items, in this lesson they will explore what happens when they do not have the exact change to pay for that item. They already have a solid foundation about the values of each coin and practice totaling a given amount of coins. In this lesson they will make connections to buying items at a grocery store, which most if not all of them have experience with outside of school. In project one I observed a local grocery store, so I can relate the lesson to that particular store.

http://justkidsgames.com/play.php?MakingChange

Materials: (Include a copy of any handouts you will be using): Everyday Math student workbooks Packet of coins for each student Magnetic coins for the front board and dry erase marker Doc Cam Pencils Laminated hundreds chart for each student and class copy of hundreds chart Sticky tack, 2 frames for hundreds chart

LAUNCH: Introduction to the Lesson ( 15 minutes)

We have been practicing using coins to pay for things, but not all coins are worth one cent, so we need to be able to skip count when we count money. Today we are going to work with money some more, so I want us to practice counting with different coins. What happens if I don’t have the exact change to buy the 48 cent toy? What if I have two quarters? Can I still buy it? What will happen? What happens at the store when you pay too much money?

Mental math: (whole class) Have students count by 5s to 100 (display nickels under doc cam while counting) Have students count by 10s to 100 (display dimes under doc cam while counting) Have students count by 25s to 100 (display quarters under doc cam while counting)

Introduce concept of turn and talk In math it helps us sometimes to talk about our answers with other people, so we are

going to practice that today. I know that we all have ideas and different ways that we do math problems and I want everyone to be able to share their ideas.

In order to share our ideas we have to organize our sharing in a certain way. On the board I have your names under a certain team (spiders or black cats). Silently take a second to find your name on the board, I don’t want to hear shouting out of which team you are on (model this). The person next to you is on the opposite team as you.

Raise your hand (no voices) if you are on the spider team (check to make sure spider team raises their hands).

Raise your hand (no voices) if you are on the black cat team (check to make sure spider team raises their hands).

In every group there will be one spider and one black cat. This will tell us when it is our turn to talk.

I will give you a sentence to talk about and put it under the document camera and you will take turns answering this question with your partner. So if I put the question up and I say “spiders go first,” the spiders will share their answer with their partner. When you are done sharing your answer you may give me a thumbs up to show me you are done. When I see lots of thumbs up, I will show you the give me five sign and I will ask the black cats to share their answers with their partner. When the black cats are done they will give me a thumbs up. After I show you the give me five symbol we will share some of our answers with the whole class.

Have the students practice this turn and talk. Model with a student as your partner. Math message: (partners) (ask them to pretend they are at the store)

You buy a toy that costs 48 cents. Which coins would you use to pay for it? Draw the coins using P, N, D, or Q.

Turn and talk with partner to share answer. Have one group report out to whole class.

I will give students about 2-3 minutes to think about the problem. Spiders go first. Show your partner what you drew in your math journal. (This should

be coins using P, N, D, Q format). Ok, show me a thumbs up when you are done. Black cats, now I want you to share what you drew in your math journal. I will then call on someone to share what them and their partner talked about. I will

draw a stick that has the student’s class numbers on each stick.

EXPLORE: Outline of Key Events During the lesson ( 40 minutes) Math message follow up (whole class discussion)

Ask one group from turn and talk to share with class Have two students draw two different ways to make 48 cents on the board. Ask the

students to check and see if they are right (have them count with you to check!) Explain that any group of coins used to pay for the item is correct as long as it totals

48 cents. Demonstrate how to make change by counting up (whole class)

Hey, what if I wanted to buy that same toy for 48 cents but I did not have exactly 48 cents? What if I had 2 quarters (50 cents)? Could I still buy it? What would happen? (I would get money back, this is my change)

Today we are going to look at what happens when we don’t have the exact coins to pay for the items we want.

Have students turn to page 54 in their math journals (fruit and vegetable stand) When we get money back the cashier will count it back to us in a certain way. We are

going to learn how they do that today. We are all going to be cashiers today. Record this transaction on the board:

I bought: I paid: My change was:an orange for 18 cents D D P P

Show students how to count up like a cashier would do. We start with the amount we paid (18 cents) and need to count up to the amount we paid (20 cents). So we say 19, 20 when we put our two pennies as change down.

Ask: why would we count up like this (to make sure we give the correct amount back) It is important that we make sure we get the right amount back, we do not want to be

shorted our money Well, Ms. Van Hekken also wants to buy an orange, but she only has a quarter. (Draw

this on the board) How much change will she get back? (Take a student response) Show that we can pay for the same item with different coins and we will get different

amounts of change back:I bought: I paid: My change was:an orange for 18 cents Q P P P P P P P or N P P

Making change is brand new to my students, so it will take some explicit modeling and practice at first. Once they get the hang of it I will ask them to do some additional problems by themselves and call on students to share out to the class.

Additional problems:

I bought: I paid: My change was:Onion for 7 cents D P P PTomato for 20 cents Q P P P P P or N(Take a student response and help them determine change)(Take a student response and help them determine change)

Wow, all this talk about food is making me hungry! Let’s go shopping and buy some food!

Let’s turn to page 72 in your math journal and see what kind of goodies we can buy. So, this is a fruit and vegetable stand, I want you to picture where you and your family

buys food. Lets take a couple seconds and picture that store in our head. I know that I shop at Meijer a lot, some of you might shop at Meijer too, or Walmart or Family Fare.

Problem #1: So I am going to pretend I am at Meijer buying my fruits and vegetables. The first thing I want to buy is a banana. How much does a banana cost? (Call on random student for response) (Write this in the journal. Well, I don’t have 9 cents but I do have a dime. So I know 9 plus 1 is 10, so I will get 1 cent back.

Problem #2: Where are you shopping today ______? Ok, what would you like to buy? What money would you use to pay for it? How much change would we get?

Problem #3: For this last one I want all of you to pick one item to buy. Write what you bought, what you would use to pay for it and how much change you would get back.

(draw a stick and ask that student to share- write in journal) Challenge problem- do this one together. Draw two sticks and ask those two students

what we should buy. We paid one dollar. Help students count change back and record in journal.

SUMMARIZE: Closing Summary for the Lesson ( 2 minutes) I have one last question for us to think about. On Friday some of you bought popcorn.

Popcorn at C.A. Frost costs 25 cents per bag. If you pay 1 dollar and only wanted to buy one bag, would you get money back? How much change should Ms. Van Hekken give you back?

Description of Formative Assessment: I will walk around and observe how students are using the hundreds chart to help them count back the change. I will also take student responses from the mental math and math message activities. I may allow them to do one of the problems on page 72 by themselves first before we share our answers as a class, while I walk around and monitor student’s responses and questions to the problem.

Day 2: 10/29/13Overall lesson topic/title:

3.8 Coin ExchangesCCSS(s):2.OA.1- Use addition and subtraction within 100 to solve one and two step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown

number to represent the problem.


Learning Target(s)/Objective(s): Students will be able to solve multi step problems for amounts under $1.00 Students will practice making change using nickels, dimes, and quarters Students will be able to pay for items using exact change

Rationale:We are going to review using coins to buy items and what happens when we need to pay in exact change or what happens when we don’t have exact change to pay for items. This will build heavily on the previous lessons and rely on student’s knowledge of coin values and totaling a group of coins. We will connect this idea to paying for items out of a vending machine, which most students will have experience with and this will make it authentic.

Materials: Student math journals Doc Cam Pencils Math masters sheet page 58 Coin packets (one for each student)

Procedures and approximate time allocated for each eventLAUNCH: Introduction to the Lesson ( 15 minutes)

Review yesterday’s lesson (whole class) Yesterday we practiced buying things with coins. Sometimes we did not have the

exact amount to pay for things, so we had to get money back. Today we are going to practice paying for things using the exact coins that we need

and sometimes paying too much and having to get money back. Mental Math (individual work followed by whole class discussion)

Show how you can pay for each item using N, D, Q.-an apple that costs 55 cents- a bottle of juice that costs 75 cents-a package of gum that costs 35 centsI will encourage students who finish quickly to show another arrangement of coins they can use to get the same amount.

Have students record answers in math journals. They may use the coins in their coin bag but they need to also draw them out using N,D,Q, format.

Share a couple student responses. (have them come show their answers under doc cam or write on board. Count coins together as class to check their answer). I will ask students to give me a thumbs up if they agree or sideways thumb if they are not sure about the answer. When a student is not sure I will ask them to show what they had. When they agree, I will ask the student to recount the change to make sure we get the

same amount. Review turn and talk procedure and math message (partner work)

Yesterday we had team names (spiders or black cats) and we used these to talk with a partner next to us.

I want us to do the same thing today. Find your name on the board again (silently). Raise your hand if you are a spider. Raise your hand if you are a black cat.

Remember I will give you a problem to think about and we use these teams to discuss the problem with a partner.

Show them the problem (display math masters page 58 under doc cam). My question to you today is: Do you know what this machine is called and do you know how it works?

Let’s take a couple seconds to think about this by ourselves. With a V zero voice I want you to look at this picture and see if you can think about what this machine is and what it does.

Now I want us to share our thoughts with our partner. I will call a team that shares first and you will say “I think this machine is called ____________ and it does ___________.” When you are finished give me a thumbs up. Once you see me give the “give me five” symbol we need to stop and listen for the next directions.

Yesterday we had the spiders go first so today I want the black cats to go first. (allow time to share, look for thumbs up and then continue by showing give me five symbol).

Ok, now I want the black cats to share. You are saying “I think this machine is called ____________ and it does ___________.” (allow time to share, look for thumbs up and then continue by showing give me five symbol).

Let’s see what we had to say about this machine (call on a group to share what they talked about with their partner.

EXPLORE: Outline of Key Events During the lesson ( 40 minutes) Math message follow up (whole class discussion)

Discuss what vending machine is and how it works-Which coins/bills can you use in this machine?-Can you buy something if you don’t have exact change (talk about exact change light being on or off)- review making change: what happens when we pay more money than the item costs? (we get money back). This will be accomplished with a turn and talk. Students will turn to their neighbor and discuss for a minute what they know about the machine.

I will then take a response from a volunteer Buying items with and without exact change (whole class)

Complete page 76 in math journal under doc cam #1: show ways to pay exact change for orange juice that costs 65 cents

- take student responses and write in journal under doc cam #2: You want to buy milk for 35 cents but do not have exact change.

- What coins might you use to pay for it?(Allow students to do this individually and go around and monitor answers. Take 1-2 student responses and write in math journal)

Making vending machine purchases (whole class) Complete math journal page 77 together as a class under doc cam #3: exact change light is on. Ask students to draw the coins they would use to pay for each item. Take a student

response and write in journal- Chocolate milk (costs 35 cents)- Yogurt drink (costs 70 cents) Let students choose the last item (prices vary), call on students to share their answers.

#4: exact change light is off. Help students pay for each of the items with larger money amounts so they will get change back.

Orange juice- costs 65 cents (pay using 3 Qs) (get 10 cents back) Chocolate milk- costs 40 cents (pay using $1) (get 60 cents back) The last three items students can choose and do individually. Call randomly on

students to share and copy down in math journal under doc cam.

SUMMARIZE: Closing Summary for the Lesson ( 10 minutes)

Wrap up To conclude the lesson, ask students to turn and talk to the person sitting next to them

about something they have bought before or that their parents have bought before. Did they pay with exact change or did they get change back?

Section 6: Parent Letter:

October 16, 2013

Dear Parents/Guardians,

My name is Jamie Black and I am an intern from Michigan State University working in your son’s/daughter’s classroom. To fulfill my internship requirements I will be teaching a two week math unit under the direct guidance and supervision of Ms. Van Hekken. Starting October 28th I will assume the position as teacher during our math block of the day and will be conducting math instruction based on lessons that Ms. Van Hekken and I have worked together to plan. At this point in the year we are on our second unit of study which focuses on place value, money, and time. Before I begin teaching, I would like to inform you about what your child will be learning in the upcoming weeks and what you can do to help support their math learning.

During unit 2, your child will be exploring money and working a lot with coins. Earlier we sent home a note with your child asking you to have him or her bring physical change to use for these lessons. We believe that it is critical that students are able to work with real money and have something to be able to manipulate to help them solve their math problems; therefore we would really appreciate if you equip your child with the mathematical supplies needed for these next couple of weeks. We will start by reviewing the value of each coin so that your child has a

solid foundation to build upon. From there, we will explore different coin equivalencies, for example, knowing that 1 quarter is the same as 2 dimes and a nickel. Next, we will talk about paying for items and what combinations of coins we can use to pay for something. Naturally, this will lead into the question “what do we do when we don’t have the exact money to pay for something?” In this case we will talk about making change and counting up from the cost of the item to the amount you paid. This will be one of the hardest ideas covered in the unit, so I want to give you a preview of what a problem like this would involve:

I bought: I paid: My change was:

an orange for 18 cents D D P P

From here, it is expected that your child will count up the money they paid (20 cents) and then say “19, 20” while they put down the change (2 pennies). This table format above will be appearing in many of our homework assignments, so I encourage you to sit down with your child and help them to see this pattern. To start, we will be working with smaller amounts of money and making change for amounts under $1.00, so if you want to practice with your child, you could give them some coins and have them give you change back from an item that you paid for with a one dollar bill.

When counting money we use skip counting as a strategy to quickly add amounts together, therefore I also suggest reviewing counting by 5s, 10s, and 25s with your child at home. I know that in our classroom we also encourage children to draw “eyelashes” on coins to help total a value of a group of coins. Therefore each “eyelash” drawn on a coin is worth 5 cents: pennies do not get an “eyelash,” nickels get one “eyelash,” dimes get two “eyelashes,” and quarters get five “eyelashes.” This way children may quickly count by fives to total larger money amounts. You will notice that many of your child’s homework problems ask them to use P, N, D, Q to explain their answers; we want them to get in the habit of drawing circles and labeling them with these letters to symbolize pennies, nickels, dimes and quarters so that they can use the aforementioned strategies.

I am very excited to start working with money in our classroom because it involves skills that children will need to be successful in everyday life. As I have mentioned, working with real coins will make the lesson authentic and tangible for our young learners. Also, in this unit we will spend some time playing games to test our knowledge of counting money, paying for items, and making change, which are always a fun and engaging way to display what we have learned.

Not only are we talking about money in unit 2, we will be spending time towards the end of the unit to review place value. We will start by looking at a number line and locating numbers in relation to one another. Students will practice moving forwards (adding) and backwards (subtracting) on a number line and coming up with number models for these problems. For example, if we are on the number 23 and we move backwards 6 spaces our number model is 23-6=17. As a part of place value we will also review the hundreds, tens, and ones places of a number. When given a number such as 456, students should be able to identify that there are 4 hundreds, 5 tens, and 6 ones to make 456.

Finally, it will be my goal for the next two weeks to make math learning as authentic and engaging as possible so I can include all learners. I am hoping that you will work with me to continue your child’s math learning at home, because continuous exposure and practice, especially for counting change, will greatly benefit every learner. Part of the practice will be the weekly homework packet. Remind your child that the homework packet is due on Fridays and must be completed to display their best quality work.

If you have any questions or concerns related to the content or my teaching of this unit, please feel free to contact me via email at [email protected].

Sincerely,

Jamie Black

Section 7:

What my students did and did not learn and summative assessment results

One concept that my students learned was how to write a number in many different ways. We practiced using base ten blocks, writing its number name, and expanded form. This learning was particularly evident in my summative assessment. One of the questions was: “What is another way to write this number?” The number was fifty and it was first shown use 5 longs (base ten blocks). As I walked around I took notes on student’s responses, here are some common ones: Answers: 0 + 50+ 0 0+ 5+ 0 (incorrect) Fifty 30+ 20= 5050

Among these answers there were two incorrect ones. The first was 0 + 5 + 0 which about 5 of my students wrote. With this answer they attempted to do expanded form but failed to recognize there are no ones in the number 50. The second misunderstanding was with the answer 30 + 20=50, this is a correct statement mathematically, but it is not one of the ways that I taught students to write numbers in my unit. The answer 50 that I saw one student write down is writing the number in standard form which was one way I taught and I also taught how to write number

mailto:[email protected]

names (fifty). One method of formative assessment I used to analyze this learning goal (writing a number in different ways), was a whispered answer.

Another skill my students learned in my unit was how to pay for an item using exact change. One of the first days of my unit I used the smartboard to play a game with my students in which they had to show coins to pay for the item using exact change. As I walked around I monitored student answers in their math journals and saw that students were able to correctly pay for that item, but I noticed not all of them used the least amount of coins possible. For example the item that came up first was 48 cents, which I noticed many students would use 4 dimes and 8 pennies.

Something my students struggled with was making change. I noticed on the homework that I graded that students did not understand the difference between making change for an item and showing exact change used to pay for the item. Therefore, on this homework page students needed to buy an item under $1, list its price, and then draw they change they would get back. Most students drew coins that added up to $1. Another struggle for my students was counting money to helping them solve a word problem. From my monitoring of math boxes and homework, I know student could count coins and total the amount, but once it got to story problems and using amounts over $1 it became harder. One problem on my summative assessment that showed this struggle was: “Mary had 9 nickels. Then she found 7 pennies. How much money does Mary have? Label your answer. ______.” Many students got the correct answer (52 cents) without showing any work, but here were some common incorrect answers: 57 cents, 54 cents, 16 cents, and 41 cents. The student that answered 16 cents simply added 7 and 9 without using her knowledge of coin values.

Overall, I changed my summative assessment three times. First I was going to use the unit test, until I realized it tested more than what was taught during my unit. Next, I had a lesson planned where we were going to play a game and I made a recording sheet and everything for each student, but this lesson got cut out of my unit, so again I was left with no summative assessment. After talking with my MT, she was concerned with all the assessments the students were being given, so we decided to have a review day where students could do a practice test and I would take student responses and ask them how they came up with their answer. During this time I was able to take notes on my student responses as well.

Formative Assessment:

In the middle of my unit I remembered this was a strategy my MT used and that it worked well, so I had students think about a problem and then on the count of three whisper the answer to me,. Using this allowed me to hear each student’s thinking. One of my lessons involved me writing the number 133 on the board to which all students whispered 133. Next, I drew 133 in base ten blocks to which I heard 133 whispered from all students. Last I wrote it in expanded form and heard a resounding 133. This was a quick and easy way for me to assess this learning goal from all students.

I used the homework as a formative assessment and was able to add worksheets that would give my students more practice with what they were struggling with. For example, I noticed they were struggling with making change so in the next homework I included a worksheet to help them practice that.

Math journals were another way I assessed my students, I walked around and check for student’s understanding, so it was a simple way for me to see which students were struggling. Along with math journals I implemented a couple turn and talks so students could discuss their answer with a partner. Once students shared an answer with the whole class I would sometimes as them if they agreed or disagreed and then called on a student or two to explain why.

The planning of my unit changed a lot! I had to re-plan at least half of my lessons throughout my unit. I even included some of the omitted lessons in my plan because I worked very hard on them. One of these lessons was one from the Ohio department of education that was meant to be split in two parts. After teaching the first part, I was not happy with it so I decided that they second part was not necessary, it would just be repetition. My MT was told that she had to teach these lessons on the curriculum drive, so I planned a lot of lessons around these. Later we discovered that we did not have to stick with these lessons and that they were not of the greatest quality, so together we made the decision to omit these lessons. Lastly, the dates of my GLT changed quite a bit too because of holiday events and a couple days off that our school had.

Tracking individual student growth: I used this chart to track growth from the pre-assessment to summative assessment of my unit. I used answers from discussion, math journals, and summative assessment to obtain my results.

P=progressing N= needs more attention R= refining

Progressing- student showed improvement in this areaNeeds more attention- student still struggles with this concept or aspects of the conceptRefining- student knew these skills on pre-assessment and was able to apply it during my unit

Exact change Making change Coin equivalencies

Writing numbers in many ways

Explaining thinking in writing

1 P R I I2 R R I I3 N R I I4 P R I I5 N R I P6 N R I I7 N R I I8 N R P P9 N I P P10 N R I P11 R R I I12 R R I I13 R R I I14 N P N P15 N N P N16 R R I I17 R R I I18 R P I I

19 N R I I20 R R I I21 R R I I22 N R I P23 R R I I24 P R I I25 N R I I26 N N I I27 N P I I28 N R I I

Re-teaching my unitIf I were to teach this unit again I would like to have some more participation structures.

As I mentioned, I implemented a couple turn and talks, but I wish I would have held students more accountable for what their partner said by asking them to explain what they talked about. I also wished I would have went around and talked with more of the partner pairs during discussion. I think I also could have made some of my math messages more high level and open ended. Some of mine were, but I failed to facilitate discussion. For example, one lesson I drew money on the board ($3.50) and asked if that was enough money to buy a package of cookies (for $3.25), but I only took one student response.

Connection to project 1My unit was focused a lot on money and using money to buy and pay for items, which

was something that I explored in project 1. In project one I observed a grocery store in the community and discovered the different ways math was used there. During my first lesson I made it a point to connect our worksheet to student’s real lives. I said we were going to go shopping and I asked them to imagine the grocery store that they normally shop at. I even told them that I usually shop at Meijer so that’s where I was pretending I was shopping that day. They seemed to enjoy this and became more engaged in the lesson because of it.

Project one also focused on the math smartnesses of my students which I tried to incorporate in my teaching as well. I allowed students to write and draw in their journals as much as possible and even allowed for turn and talks for those who like to discuss.

What I learned about teaching As I reflected on my lessons and asked for feedback from my MT I discovered a lot about

student engagement and how it can propel your lesson or take it to a screeching halt. One piece of advice my mentor gave me is “Being a teacher means being an actress, sometimes you have to play the fool to get kids interested.” At first this is not something I was comfortable with, and I am still struggling with it a little, but I have noticed some improvement since the start of GLT. I have been trying to show my enthusiasm in my lesson and connecting my teaching to real life as much as possible. When you give engaging tasks students want to learn, I saw this when I used the smartboard and in other lessons when I would ask students to come to the board to share their answers. Students want to have some input and want to share their answers with others and

become very engaged in learning, especially when you mention they might get to write on the board!

A struggle for me was facilitating discussion. I think I had intentions to have great discussions but most of them fell flat. As we have discussed in class, there are certain teacher talk moves that can help facilitate discussion and I think this what I need to work on. I was aware of my talk moves during one of the lesson but on others I failed to make these connections between student responses.

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