Anchor Task Lesson Planning: An Overview Standards/Objectives: Materials: Notes for the teacher: Explore: This is the problem you will pose to students. There may be instances where a simpler problem is posed to help introduce Extensions during the task for early finishers: What questions will you ask to extend the thinking of all? Structure/Board Plan: Anticipating what methods students might use, what questions will you ask to elicit those methods so they can be recorded for the class on the board? Then think through a rough sketch of how you will record the thinking of the students as they share it during the structuring discussion. Remember that being intentional about the visual organization of the board can help students see patterns in the work. Journal: For every journal entry, have students write a title in their own words and the date. Beyond that, teachers have freedom to choose what students record. They might record their own method, a method that was new to them, or the teacher may choose what is written in the journal. Reflect: The textbook can be opened here. This part of the lesson connects the thinking of the exploration with the methods used by the textbook. What questions will you ask so that key concepts, notation or methods are noticed by students and compared with their own work from the Exploration? Practice (Guided): What parts of the guided practice suggested by the text are best suited for your students after experiencing the anchor task? Keep in mind that this practice is not necessarily independent. Students can help “guide” one another’s practice when working in small groups. The teacher’s role is to circulate and listen to students as they think aloud or discuss their work with a friend. Practice (Independent): Which tasks/problems in the text are best suited for students to work completely independently? Remember that not all tasks are equally worthy of your students’ time and energy. Choose wisely. This part of the lesson may or may not take place at home. Consider using a self-reflection rather than simply producing “answers” for calculation exercises or word problems.

Title: Date___

Method 1: Method 2: Possible Method 3:

Grade K MIF Chapter 1: Lesson 5 (TE p 22-24) This task can take place directly following Activity 1 (BigBook p5). It is adapted from The Super Source: Color Tiles Grades K-2, ETA/Cuisenaire, 1996. Objectives: Count groups of 5. Write the numeral 5. Materials: 25-30 one-inch square tiles, 1 inch grid paper, crayons, scissors for each student or pair of students. Personal white boards if desired.

Explore : Opening task for modeling and setting constraints on allowable shapes: Show your friend 3 squares tiles. Make a shape with your 3 tiles.

Allow students to create anything they would like. Then set constraints: Your shape must lie flat on the table. Does it follow this rule? If not, change it.

Once students have examined their work to fit the first “rule,” demonstrate other “rules” for the task:

This shape is OK. This shape is not OK. This shape is OK. Is this shape OK? How many different shapes can you make with 3 tiles that follow our rules? Talk to your friends. Encourage students to check the uniqueness of their shapes by coloring the shapes on grid paper, cut and lay on top of other shapes. Anchor: How many different shapes are OK if you use 5 squares? Extensions during task for early finishers:

Work with your partner to color all the shapes you found for 5 tiles on your grid paper and cut them out. These can be used during the structuring discussion to test for rotations/reflections.

If there are 12 different shapes with five tiles, how many do you think there will be for 6 tiles? See if you can find them all. Draw them on your grid paper and cut them out.

Predict how many shapes can be made with 8 tiles. Test your prediction.

Structure/Board Plan :

As students describe the shapes they made, record them or have them come and stick their cut-outs on a common board. To meet the objective of the lesson, have students count the tiles aloud as shapes are shared and write the numeral “5” beneath and/or have students write “5” in the air or on a personal whiteboard.

How many shapes did you and your partner find? What shapes did your friends find that are different from yours?

Are any of these shapes the same shape? How could we be sure? If rotations/reflections are offered, encourage color and cut to verify or use the early finishers’ cut-out shapes. Encourage students to describe how they “see” that the shapes are the same even if they are oriented differently.

Journal: Have students write a title in their own words. (Possible responses: “Shapes” “5 squares” or simply, “5”). Students might also copy the statement, “We found ___shapes.” into their journal or could be provided an adhesive label with the words on it to be stuck onto their journal page. Then have them draw 2-3 of their favorites on grid paper, color, cut and paste into journal. Underneath each one they should write the numeral “5”. If they have more time, they can choose others to color and cut. Reflect: Proceed with Activity 2 (TE KA p23) Which of the things we can count on these pages is the same number as the tiles we used to make our shapes? How do you know? How can we be sure? Practice (Guided): If teacher feels students need a bit more guided work on counting 5 objects or matching sets, show a numeral card 1-5 and ask student to build a tower of linking cubes to match. Students may also be allowed to make a tower of any height between 1-5, then find someone whose tower is the same. Practice (Independent): SB KA1 p22 – Count and write the numeral 5. Alternately, for more interactive numeral writing practice, pairs of students can work together. While one student builds a tower of cubes, the other can write the number of cubes in the tower on a personal white board. They may then switch jobs.

5 5 5

5 squares

Date___

We found ___ shapes.

Grade 1 MIF Chapter 2: Opening/Lesson 1, Day 1 (TE p 28-32) Objectives: Using objects to find number bonds. Find different number bonds for numbers to 10. Materials: 10 cotton balls (or other types of counters) ,2 sticky notes (or small containers) and a piece of blank paper per student or pair of students

Explore: Opening task for modeling: Skippy bought 4 sheep. How many ways can he put his 4 sheep in two pens? Show me 4 cotton balls. Use your sticky notes to show me 2 pens. (Record by drawing student responses in an organized listing.)

Anchor: What if Skippy bought 5 (6) sheep instead? How many ways can he place his 5 (6) sheep in two pens? Draw all the ways you find on your paper. Extensions during task for early finishers:

Did you find all the ways? How do you know for sure?

What if Skippy bought 10 sheep? How many ways could he put them in the pens?

What if Skippy had 3 pens….how many ways can he put 10 sheep in three pens? How did your thinking change when there were three pens?

If there are 3 ways (6 ways) to put 5 sheep in the pens and 4 ways (7 ways) to put 6 sheep in the pens, how many ways do you think there will be to put 7 sheep? 8 sheep? 10 sheep? 50 sheep? Draw or write something that explains your predictions.

Structure/Board Plan:

How many ways did you find to put the sheep in the pens? Do you think we found them all? How could we be sure?

What did you draw to show your thinking? How is it the same as other friends drawing? How is it different?

Method 1: Method 2: I just put some in each pen at first and then switched them around I put a sheep in one pen, then a sheep in the other pen ‘til I ran out of sheep.

Possible Method 3 – I put all the sheep in the first pen and no sheep in the other pen. Then I moved one sheep at a time to the second pen til there weren’t any sheep left in the first pen.

5

5

0

5

4

1

5

3

2

5

3

2

5

4

1

5

5

0

Let’s show all the ways we found. I’m not good at drawing sheep so I will use some circles. I will write the total number of sheep in the bigger circle and then use the smaller circles to show the pens. When we connect the circles with the lines, we can call them number bonds! As each way is recorded, say a number sentence in this form, “4 and 1 make 5.” 5 is all the sheep – it’s the whole. As you point to a smaller circle say, “This part is the first pen and this part is the second pen.” (This discussion point formalizes the notation of number bonds. It may not be appropriate for every class.)

What do you notice about the how the part of the sheep in the first pen changes when you put sheep in the second part?

Does it matter where we draw our part/ the smaller circles? Why or why not? (Draw alternate bonds as seen on Teacher’s Edition 1A p31) Is 3 sheep in the first pen and 2 sheep in the second pen the same as 2 sheep in the first pen and 3 sheep in the second pen? This will be up for

debate…the way your class answers this will affect the responses to last extension question above. Allowing the “turn-around” bonds to be recorded helps

students to see pattern and encourages discussion, but classes will vary in their ability to think at this level, so teacher judgment is essential.

Journal: Have students write a title of their own and date the entry. (Possible response: “Sheep in the pens” “5 Sheep”) Students might copy, “I can make 5.” into the journal before continuing. Today I will choose what we will write in our journal. Copy all the ways we made 5 using number bonds. Students can be allowed to use representations other than number bonds to record their thinking. Reflect (go to Online Student Book): Display Online Student Book (OLSB) page 30.

How is this picture the same as what we did? How is it different?

If we had used cubes instead of cotton balls, which circle would show all the sheep? Which circles would be the pens?

Let’s say a number sentence for this way to make 4. (Allow them to go back to the other bonds for 4 they found in the anchor task and say number sentences for them.)

Display OLSB p32. Demonstrate on an actual balance if possible. Review what it means when the balance is level.

How does this picture (this number balance) show the whole amount of sheep and the parts that are in the pens?

Let’s say a number sentence for the whole and these parts. (7 is the same as 4 and 3.) Practice (Guided): Continue with Guided Practice on OLSB p32. Use your cotton balls to show another way to make 7. Let’s test it on our number balance. Alternatively: Display OLSB p33. Use your cotton balls (or counters) to find ways to make 6, 8 and 9. Practice (Independent): Workbook 1A p21-22

5 sheep

Date___

I can make 5.

5 5

0

5

5

0

Grade 2 MIF Chapter 4, Lesson 1.1 (Teacher’s Edition p 96-99 Introduction to bar models) Objectives: Use bar models to solve addition and subtraction problems.

Materials: linking cubes of two colors and paper strips of matching colors Notes for the Teacher: This task begins the chapter on bar modeling. Rather than begin with the suggested problem in the text, the task uses a “both addends unknown” problem type to make the task more exploratory and allows students to make several bar models for the same whole. This leverages number bond knowledge and gives more practice in actual construction of models. Students will translate concrete models using linking cubes & paper strips to pictorial models that are increasingly abstract. This will then be structured to guide students to model “total unknown”problems with paper strips and then to draw actual bar models based on the concrete work. Depending on how quickly students work, this lesson will probably take more than one day. Please also note that the text suggests doing models for “addend unknown” (missing part) problem types also. Follow the same teaching sequence shown here for the missing part problems. If both problem types are covered in one lesson as suggested by the text, guided and independent practice should also include both types. Explore (Day 1): Tim made 15 cookies. He put part of the cookies on a blue tray and the other part of the cookies on a red tray. If he used all the cookies, how could he have arranged the cookies on the two trays? Use your cubes to show your thinking. Structure A/Board Plan (Day 1): After recording the ways students arranged the cookies using cubes, hold up a blue strip of paper and a red strip of paper and follow the line of questioning below:

Let’s focus on one of the ways you found that Tim could have arranged the cookies – 3 cookies on the blue tray and 12 cookies on the red tray. Imagine that these strips represent the cookies on each tray (display equal length strips in the two colors.)

Look at the length of these strips. Do they show that there are more cookies on the red tray? Why or why not? (no, they are same “size” - length) What could we do to show there are fewer cookies on the blue tray? Talk to your partner. (Cut the blue strip so that it is shorter).

If this red strip represents 12 cookies on the blue tray, how much should we cut off the blue paper to show only 3 cookies? How do you know? (accept any reasonable answer that gets the blue strip proportional to 3 cookies.)

Cut your strips so that they show more cookies on the red tray.

Method 1: Method 2: Others ways to show 15 cookies

3 12

15

Cookies

12

15

Red tray

3

Blue tray 7 8

6 9

How could we place these strips on our paper to show all the cookies that Tim made? (Ask students to glue their own strips then record their ideas on the board.)

Now that we have such a great pictures of arranging the cookies, let’s write our thinking on these strips so we can remember all we said. o What do these strips of paper represent? (Write “cookies” or “Tim’s cookies” to the left of the strips.) o Remind me how many cookies are on the red plate. (Use a simple bracket to label the red strip with 12) o Remind me how many cookies are on the blue plate. (Use a simple bracket to label the blue strip with 3) o Remind me how many cookies Tim made altogether. (Use a simple bracket to label strips end to end with 15.)

What we’ve made is called a part-part-whole model. Where are the parts? Where is the whole? How does it show our math story? Journal: Use your paper strips to create pictures for some of the other ways Tim could arrange the cookies on the trays and glue it on your paper or draw them in your journal. Don’t forget to label your paper strips with your thinking. Share your pictures with the people at your table.

Practice (Guided/Independent) The journaling for this part of the lesson serves as the guided and independent practice for this part of the lesson.

Tim’s cookies

Date___

7 8

6 9

Explore (Day 2): To focus students on making a model before solving, wait to supply the question until bar models have been constructed out of paper. Use your paper strips to make a picture of this math story. Tim baked some cookies. He put 28 cookies on a red tray and 43 cookies on a blue tray. Extensions during the task for early finishers: Because this lesson requires a good bit of fine motor skill, there may be those who complete the models/calculations quickly. In that case, the following may be used to further the thinking after the total number of cookies has been found.

Answer one of the other questions that your classmates posed.

How many more cookies would Tim need to bake to have 100 cookies? How do you know?

Use your strips to make a model of this same total of cookies (71), but put the cookies on three plates. How many ways can you find to arrange the cookies on three plates?

Structure/Board Plan B:

How is this story like the one we explored yesterday? How is it is different? (now there are fewer on the red plate, there are more cookies on both plates, we don’t know how the total at that beginning of the story, we do know what he put on the trays this time, no question to answer, etc)

To make a good bar model of this story, what do you need to think about? Talk to your friends then make a model with your paper strips.

What questions could we ask about this story? (How many in all? How many more on the blue plate? How many fewer on red?)

Let’s answer the question, “How many cookies in all?” How might we place our strips on the paper to show we are interested in answering this question?

Glue your strips down and then label what we’ve made so far. (Lead students to label each colored strip and put a question mark for the whole.)

Let’s also write a sentence that will answer our question. We will put an “umm” (a blank) in our sentence to write the answer. (Write “Tim has _______cookies altogether.”) Now work with your partner to answer the question.

How did you find the answer to the question?

Write the answer to the question in the “umm” sentence. Journal: Have students write a title in their own words and the date. Copy the bar model for our story , your favorite method for finding the total number of Tim’s cookies and the “umm” sentence that answers our question. Reflect: Go to SB p.96. Compare this problem to the one we did about Tim’s cookies. What do you notice is like our bar model? What do you notice that is different?

Practice (Guided): Proceed with SB p. 97. Allow students to work together to model with paper strips or allow them to draw the bar model. Practice (Independent): Go to SB p.102. Have students model #1 and #3 independently. They may use paper strips or simply draw. Again, please note, if the class constructs bar models for the “addend unknown” problem on SB p.98, then guided practice for this problem type is found on SB p.99 and independent practice can be found on SB p.102.

Tim has ___________cookies altogether. Method 1: Method 2: I wrote my numbers under each other I added my tens, then my ones. Then added and added my ones then my tens. them altogether. Possible Method 3: I broke my 43 into 41 and 2. I added 2 and 28 to get 30, then added 41 to that.

28 43

?

Cookies

More cookies

Date___

28 43

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Cookies

Anchor Task Lesson Planning Worksheet Standards/Objectives: Materials: Explore: Extensions during the task for early finishers: Structure/Board Plan:

Journal: Reflect: Practice (Guided): Practice (Independent):

Title: Date___