Good Spirit School Division UbD Unit Plan Teacher: Susan Muir & Bethany Wagner Subject: Mathematics Grade: Five Unit Title: Patterns and Relations Context (ELA only): Type of Unit (ELA only): Time Frame: 4 weeks STAGE ONE: IDENTIFY THE DESIRED RESULTS Outcomes Addressed in the Unit SK curriculum outcomes can be copied and pasted, focuses highlighted. Outcome: P5.1 Represent, analyze, and apply patterns using mathematical language and notation. [C, CN, PS, R, V] Outcome: P5.2 Write, solve, and verify solutions of single-variable, one-step equations with whole number coefficients and whole number solutions. [C, CN, PS, R] Big Ideas/Enduring Understandings What do you want students to understand and be able to use several years from now? What are the BIG ideas? Essential Questions Open-ended questions that stimulate thought and inquiry linked to the content of the enduring understandings. Why are we learning about patterns? Is mathematics really just the study of patters? How does being a pattern seeker help me understand the world around me? How do patterns help us solve problems? What do you think of when I say the word “pattern”? Where and how do you use patterns in your everyday life?
Transcript
Good Spirit School Division UbD Unit PlanTeacher: Susan Muir & Bethany Wagner Subject: Mathematics Grade: FiveUnit Title: Patterns and RelationsContext (ELA only): Type of Unit (ELA only):Time Frame: 4 weeks
STAGE ONE: IDENTIFY THE DESIRED RESULTSOutcomes Addressed in the Unit
SK curriculum outcomes can be copied and pasted, focuses highlighted.
Outcome: P5.1
Represent, analyze, and apply patterns using mathematical language and notation. [C, CN, PS, R, V]Outcome: P5.2
Write, solve, and verify solutions of single-variable, one-step equations with whole number coefficients and whole number solutions. [C, CN, PS, R]
Big Ideas/Enduring UnderstandingsWhat do you want students to understand and be able to use several
years from now?What are the BIG ideas?
Essential QuestionsOpen-ended questions that stimulate thought and inquiry linked to the
content of the enduring understandings.
Why are we learning about patterns? Is mathematics really just the study of patters? How does being a pattern seeker help me understand the world around me?
How do patterns help us solve problems? What do you think of when I say the word “pattern”? Where and how do you use patterns in your everyday life?
o Why do we need variables in math?o How is this information useful to me?o How can one equation mean more than one thing?o How can I solve problems with unknown parts?o How do I know if I’m right?
Knowledge and Skills (Students will know and do…)What key knowledge and skills will students acquire as a result of this unit?
(These may be indicators from the curriculum)Knowledge (Students will know…)
What key knowledge will students acquire as a result of this unit?Skills (Students will know how to…)
What key skills will students acquire as a result of this unit?a. What is pattern?b. How do you make a pattern?c. Vocabulary: pattern, increasing pattern, consecutive numbers,
d. Describe situations from one’s life, family, or community in which patterns emerge, identify assumptions made in extending the patterns, and analyze the usefulness of the pattern for making predictions.
e. Describe, using mathematics language (e.g., one more, seven less) and symbolically (e.g., r + 1, p – 7), a pattern represented concretely or pictorially that is found in a chart.
f. Create alternate representations, including concrete or pictorial models, charts, and mathematical expressions, for a given pattern (numeric or geometric).
g. Predict subsequent elements (terms or values) in a pattern (with and without concrete materials or pictorial representations) and explain the reasoning including the assumptions being made.
h. Verify whether or not a particular number belongs to a given pattern.
i. Solve problems and make decisions based upon the mathematical analysis of a pattern and other contributing factors.
j. Identify aspects of experiences from one’s life, family, and community that could be represented by a variable (e.g., temperature, cost of a DVD, size of a plant, color
Describe patterns using mathematical language symbolically, concretely and pictorially
Describe situations in daily life when patterns emerge Identify assumptions made in extending patterns Create representations Predict subsequent elements in patterns then verify the results
and explain reasoning Verify whether a particular number belongs in a pattern
P5.1 Represent, analyze and apply patterns using mathematical words and notation
* I can describe patterns with mathematical words and symbols
* I can create models, pictures, charts and pattern rules for patterns
* I can use variable to write expressions for patterns* I can determine whether or not a number belongs
to a given pattern* I can use variable to write equations for patterns
of shirts, or performance of a team goalie).
k. Describe a situation for which a given equation could apply and identify what the variable represents in the situation.
l. Solve single-variable equations with the variable on either side of the equation, explain the strategies used, and verify the solution.
P5.2 Write, solve and confirm solutions of single-variable, one-step equations (with
whole numbers)* I can solve equations with variables* I can explain what part of a problem a variable
Summative Assessments/Performance TasksAssessments of what students know and can do aligned to the outcomes. They are a snapshot in time used for reporting and evaluating.
Outcomes/ObjectivesOutcome: P5.1
Represent, analyze, and apply patterns using mathematical language and notation. [C, CN, PS, R, V]
Post assessment :Name:1. Write the pattern rule for these patterns. a) 99, 94, 89, 84, 79 b) 10, 8, 11, 9, 12, 10, 132. Find and correct the error in this pattern: Start at 3. Add 1. Increase the number you add by 1 each time. 3, 4, 6, 9, 13, 18, 26, 31, 39, 48, 583. Write the first 4 terms of this pattern. Start at 20. Alternately, add 10 then subtract 4.
______, _______, ______, _______4. Find the missing terms in these patterns. a) 25, 50, _______, 100, 125, 150, 175 b) 80, 74, 68, 62, 56, _______, 44, 38, _______ c) 7, 8, 10, 13, 17, _______, 28, 35 d) 20, 30, 25, 35, 30, _______, 35, 45 e) 100, 300, 200, 400, 300, _______, 400
5. Here is a table that shows a pattern of dots.Figure Number of Dots
1 51
2 49
3 47
4 45
5 43
Which figure will have 37 dots? Figure 6. What is the 9th term in these patterns? a) Start at 15. Alternately increase by 10 and then increase by 5. ________ b) Start at 90. Subtract 4. Increase the number you subtract by 1 each time. _______7. Sue and her dad made a deal. For each week that Sue does chores her dad increases her allowance by $5 per week.
The first week, her allowance is $10. If she saves it all, how much money will Sue have after 6 weeks?
Show your results in a table.
Outcome: P5.2
Write, solve, and verify solutions of single-variable, one-step equations with whole number coefficients and whole number solutions. [C, CN, PS, R]
Post Assessment: Outcome: P5.2 I can use a variable to solve and check one-step equations.Name:
1. Solve the equations. Use counters or pictures to help you. a. y + 18 = 27 b. 21 – r = 72. Write a story problem you could solve using this equation: y – 5 = 213. Solve the equation. Show your work.
a. 31 + n = 68 b. 75 – 11 = t
c. b + 25 = 50 d. 8y = 32
e. 36 ÷ k = 4
4. Write an equation using a variable for these sentences a. Fifteen is four less than a number. _________________ b. A number times two is sixteen. ________________ c. Three is a number divided by nine. ____________5. In the equation 36 - 11 = n, 36 represent the number of cans of juice. 11 represent the number of cans of juice that Scott drinks. What does n represent?6. Write 2 equations for this problem. Four friends had book bags. Each bag had the same number of books. Altogether they had 120 books.7. Write an expression for the following pattern: 27, 26, 25, 24, 23, …
Formative AssessmentsThrough what multiple sources of evidence will students demonstrate their understanding on a continual basis?
These help guide instruction and provide feedback to students.These two rubrics will be used as both formative and summative throughout the unit. Each student will have their own page and I will record notes during small group and large group instruction. These will also be used as a student self-assessment.
Entrance Slip Week 2
Pre-AssessmentsPre-assessments are used to determine what students know and their readiness level to inform instruction.
Week One
Outcome: P5.1 I can describe, extend and use patterns.
Name:
1. Here is a pattern. The number of squares continues to increase. Draw the next picture in this pattern.
Figure 1 Figure 2 Figure 3 Figure 4 Figure 5
2. Here is a table that shows a pattern using blocks.Figure Number of Blocks
1 2 2 5 3 8 4
5 14 6
a. Fill in the missing number in the table for Figure 4.b. Extend this pattern for Figure 6. How many blocks will be in Figure 6? ______c. What is the pattern rule? _________________________________________________d. Will any figure in this pattern have 21 squares? How do you know?_______________________________________________________________________3. Here is a pattern of dots.
Figure 1 Figure 2 Figure 3 Figure 4
What is the pattern rule for this pattern? _______________________________________4. Here is a pattern rule: Start at 4. Add 3 each time. a. Draw a set of 4 pictures to show this pattern. Figure 1 Figure 2 Figure 3 Figure 4
b. Write the first 5 terms of this pattern. _______, _______, _______, ______, _____5. Here is a pattern rule: Start at 98. Subtract 4 each time. Write the first 5 terms of this pattern. _______, _______, _______, ______, ______6. Write the next number in the following number pattern.
10, 11, 13, 16, 20, 25, _____
7. Here is a pattern of blocks. Figure 1 Figure 2 Figure 3 Figure 4
If this pattern continues, which figure will have 19 dots? Figure 8. Here is a pattern rule: Start at 2. Add 2. Increase the number you add by 1 each time. What is the 7th term in this pattern? ________
9. John and his dad made a deal. Each week that John does his chores; he gets $3 more than the week before. In the first week, John gets $5. How much will John earn on the 10th week? Show your results in a table.
Week 2 Pre-assessment for P5.2
STAGE THREE: CREATE THE LEARNING PLAN
Instructional PlanThe Instructional Plan should include a sequence of lessons, teaching strategies, and information on First Nation, Inuit and Metis Content integration
and technology integration.
Week One- day One Pretest-: P5.1 I can describe, extend and use patterns.
Week One Monday Full group lesson:
How Many Feet are in the Bed? This is typically a book that I have used in grade 1-2 math however; it lends itself to exploring patterns in greater detail.
http://blogs.gssd.ca/smuir/?p=2974 Personal File Cabinet
Represent, analyze, and apply patterns using mathematical language and notation. [C, CN, PS, R, V]m. Describe situations from one’s life, family, or community in which patterns emerge, identify assumptions made in extending the patterns, and analyze the usefulness of the pattern for
making predictions.
n. Describe, using mathematics language (e.g., one more, seven less) and symbolically (e.g., r + 1, p – 7), a pattern represented concretely or pictorially that is found in a chart.
o. Create alternate representations, including concrete or pictorial models, charts, and mathematical expressions, for a given pattern (numeric or geometric)
P2.1 Demonstrate understanding of repeating patterns (three to five elements) by:• describing• representing patterns in alternate modes• extending• comparing• creating patterns using manipulatives, pictures, sounds, and actions.P3.1 Demonstrate understanding of increasing and decreasing patterns including:
observing and describing extending comparing creating patterns using manipulatives, pictures, sounds, and actions.
Materials Needed:“How Many Feet in the Bed?” by Diane Johnston Hamm
SMART board lesson if a SMART board is availableT-chartUse or Make a Table Strategy ChartUse or Look for a Pattern ChartFour Step Method- systematic approaches to problem solvingStory Board and FeetStudent copies of Double T-charts
Determine how the learning will be observed
What will the children do to know that the learning has occurred?What should children do to demonstrate the understanding of the mathematical concepts, skills, and big ideas?What assessment tools will be the most suitable to provide evidence of student understanding?How can I document the children’s learning?
3- Point Rubric Does the student extend his or her thinking?
Plan the learning environment and instructionWhat learning opportunities and experiences should I provide to promote the learning outcomes?What will the learning environment look like?What strategies do children use to access prior knowledge and continually communicate and represent understanding?What teaching strategies and resources will I use?
Warm- up game- Skip counting: I have Who Has Game
Before: Have students gather at the story corner or in front of the Smart Board.Display a picture of a Human Foot. Have students describe what they see.Back ground information that they must know is that a human (assuming that they have two feet, etc.) has two feet and each foot has 10 toes.
Read the story through once without stopping. Reread the story through a second time but now introduce the T-chart labeled People and Feet. Have the story mat or SMART lesson in view of all children.This time, read the story but have students represent, using manipulatives on the story mat or Smart board. Record work on the t-chart.
Once all 5 people are ‘in the bed’, stop to look at the patterns in the t-chart. Spend time with a discussion.Now pass out clip boards with the double t-chart. Have students, with a partner; fill out the third column of the chart labeled TOES.
Come back full group to record findings and discuss patterns.
Using the Think Pair Share strategy… Have students extend their thinking of the pattern and record information for 6 and 7 people.Share in full group. What patterns do we see?Is there anyone who can take what they know and find the number of feet and toes for 12 people? 25 people? What are you thinking?
Display Picture of Ducks Feet.Discuss.
During: You and a partner will work together to solve a new problem.You will need to record your work using manipulatives, pictures and also numbers on a t-chart.The problem is differentiated into 5 levels of difficulty. The last 2 questions are at the grade 5 level.
When Samantha was at the petting zoo she saw baby ducks lined up behind their mother.Samantha saw 14 duck feet all lined up.How many ducks did Samantha see? How many toes?Use manipulatves, pictures and record your number patterns on a t-chart.
When Samantha was at the petting zoo she saw baby ducks lined up behind their mother.Samantha saw 24 duck feet all lined up.How many ducks did Samantha see? How many toes?Use manipulatves, pictures and record your number patterns on a t-chart.
After: Share in small groups. What patterns did you find? Make connections with journal
writing.
Assess student learning and follow up
When Samantha was at the petting zoo she saw baby ducks lined up behind their mother.Samantha saw 32 duck feet all lined up.How many ducks did Samantha see? How many toes?Use manipulatives, pictures and record your number patterns on a t-chart.
When Samantha was at the petting zoo she saw baby ducks lined up behind their mother.Samantha saw an increasing pattern of ducks. It began with one duck (mother) then 2 ducks, 3 ducks… all the way to 6 ducks.How many ducks did Samantha see? How many toes?Use manipulatives, pictures and record your number patterns on a t-chart.
When Samantha was at the petting zoo she saw baby ducks lined up behind their mother.Samantha saw an increasing pattern of ducks. It began with one duck (mother) then 2 ducks, 4 ducks, 8 ducks… all the way to 64 ducks.How many ducks did Samantha see? How many toes?Use manipulatives, pictures and record your number patterns on a t-chart.
What conclusions can be made from assessment information?How effective have instructional strategies been?What are the next steps for instruction?How will the gaps in the development of understanding be addressed?How will the children extend their learning?
How is the duck problem similar to the human foot problem? How is it different?
Week One Centers
Mastering the Basics- skip counting patterns ( taken from EDUGUIDE)
At Your Desk Math Makes Sense Lesson One practice page 8 #3 and Step by Step #7
Teacher Focus on Math Language: mathematical language
Record on the chart“What patterns do you notice?”n “How does the second term differ from the first term? The third term?”n “Are there other patterns that describe how the pattern grows? What are they?”
Decreasing patternIncreasing patternPatternTermTerm numberTerm value
Teacher questions to ask students:“What is a pattern?”n “How do you know the example you gave is a pattern?”n “What comes next in your pattern? How do you know?”n “How can you describe your pattern?”n “Is there another way you could describe your pattern?”
Hands On – Turn over a start card- then turn over a pattern rule card. Build terms 1, 2, 4, and 7.
S Integration (computers)http://hzsd.ca/Learningcenter/library/Math%20Resources/Grade%205%20Math%20Websites
The learning experiences in this section focus, in part, on translating word problems into equations and then solving them. This is not new to students. In the Early Years, students were introduced to whole-number operations through routine problems. In the beginning, students solved these problems using concrete and pictorial representations.Later, they translated these problems into equations, often using an empty square to represent the unknown value.Consequently, the learning experiences provide students with additional experience with solving routine problems and, at the same time, beginning the transition to using letters to represent unknown quantities. They also serve as an informal introduction to the terms “equation,” “mathematical expression,” and “variable.” These terms aredefined as follows:An equation is a mathematical sentence stating that one or more quantities are equal.Equations that contain variables, such as 3 + x = 21 and 2y + 3 = 15, are sometimesreferred to as open sentences, while equations that have no variables, such as 3 + 5 = 8 and 24 3 = 8, are referred to as closed sentences.A mathematical expression comprises numbers, variables, and operation signs, but does not contain a relational symbol such as =, , <, >, , and . For example, 6x + 3 and are mathematical expressions.A variable is a symbol for a number or group of numbers in a mathematical expression or equation.
Week Three
Full Group Monday Lesson : Function Machines Outcome: P5.2
Write, solve, and verify solutions of single-variable, one-step equations with whole number coefficients and whole number solutions. [C, CN, PS, R]o Why do we need variables in math?o How is this information useful to me?o How can one equation mean more than one thing?o How can I solve problems with unknown parts?o How do I know if I’m right?
Resources:
Assessing Prior KnowledgeMaterials: NoneOrganization: Pairs/Whole classProcedure:a) Tell students they will be solving some problems involving equations, but before you can give them these problems you need to know what they already know about equations.b) Pose this question: “What is an equation?” Have students think about the question for a few moments, then share their answer with their partner.c) Have students share their answers with the other members of the class. Encourage discussion by asking students questions, such as thefollowing:n “What is an example of an equation?”n “What does the equation tell you?”n “Is 6 x 7 an equation? Why or why not?”n “Is 5 = 14 — 9 an equation? Why or why not?”n “Is n 4 = 16 an equation?”
n “When do you use equations?”
Materials: Math journalOrganization: Whole classProcedure:
a) Present this problem:b)
n Nancy and Jessica were asked to write an equation for this story. I want to buy35 pencils. Pencils come in packages of 7. How many packages do I need to buy?Nancy wrote 7 x n = 35 and Jessica wrote 35 7 = n. Who is right? Why?
b) Ask students to think about the problem, and then record their answer in their math journals.
c) Have students discuss their answer with the other members of the class.
Centres for the week:
Mastering the Basics: Function Machines
At Your Desk: Lesson #5 Math Makes Sense #1-4 and & 7
Teacher:
Hands On using virtual and concrete pan balances: http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/weigh/1c.htm
Virtual Tools and concrete pan balance tools will be used to solve situational problems:
The following is taken from :Illuminations
Examples of discoveries may include:
one red square = one red square, or 1s = 1s, using variables. This demonstrates the Reflexive Property of Equality, a = a.Remind students to “Reset” the balance to show 2 pink triangles = 2 pink triangles, or one yellow diamond on each side.This property may also be demonstrated with
with a pan balance in the classroom, placing 3 blue blocks in the left pan, and 3 blue blocks in the right pan. To develop kinesthetic understanding of the Reflexive Property of Equality, have students hold 3 cubes in their left hand, and 3 cubes in their right hand.When demonstrating to the class, you may use the following linkto keep a constant set of relationships, which may be helpful when leading the discussion.
To demonstrate the Symmetric Property of Equality, if a = b, then b = a,place 1 red square in the left pan and 2 blue circles in the right pan. Ask students, “What if I put 2 blue circles in the left pan? What must I put in the right pan?”
[1 red square].
Reset, and demonstrate 1 pink triangle = 3 yellow diamonds. Using the Symmetric Property of Equality, ask students, “What will balance 3 yellow diamonds placed in the left pan?
Drawings can also incorporate unknown amounts. Use the drawings to help solve the unknown.
Singapore Math
Thinking Blocks I really like Thinking blocks as it gives a great problem and allows you to build the problem based on what you know and do not know. It models the math problem to help you find the unknown.
Science/Social integration (Computers):
Function machines: http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_1.html
Easier version http://teams.lacoe.edu/documentation/classrooms/amy/algebra/3-4/activities/functionmachine/functionmachine3_4.html
