MAA G3 D2 FNL - Education Service Center Region...

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MATHEMATICS ACHIEVEMENT ACADEMY, GRADE 3

Day 2: Multiplication and Division

Purpose and Outcomes

• What is the purpose of the mathematics academies?

• What are the outcomes of the mathematics academies?

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Materials

Texas Gatewayhttp://www.texasgateway.org/

• Mathematics TEKS: Supporting Information

• Vertical Alignment Charts

Participation Norms

• Be fully present.

• Minimize distractions.

• Minimize “air time.”

• Take a chance.

• Celebrate accomplishments.

Discourse Norms

• Listen.

• Be involved.

• Contribute ideas.

• Participate by asking questions.

• Develop understanding, if not at the beginning, by the end.

Krusi, 2009

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Mathematics Norms

• Look for patterns in order to make generalizations.

• Make connections among models, representations, and generalizations.

• Communicate using academic vocabulary.

• Use mistakes as opportunities to support new learning about mathematics.

Yackel & Cobb, 1996

Learning Progression: Addition and Subtraction

Learning Progression: Multiplication and Division

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Grade 2: Multiplication and Division

• 2(6)(A) The student is expected to model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined.

• 2(6)(B) The student is expected to model, create, and describe contextual division situations in which a set of concrete objects is separated into equivalent sets.

Grade 3 STAAR®: Multiplication and Division

STAAR® Grade 3 Mathematics 2015 Release Questions

Modeling Whole Number Multiplication

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• Modeling Multiplication

• Check Point: Modeling Understanding of Multiplication

Think about the following:• Mathematics• Thinking• Vocabulary

o Academico Contextual

Modeling Whole Number Multiplication

Debrief: Modeling Whole Number Multiplication

• What mathematics are we expecting students to do in these activities?

• Describe the thinking that is expected of students in these activities.

• What mathematics vocabulary are we expecting students to use?

• What contextual vocabulary are we expecting students to use?

Using Anchor Charts

Concept Process Exemplar

A record of meaningful information and ideas about a concept or vocabulary of the mathematics being studied that may grow over multiple lessons

A record of complex mathematics skills broken down into a sequence of steps and may be extended to include additional solution strategies

An annotated example created by the teacher, student or teacher and students together that can be used as a guide

Example Example Example

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Concept


Example

Anchor Charts:Created with students as a summary of learning

Using Anchor Charts

Modeling Whole Number Division

• Modeling Division

• Check Point: Modeling Understanding of Whole Number Division

Think about the following:• Mathematics• Thinking• Vocabulary

o Academico Contextual

Modeling Whole Number Division

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Debrief: Modeling Whole Number Multiplication and Division

• What mathematics are we expecting students to do in these activities?

• Describe the thinking that is expected of students in these activities.

• What mathematics vocabulary are we expecting students to use?

• What contextual vocabulary are we expecting students to use?

Situation 1Ann has 12 pieces of candy. She eats 2 pieces of candy every day. How many days will Ann have candy to eat?

Situation 2Bill has 12 pieces of candy. He shares the candy equally with a friend. How many pieces of candy will each person receive?

12 2 6 Quotative Division

Division by Grouping

Types of Division

Situation 1Ann has 12 pieces of candy. She eats 2 pieces of candy every day. How many days will Ann have candy to eat?

12 2 6 Quotative Division

Division by Grouping

12 2 6 Partitive Division

Division by Sharing

Situation 2Bill has 12 pieces of candy. He shares the candy equally with a friend. How many pieces of candy will each person receive?

Types of Division

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TEKS Connection

3(4)(H) The student is expected to determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally.

3(4)(K) The student is expected to solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts.

Representing Multiplication and Division Problems

• Form groups of four by locating people around the room with cards that match yours.

• A matched group will consists of:o A word problemo An equationo A strip diagramo A number line or an array

Representing Multiplication and Division Problems: Card Match

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• How does the strip diagram represent the problem situation?

• How does the array or number line represent the problem situation?

• How does the equation represent the problem situation?

• How does the equation represent the strip diagram?

• How does the equation represent the array or number line?

Discussion Questions

• What models did you use to represent the problem situation? Why? I used _______ and _______ because _______.

• How does your model represent the problem situation?My _______ model represents the problem situation by _______.

• What other representation can be used to model the problem situation? I think we can use _______ to model the problem situation because _______.

Representations for Multiplication and Division

Select the Operation: Multiplication or Division

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• Represent the problem situation using at least two different models.

• Locate other groups with the same problem situation as your group.

• Hang your posters together, and look for similarities and differences among your representations.

Two-Step Problems

Check Point: Representing Multiplication and Division Problems

Check Point: Representing Multiplication and Division Problems

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• What representations included in this set of activities were different from the first two building blocks?

• How do these representations help students solidify their understanding of multiplication and division?

Debrief: Representing Multiplication and Division Problems

Concept


Example

Using Anchor Charts

Solving Multiplication and Division Problems Using Models

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• Use the counters and grid paper to model and solve the problems individually.

• Share your models and solutions.

• Record one participant at your table explaining how they used the counters and grid paper to model and solve one of the problems.

Cafeteria Counters

• How did you use the counters and/or grid paper to model the situation?

• How did you use the counters and/or grid paper to determine the solution?

Cafeteria Counters

1. The Flower Farm 2. Petunia Palace3. The Pumpkin Patch 4. The Zucchini Garden

Solving Problems with Area Models

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Petunia Palace and Zucchini Gardeno How are the models alike? How are they different?o How did you decide how to decompose the factors?

The Flower Farm and The Pumpkin Patcho How are Aaron’s model and Carter’s model alike? How are they

different?o How do all four models help solve the problem?

Debrief: Solving Problems with Area Models

The Flower Farm planted 8 rows of bluebonnets with 12 bluebonnet plants in each row. How many bluebonnet plants were planted?

Farmer Brown planted 96 total pumpkins in his pumpkin patch. He planted 8 rows of pumpkins. How many pumpkins were planted in each row?

Debrief: Solving Problems with Area Models

Check Point: Solving Problems with Area Models

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Solving Multiplication and Division Problems Using Strategies and Algorithms

• Multiplying with the Associative Property• Multiplying with the Distributive Property• Dividing with the Distributive Property

Solving Multiplication and Division Problems Using Strategies and Algorithms

Debrief: Solving Multiplication and Division Problems Using Strategies and Algorithms

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48 750 7 350

2 7 14

35014

336 Fifty groups

of seven minus two groups

of seven makes 48 groups of

seven.

93 3

90 3 390 3 30

3 3 130 1 31


Check Point: Solving Multiplication and Division Problems Using Strategies and Algorithms

Debriefing Mental Strategies

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Solving Multiplication and Division Problems

How does the use of mental strategies connect to the standard algorithm?

Problem A Problem B

Partial Products Bridging

237

21 7 3140 7 20161

20 3

7140 21

7 20 7 3

140 21 161


237

21 7 3140 7 20161

223

7161

How does the use of mental strategies connect to the standard algorithm?

Problem A Problem B Problem C

20 3

140 21 161

140 21 7 20 7 3

7

Partial Products Bridging Standard Algorithm


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Making Connections to the Standard Algorithm

Solving Multiplication and Division Problems

Round Robin: Solving Problems

Making Connections to the Standard Algorithm

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• What connections do you see between the strategies your group used to solve the problems?

• Were there any answers that you disagreed with? Why?

• Did any of your group members think differently than you about how to solve a problem? Was the solution still the same?

Debrief: Making Connections to the Standard Algorithm

Check Point: Solving Multiplication and Division Problems

Fluency and Automaticity of Facts

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• Sort the cards into a strategy continuum.

• Why did you place the cards in the order that you did?

• Place your hand over one of the middle cards. What are the implications of that strategy being missed with students?


• Multiplication Facts: Find Someone Who . . .

• Exploring Facts

• Double the Fun

• Determining the Unknown

Fluency and Automaticity of Facts

× Description Examples

× 2× 10× 5× 1× 0

Students build on their understanding of skip‐counting and doubling for 2, 10, and 5. Multiplying by 1 is quick to memorize, but saved until students explore multiplication with groups greater than 1. Multiplying by 0 is also quick to commit to memory. Concrete thinkers may have difficulty visualizing groups of 0.

2 3 6 10 9 90

5 4 20 1 8 8

0 7 0

Debrief: Multiplication and Division Facts

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×3 Students build on their understanding of multiplying by 2 and adding 1 more group.

3 4 12

2 4 1 4 12



×4 Multiplying by 4 can be thought of as doubling a double. 4 6 24

2 2 6 24

2 6 12

2 12 24



×6 Multiplying by 6 can be thought of as doubling a multiple of 3. 6 7 42

2 3 7 42

3 7 21

2 21 42


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×9 Students build on their understanding of multiplying by 10 and subtracting 1 group.

9 8 7210 1 8 72

10 8 8080 8 72



×8 Multiplying by 8 can be thought of as doubling a 4.

×7Students use number sense and mental strategies to explore decomposing 7.

8 6 48

2 4 6 48

4 6 24

2 24 48

7 8 56

5 8 40

2 8 16


5 x 5

2 x 5

7 x 5

5

5 25

52 10

5

5

2

25

10

5

7 35

Number Sense Practice

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8 x 5

8 x 6

6 x 8

40

5

8

5

8 40

1

88

6

48

8

6 48

35

5

5

7

1


3 x 8

3 x 7

3

8

246

8

483

8

‐ 3

7

3 21


Multiplication and Division Facts

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Supporting Diverse Learners:Students with Special Needs

Expert Groups: Memory Challenges

0 1 2

Short‐termmemory

Workingmemory

Long‐term memory

Blended Groups: Memory Challenges

0 1 2

Short‐termmemory

Workingmemory

Long‐term memory

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Concepts

Mental Strategies, Procedures, and Algorithms

Applications

Supporting Diverse Learners: Students with Special Needs

Participation Norms

• Be fully present.

• Minimize distractions.

• Minimize “air time.”

• Take a chance.

• Celebrate accomplishments.

Discourse Norms

• Listen.

• Be involved.

• Contribute ideas.

• Participate by asking questions.

• Develop understanding, if not at the beginning, by the end.

Krusi, 2009

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Mathematics Norms

• Look for patterns in order to make generalizations.

• Make connections among models, representations, and algorithms.

• Communicate using academic vocabulary.

• Use mistakes as opportunities to support new learnings about mathematics.

Yackel & Cobb, 1996

• Anchor Chart• Learning Progression• Partitive Division (Division by Sharing)• Quotative Division (Division by Grouping)• Represent

• Array• Equation• Number Line• Number Sentence• Pictorial Model• Strip Diagram

• Standard Algorithm• Strategies/Mental Strategies/Solution Strategies

• Place Value• Properties of Operations• Relationship Between Multiplication and Division

Academic Vocabulary

Exit Slip

Learning ProgressionWhole Number Addition

and SubtractionDiverse Learners

What confirming/new ideas did you hear today?

How can you move new and intriguing ideas to action?

MAA G3 D2 FNL - Education Service Center Region...

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