vacaville usd november 4, 2014. agenda problem solving, patterns, expressions and equations math...

FIFTH GRADESession 2

Vacaville USD

November 4, 2014

AGENDA• Problem Solving, Patterns, Expressions and

Equations• Math Practice Standards and High Leverage

Instructional Practices• Number Talks

– Computation Strategies

• Fractions

Expectations• We are each responsible for our own

learning and for the learning of the group.• We respect each others learning styles

and work together to make this time successful for everyone.

• We value the opinions and

knowledge of all participants.

Cubes in a Line

How many faces (face units) are there when: 6 cubes are put together?

10 cubes are put together?


n cubes are put together?

Questions?

What do I mean by a “face unit”?

Do I count the faces I can’t see?

Cubes in a Line

How many faces (face units) are there when: 6 cubes are put together?



n cubes are put together?

Cubes in a Line

Cubes in a Line

We found several different number sentences that represent this problem.

• What has to be true about all of these number sentences?

5.OA.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Math Practice Standards

• Remember the 8 Standards for Mathematical Practice

• Which of those standards would be addressed by using a problem such as this?

CCSS Mathematical PracticesO

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nREASONING AND EXPLAINING2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others

MODELING AND USING TOOLS4. Model with mathematics5. Use appropriate tools strategically

SEEING STRUCTURE AND GENERALIZING7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

High Leverage Instructional Practices

High-Leverage Mathematics Instructional Practices

An instructional emphasis that approaches mathematics learning as problem solving.

1. Make sense of problems and persevere in solving them.

An instructional emphasis on cognitively demanding conceptual tasks that encourages all students to remain engaged in the task without watering down the expectation level (maintaining cognitive demand)

1. Make sense of problems and persevere

in solving them.

Instruction that places the highest value on student understanding


2. Reason abstractly and quantitatively

Instruction that emphasizes the discussion of alternative strategies

3. Construct viable arguments and critique the reasoning of others

Instruction that includes extensive mathematics discussion (math talk) generated through effective teacher questioning 2. Reason abstractly and quantitatively


6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Teacher and student explanations to support strategies and conjectures

2. Reason abstractly and quantitatively


The use of multiple representations


4. Model with mathematics

5. Use appropriate tools strategically

Number Talks

What is a Number Talk?• Also called Math Talks• A strategy for helping students develop a

deeper understanding of mathematics– Learn to reason quantitatively– Develop number sense– Check for reasonableness

– Number Talks by Sherry Parrish

What is Math Talk?

• A pivotal vehicle for developing efficient, flexible, and accurate computation strategies that build upon key foundational ideas of mathematics such as – Composition and decomposition of numbers– Our system of tens– The application of properties

Key Components

• Classroom environment/community• Classroom discussions• Teacher’s role• Mental math• Purposeful computation problems

Classroom Discussions

• What are the benefits of sharing and discussing computation strategies?

• Students have the opportunity to:– Clarify their own thinking– Consider and test other strategies to see if

they are mathematically logical– Investigate and apply mathematical

relationships– Build a repertoire of efficient strategies– Make decisions about choosing efficient

strategies for specific problems

5 Goals for Math Classrooms

• Number sense• Place Value• Fluency• Properties• Connecting mathematical ideas

Clip 5.6 – 5th Grade

Subtraction: 1000 – 674 • Before we watch the clip, talk at your

tables–What possible student strategies might

you see?–How might you record them?

• What evidence is there that the students understand place value?

• How do the students’ strategies exhibit number sense?

• How does fluency with smaller numbers connect to the students’ strategies?

• How are accuracy, flexibility, and efficiency interwoven in the students’ strategies?


Multiplication: 12 x 15• Before we watch the clip, talk at your



• What evidence is there that students understand place value?

• How do student strategies exhibit number sense?

• How do the teacher and students connect math ideas?

• What questions does the teacher use to facilitate student thinking about big ideas?


Division String: 496 ÷ 8 • Before we watch the clip, talk at your



• What evidence is there that students understand place value?

• How do students build upon their understanding of multiplication to divide?

• How does the teacher connect math ideas throughout the number talk?

Solving Word Problems

3 Benefits of Real Life Contents

• Engages students in mathematics that is relevant to them

• Attaches meaning to numbers

• Helps students access the mathematics.

A crane operator unloaded the following cargo: • 5 pallets of lumber. Each pallet weighs 7.3 tons.

• 9 pallets of concrete. Each pallet weighs 4.8 tons.

a) How many pounds of cargo were

unloaded?

b) Which load of cargo was heavier, the

lumber or the concrete? How many pounds

heavier?

Ava is saving for a new computer that costs

$1,218. She has already saved half of the

money. Ava earns $14.00 per hour. How

many hours must Ava work in order to save

the rest of the money?

Mrs. Onusko made 60 cookies for a bake

sale. She sold 2/3 of them and gave 3/4 of the

remaining cookies to the students working at

the sale. How many cookies did she have

left?

Equivalent Fractions

5th Grade

Use equivalent fractions as a strategy to add and subtract fractions.

CaCCSS

• Fractions are equivalent (equal) if they are the same size or they name the same point on the number line.

.......30

18

25

15

20

12

15

9

10

6

5

3

.......12

6

10

5

8

4

6

3

4

2

2

1

.......18

6

15

5

12

4

9

3

6

2

3

1

Fraction Families

Equivalent Fractions

• Fraction Family Activity

• Equivalent Fraction Activity

5th Grade CCSS-M

5.F.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Adding Fractions

• Add

0 1

810

87

83

821 2

411

1

43

85

2

43

85

43

85

86

85

43

85

86

85

831

811

43

65

3

43

65

43

65

129

1210

43

65

129

1210

1219

1271

Subtracting Fractions


Possible sequence of instruction• Subtracting 2 fractions less than 1

8

1

4

3


• Subtracting when 1 fraction is between 1 and 2 and 1 fraction is less than 1

85

431

85

411


• Subtracting mixed numbers

322

434

652

315


• Strategies: Change to improper fractions

322

434

652

315

1232

1257

38

419

1225

121

2

617

316

617

632

615

632

212


• Strategies: Borrow

322

434

652

315

128

2129

4 121

2

652

625

652

6214

632

212


• Strategies: Shift (Compensate)

652

315

361

635

61

632

212

Multiplying Fractions

5.F.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

5.F.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side

vacaville usd november 4, 2014. agenda problem solving, patterns, expressions and equations math...

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