CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP · CCSS draft Math Progressions, consider how the...

$: CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP · CCSS draft Math Progressions, consider how the conceptualizations of division grow from whole numbers to fractions laying the groundwork$
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP

Develop an understanding of the different

models of division culled out in the CCSS and

use number line, paper strips, and bar models to

unpack their conceptualizations. Using the

CCSS draft Math Progressions, consider how the

conceptualizations of division grow from whole

numbers to fractions laying the groundwork for

ratios and proportions.

Big Ideas of Module 9

CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP

M9 A1

Module 9: Divide and Conquer

Activity 1: Opening for Module 9

Activity 2: Division Problem Types

Activity 3: Division on Number Line

Activity 4: Sequence of Lesson Problems

Activity 5: Remainders

Activity 6: Unit Fractions Divided by Whole Numbers

Activity 7: Whole Numbers Divided by Unit Fractions

Activity 8: Fractions Divided by Fractions

Activity 9: Math Progressions

Activity 10: Summarizing Learning

Activity 11: Textbook Connections

Agenda for Module 9


M9 A1 Participant page 97

Division Problem Types – Equal Groups


M9 A2

A X B = ? A X ? = C C ÷ A = ?

? X B = C C ÷ B = ?

Unknown product Group size unknown (Partitive / Fair Share)

Number of groups unknown

( Quotative /Measurement)

There are A bags with B plums in each bag. How many plums are there in all?

If C plums are shared equally in A bags, then how many plums will be in each bag?

If C plums are to be packaged B to a bag, then how many bags are needed?

Participant page 98

Division Problem Types – Equal Groups


M9 A2

A X B = ?

2 X 3 = ? A X ? = C

2 X ? = 6

C ÷ A = ?

6 ÷ 2 = ?

? ?

Total = ?

? X B = C

? X 3 = 6

C ÷ B = ?

6 ÷ 3 = ?

How many groups?

Unknown Product Partitive / Fair Share Quotative Measurement

How many in each group?

Whole Number Division

M9 A3


Partitive Division

Know total and number of groups,

want to find the value of each group

There are 18 people (total) in the class.

We want to divide the class into 6 teams (number of groups)

How many children (value of groups) will be on each team ?

Team 1 Team 2 Team 3 Team 4 Team 5 Team 6

0 1 2 3 There will be 3 on each team.

Participant page 99

Whole Number Division

M9 A3 Participant page 100


Measurement Division

Know total and value of groups,

want to find the number of groups

A teacher has 32 students (total) and puts them in table

groups of five (value of group) . How many tables (number

of groups) will she need?

6 table groups of 5 with 2 students left over … need 7 tables

1 table / 1(5) 1(5) 1(5) 1(5) 1(5) 1(5) + 2

0 1 2 3 4 5

value (5 students each)


M9 A4

Mental Math

Grade 5

97 × 4

FNL_v.8_M9_Movies_MPG4%5CMovie 9.1_Daniel (1m34 sec)_97x4.mp4









M9 A4

Meaning of Division

Grade 5

60 ÷ 5

FNL_v.8_M9_Movies_MPG4%5CMovie 9.2_Group_Value(4min).mp4








Remainders

M9 A5


How the remainder relates to the problem

dictates how remainder is dealt with.

• An extra car must be included. Round up.

There are 29 students, 4 in a car. How many cars will we need? (8)

• Remainder is left over and not taken into account. Round down.

There are 29 balloons and 4 children. How many balloons will

each child get? (7 balloons with 1 left over – goes to the adult)

• Divide into smaller units - fractional part.

5 brownies shared equally by 4 girls..

How much did each girl get? (1¼ brownies)

4 boys found $29.00 (total).

How much money will each boy get? ($7.25)


M9 A4

Meaning of Division

Grade 5

32 ÷ 5

FNL_v.8_M9_Movies_MPG4%5CMovie 9.3_Remainders (13mins).mp4








Unit Fraction Divided by Whole Number

M9 A6


Paper strips

How much chocolate will each person get

if 3 people share ¼ lb. of chocolate equally?

What type of division problem?

Solve with paper folding then number line.

Pay attention to changing wholes.

Unit Fraction Divided by Whole Number

M9 A6


Measurement language:

There are (is) __ groups of __ in __.

½ ÷ 1

½ ÷ 2

½ ÷ 3

½ ÷ 4

½ ÷ 5

Participant page 105

Whole Number Divided by Unit Fraction

M9 A7


Comparison language:

I’ve run (1) mile.

It’s (two times farther) than I have to run.

How far did I need to run?

1 ÷ 2

1 ÷ 3

1 ÷ 4

1 ÷ 5

1 ÷ 6


Whole Number Divided by Unit Fraction

M9 A7


I’ve run (1) mile.

It’s (one-half the distance) that I have to run.

How far did I need to run?

1 ÷ ½

1 ÷ ⅓

1 ÷ ¼

1 ÷ ⅕

1 ÷ ⅙

3 ÷ ½

3 ÷ ⅓

3 ÷ ¼

3 ÷ ⅕

3 ÷ ⅙


M9 A4

Mental Math

Grade 5

3 ÷ 1/2

FNL_v.8_M9_Movies_MPG4%5CMovie%209.4_Mental%20Math%203%20%C3%B7%20one-half%20(5%20min%2034%20sec).mp4









M9 A4

Noticing Patterns

in Products

Zach and Brandon

Grade 5

FNL_v.8_M9_Movies_MPG4%5CMovie 9.5_Noticing Patterns in Products (5m13s).mp4









M9 A4

Representations

4 ÷ 1/3

Grade 5

FNL_v.8_M9_Movies_MPG4%5CMovie 9.6_Representations 4%C3%B7onethird (6 mins).mp4









M9 A8


2 ÷ ¼ =

1 ÷ ¼ =

¾ ÷ ¼ =

½ ÷ ¼ =

¼ ÷ ¼ = 1/8 ÷ ¼ = 1/16 ÷ ¼ =


Math Progressions

M9 A8


Participant pages 13-16, Appendix

Read the Math Progression for

3-5 Number and Operations – Fractions (Appendix)

Choose to read Grade 3, 4, and/or 5

Summarize Learning from Module 9

M9 A9



What do you think about:

How the ideas of division grow?

The use of the number line to build

conceptualizations of division?

Starting with conceptual fluency and building

toward procedural fluency?

Textbook Connections

M9 A10



How will you incorporate what you have learned

about division into your classroom instruction?

Record your ideas in the Textbook Connection

section of your binder and post notes in your

Teacher’s Edition.

3-2-1 Reflection


Final Reflections

3 big ideas you have learned this week

2 ways you will change your classroom practice

1 thing you need to learn more about

3-2-1Reflection


Final Final Reflection (I promise!)

What would you like your administrator to know

about your experiences this week and how it will

impact your classroom teaching?

What tools / resources do you need to be a more

effective teacher?

Name two challenges you will face in teaching to

the Common Core Standards.

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