ccssm task force: camte, cde, cisc, cmc, cmp · ccss draft math progressions, consider how the...
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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
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
M9 A1 Participant page 97
Division Problem Types – Equal Groups
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
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
CCSS-M Task Force: CaMTE, CDE, CISC, CMC, CMP
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
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
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
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
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)
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
M9 A4
Mental Math
Grade 5
97 × 4
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
M9 A4
Meaning of Division
Grade 5
60 ÷ 5
Remainders
M9 A5
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
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)
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
M9 A4
Meaning of Division
Grade 5
32 ÷ 5
Unit Fraction Divided by Whole Number
M9 A6
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
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
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
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
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
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
Participant page 106
Whole Number Divided by Unit Fraction
M9 A7
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
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
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
M9 A4
Mental Math
Grade 5
3 ÷ 1/2
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
M9 A4
Noticing Patterns
in Products
Zach and Brandon
Grade 5
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
M9 A4
Representations
4 ÷ 1/3
Grade 5
M9 A8
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
2 ÷ ¼ =
1 ÷ ¼ =
¾ ÷ ¼ =
½ ÷ ¼ =
¼ ÷ ¼ = 1/8 ÷ ¼ = 1/16 ÷ ¼ =
Participant page 108
Math Progressions
M9 A8
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
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
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
Participant page 109
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
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
Participant page 110
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
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
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
CCSSM Task Force: CaMTE, CDE, CISC, CMC, CMP
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.