a story of units

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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units

A Story of UnitsGrade 4 – Module 3 – Second Half


N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Units

Session Objectives

• Examination of the development of mathematical understanding across the second half of the module with a focus on the Concept Development within the lessons.

• Introduction to mathematical models and instructional strategies to support implementation of A Story of Units.



Agenda

Introduction to the ModuleConcept DevelopmentModule Review



Curriculum Overview of A Story of Units



Module Overview – First Half

• Scan over the Topic Titles and lessons for Topics A-D.

• Form a general understanding of where the first half of the module begins and where it ends.



Module Overview – Second Half

• Scan over the Topic Titles and lessons for Topics E-H.

• Form a general understanding of where the second half of the module begins and where it ends.



Agenda




Topic E: Division of Tens and Ones with Successive Remainders• Read Topic Opener E. • What types of models will

be used?• What Standard is

addressed?• What is the content of the

Topic?



Divide with Remainders Fluency

T: How many groups of ___ are in ___?T: Prove it by counting by ____.T: Show and say how many groups.T: How many left?

Lesson 14, Fluency

12÷3

13÷3

15÷5

17÷5

20÷4

23÷4

50÷5

55÷5



Divide a 2-digit number by a 1-digit number with a remainder using an array and a tape diagram

Lesson 14, Problem 3

13 ÷ 6



Debrief: Solve a division problem using an array and the area model.

What does the quotient represent in the area model? When does the area model present a challenge in

representing division problems? How is the whole represented in the area model? The quotient represents a side length. The remainder

consists of square units. Why?

Lesson 15, Application Problem, Problem 2 and Debrief



Division of tens and ones

6 ÷ 3

Lesson 16, Problems 1 and 2

36 ÷ 3



Divide 2-digit numbers by 1-digit numbers, regrouping in the tens

3 ones ÷ 2


3 tens ÷ 2



Find whole number quotients and remainders

86 ÷ 5




Solve division problems using area models48 ÷ 4

Decompose whole to part.

Lesson 20



Solve division problems using area models96÷ 4

Compose part to whole.

Lesson 20



Division area models with remainders


Solve for 37÷2



Topic F: Reasoning with Divisibility

• Read Topic Opener F. • Why is this Topic placed

between multiplication and division in the module?



Use division and the associative property to test for factors• Can 54 be divided evenly by 3? 2?• Do we need to divide to determine if 5 is a factor of

54?• Is 6 a factor of 54?• If 54 = 6×9, then is 54 = (2×3)×9 true?• Use the associative property to show both 2 and 3

are factors of 42.Lesson 23



Multiples • Use division and the associative property to determine whether a whole

number is a multiple of another number (Lesson 24).• Explore properties of prime and composite numbers to 100 by using

multiples (Lesson 25).

Lesson 24 & 25



Topic G: Division of Thousands, Hundreds, Tens and Ones• Read Topic Opener G. • Why is division of larger

dividends separated in this module?



Lesson 26: Divide multiples of 10, 100 and 1,000 by single-digit numbers.• Take 5 minutes to read through the entire lesson.• Highlight 2 “ah-has” to share at your table.• Complete the Problem Set.• Consider today’s lesson only has a 45

minute period. What will you do to keep the balance of rigor and honor the objective?

• Share solutions and strategies.

Lesson 26



Decompose a remainder in the hundreds place to solve a division problem.

783 ÷ 3




Represent numerically four-digit dividend division with divisors of 2, 3, 4, and 5, decomposing a remainder up to three times.

4,325 ÷ 3




Solve division problems with a zero in the dividend or quotient.

804 ÷ 44,218 ÷ 3

Lesson 30, Problem 1 and 2



Interpret division word problems as either number of groups unknown or group size unknown.

Two hundred thirty-two people are driving to a conference. If each car holds 4 people, including the

driver, how many cars will be needed?




Division word problems with larger divisors of 6, 7, 8, and 9.

Mr. Hughes has 155 meters of volleyball netting. How many nets can he make if each court requires 9

meters of netting?




Connect the area model to division.

Use decomposition for 1,344 ÷ 4




Topic H: Multiplication of Two-Digit by Two-Digit Numbers• Read Topic Opener H. • How have the students

prepared for this type of multiplication?

• How are the students prepared to use the area model?



Fluency: Draw a Unit FractionT: Draw a quadrilateral with 4 equal

sides and 4 right angles.T: Name it.S: Square.T: Partition it into 3 equal parts. Shade

in 1 part.T: Write the name of the shaded

portion of the square.Students write ⅓.

Lesson 34, Fluency

Repeat with:

• Rhombus into fourths

• Rectangle into fifths

• Rectangle into eighths



Application Problem

Lesson 34, Application Problem

Mr. Goggins planted 10 rows of beans, 10 rows of squash,

10 rows of tomatoes, and 10 rows of cucumbers in his

garden. He put 22 plants in each row. Draw an area

model, label each part and then write an expression that

represents the total number of plants in his garden.



Find the product of 60 and 34 using an area model.


60

430

3 4

x 6 060×30

6 tens×3 tens

18 hundreds

1,800

60×4

6 tens×4

24 tens

240

2 4 0

+1, 8 0 0

2, 0 4 0



Find the product of 23 and 31 using an area model.


3

130

3 1

x 2 33×30

9 tens

3×1

3 ones 3

+ 6 0 0

7 1 3

20×30

6 hundreds

20×1

2 tens20

9 0

2 0

23×31=(3×1) + (3×30) + (20×1) + (20×30)



4 partial product 2 partial products

Draw an area model and solve for 26×35.

Lesson 37 Problem 1



Solve 2-digit by 2-digit multiplication using the algorithm.




Regrouping.

Work with a partner to solve:• 29×62• 46×63

Lesson 32, Problems 2 and 3



Agenda




Complete the End-of-Module Assessment.

• Now with all of the mathematical knowledge and understanding of the models, complete the assessment.

• You may work alone or with your table to discuss challenges or successes.

• How did Module 1 and 2 prepare you for Module 3?



Biggest Takeaway

Turn and Talk:• I am ready to…• I still want to know more about…• I am better prepared to…• My students will…



Key Points

• Number disks and area models are used heavily throughout the module to support the

algorithms.

• The multiplication and division algorithms are not expected fluencies in Grade 4.

• Unit language and place value understanding drives the experience of the algorithms.

• Keep a balance of rigor by addressing each component of a lesson.

• Honor and respect the objectives.

• Find a balance between success and mastery.

a story of units

Documents

half of lessons

half scan

story of unitsgrade

minutes materials

mathematical models

minute materials

brief overview of lesson

instructional strategies