A Story of Units

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NYS COMMON CORE MATHE MATICS CURRI CULUM A Story of Units

A Story of UnitsModule Focus


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

Session Objectives

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• Draw connections between the progression documents and the careful sequence of mathematical concepts that develop within each module.

• Articulate how the topics and lessons promote mastery of the focus standards and how the module addresses the major work of the grade.

• Prepare to implement the module and make appropriate instructional choices to meet the needs of students while maintaining the balance of rigor that is built into the curriculum.



Participant Poll

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• Classroom teacher• School leader• Principal• District leader• BOCES representative• Attended Grade 4 Presentation at the May NTI



AGENDA

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Study of the Progression DocumentExamination of Module Overview and AssessmentsExploration of Selected LessonsBringing the Module to Life

5



Progression Study

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• Read the Geometric Measurement Progression page 20.

• Highlight the information relevant to the content of this module.

• Which measurement concepts are students expected to learn in Grade 4?



Progression Study

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• Which measurement concepts are students expected to learn in Grade 4?

• What appears to be missing from this Progression that you would expect to find when teaching about measurement?



AGENDA

8




Review of Module Structure

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Module Overview

Topic

L1 L2 L3

Topic

L4 L5

Topic

L6 L7 L8



Module Overview

10

• Read the descriptive narrative. • Make note of important

information that will help educators understand the content and prepare to implement this module.



Module Overview

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• How does this Module compare to your past experiences with this content?

• How does each component of the Module Overview prepare you to implement this material in your classroom?

Turn and talk with others at your table about your observations.



Module Mathematics in Practice

12



Module Mathematics in Practice

13

500 m



Module Assessments

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• Complete the End of Module Assessment.

• Label each problem with the standard it assesses.



Module Assessments: Rubrics

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Module Assessments: Scoring Sample Student Work

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• Score the assessment assigned to your table using the Rubric.

• Discuss the scores at your table.• How can the Levels of Performance

and the Step descriptions assist a teacher in assessing student understanding?



Module Assessments: Reflection

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How could this rubric be used?



Lunch Break

18



AGENDA

19




Topic Openers

20

• Read the descriptive narrative. • Make note of important

information that will help educators implement these lessons.



Topic Openers

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• How does Topic A lay the foundation for the work in Topic B?

• How do Topic Openers A and B allow teachers to understand the vertical alignment amongst grade levels?

• How are the Topic Openers useful as a planning tool for this model?



Lesson Study

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• Fluency Practice • Application Problems• Concept Development• Student Debrief



Lesson 1-3 Unit conversions with metric measurements of length, weight, and capacity.

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• Application of Module 1: addition and subtraction; algorithms and strategies

• New Terms: kilometer, milliliter, mass, mixed units

• 2-column table used to show conversions

• Number line used as a strategy for counting up or down.

• Simplifying strategies are encouraged.• Standards alignment



Lesson 1

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2- column tables Distance

km m

1

2

3

7

10



Lesson 2

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Number Lines 10 kg – 2 kg 250g



Lesson 3

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Label the strategy modeled in each solution.Problem 1:

Algorithm with mixed units

Algorithm using smaller units

Special Strategy, one unit at a time

Special Strategy, number line

Special Strategy, counting up



Lesson 3

27









Lesson 3

28









Lesson 3

29









Lesson 3

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Lesson 4: Know and relate metric units to place value units in order to express measurements in different units.

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• Connect metric units to place value units.

• Compare and order measurements



Lesson 4

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What do you notice about the relationship between grams and kilogram?

1 kilogram = 1,000 grams

Write your answer as an equation.

1 kg = 1,000 x 1g



Lesson 5: Use addition and subtraction to solve multi-step word problems involving distance, liquid volume, and mass.

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• Apply what students learned in Lessons 1-4

• Structured to use the Problem Set within the Concept Development

• Utilize the RDW strategy



Lesson 5:

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Problem Set- Problem 1• The potatoes Beth bought weighed 3 kilograms 420 grams.

Her onions weighed 1050 g less than the potatoes. How much did the potatoes and onions weigh altogether?



Balanced, Rigorous Instruction

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Biggest Takeaways

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• How do these lessons compare to your past experiences with mathematics instruction?

• Turn and talk with a partner at your table about your reflections.



Key Points

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• Measurement provides a context to apply addition and subtraction skills and strategies.

• Measurement provides a context to strengthen place value patterns and number theory.

• Students are encouraged to track their thinking through written work (simplifying strategies vs. mental math).



Module 3

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Multi-Digit Multiplication and Division

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Module 3 Overview

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• Read the Module Overview independently.

• Mark important information that will help the implementation of this module.



Module 3 Overview

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• Re-read the Overview to find your table’s assigned Topic

• Using the Topic Analysis Handout, complete the focus question for your Topic and list the standards.• Column 1 - Focus questions• Column 2 - Answers• Column 3 - Standards addressed



Module 3 Topic A

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• Multiplicative Comparison Word Problems• What context will students use to explore multiplicative

comparisons?• What does Topic A lay the foundation for in upcoming year?

The width of David’s tent is 5 feet. The length is twice the width. David’s rectangular air

mattress measures 3 feet by 6 feet. If David puts the air mattress in the tent, how many

square feel of floor space will be available for the rest of this things?



Module 3 Topic B

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• Multiplication by 10, 100, and 1000• Why are students asked to reason between number disks and

numerical work?• Topic B lays the foundation for which upcoming Module 3

Topics?

Brianna bought 3 packs of balloons for a party. Each pack had 60

balloons. How many balloons does Brianna have?



Module 3 Topic C

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• Multiplication of Up to Four-Digit by Single-Digit Numbers• What methods will students use to record their work in Topic C?• What clarification does the footnote 1 provide for the

multiplication algorithm?



Module 3 Topic D

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• Two-Step Multiplication Word Problems• What is the purpose of Topic D?• What operations will students be able to use to solve the

problems?

In one month, Charlie read 814 pages. In the same month his mom read 4 times as

many pages as Charlie, and that was 143 pages more than Charlie’s dad read. What

was the total number of pages read by Charlie and his parents?



Module 3 Topic E

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• Division of Tens and Ones with Successive Remainders• Which foundational concepts does Topic E build upon?• What clarifications are provided by footnotes 2 and 3?

22 ÷ 5

Solve using an array and an area model.



Module 3 Topic F

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• Reasoning with Divisibility• How is Topic F connected to the work of this module?• Topic F provides the foundation for which upcoming Module 3

Topic?

Is the following statement true?

Any number that has 2 as a factor and 4 as a factor also has 8 as a

factor. Prove your answer.



Module 3 Topic G

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• Division of Thousands, Hundreds, Tens and Ones• Topic G builds upon the work of which Topics that came

earlier in the Module?• What is the purpose of using number disks in this Topic?

Use number disks to model this problem:

Zach filled 581 one-liter bottles of apple cider.

He distributed the bottles to 4 stores.

How many liter bottles will each store receive?

Will there be any bottles left over?

If so, how many?



Module 3 Topic H

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• Multiplication of Two-Digit by Two-Digit Numbers• Why is the work of Topic H placed last in this Module?• What should students understand about partial products

written vertically?

Use the area model to solve

23 × 15.



AGENDA

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Another Look

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Given your role, consider the next steps you would need to take to move forward with this work.

Jot down a mini action plan of 3-5 steps.



Action Plans

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Meet with a group of 4-6 people who have a similar role.

Create a combined action plan.



Biggest Takeaways / Next Steps

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• I now know…

• I need to figure out…

• The first thing I’ll do is…

Turn and talk with a partner at your table.



Key Points

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• These lessons are carefully designed.• Teaching these lessons requires thought and

preparation. • Preparing teachers to use these lessons also requires

thought and preparation.• Collaboration and communication are key!

CONFIDENTIAL – DO NOT CIRCULATE

DRAFT-DO NOT CIRCULATEEngageNY.org

Pulse CheckPlease go to

http://www.engageny.org/resource/network-team-institute-materials-july-8-12-2013

and fill out the online plus-delta for the

P-5 Math session.

Thank You!



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