BOXES 1 & 2 BRIDGES - North Slope Borough School District€¦ · BOXES 1 & 2 BRIDGES Teachers...

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BOXES 1 & 2 BRIDGES

Teachers Guides

Your Teachers Guides are divided into eight units, each of which includes a unit introduction, 20 lessons, and the ancillary pages you’ll need to teach them. Keep the Unit 1 binder handy, and store the other binders in your bookcase or cabinet for now. The Assessment Guide is also included in this box.

your kit

QUICK START GUIDE

Before unpacking and organizing, you’ll want to have the following materials on hand:

❚ One plastic box with a lid or a file drawer for your Bridges mats, game boards, and card decks

❚ One plastic box with a lid or a file drawer for your Number Corner materials (calendar markers, card decks)

❚ Six containers, with or without lids, large enough to accommo-date 8 ½” × 11” game boards or stackable file trays (for Bridges Work Place materials)

❚ One basket or shoebox for your bags of dice, game markers, and spinner overlays

❚ Eight tubs, one each for larger manipulatives. See list on page 6.

Give yourself plenty of space to unpack your boxes—you have three boxes of materials! Box 1 is filled with your Bridges Teachers Guides and components. Box 2 includes Bridges manipulatives, and box 3 has your Number Corner materials.

The Teachers Guides and ancillary pages are also available for viewing and download on the Bridges Educator site at bridges.mathlearningcenter.org.

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Bridges in Mathematics Grade 4 Quick Start Guide

Bridges Components

In this box, you’ll find an assortment of card decks that students will use to play partner games. Keep each of these card decks in its own labeled bag. You’ll need access to them throughout the year.

Keep the cards in their labeled bags in a box or file drawer. Store them where you can retrieve them easily. They do not need to be accessible to students.

1 Card decks



Bridges Manipulatives

Your kit contains a variety of manipulatives. We’ll talk about ways to keep the manipulatives organized in the next section.

1 Pan balance scale

2 Pattern blocks

3 Colored tiles

4 Platform scale

5 Geoboards and geobands

6 Measuring cups – 1 cup & 1 quart

7 Plastic cubes

8 Oral syringe

9 Adding machine tape

10 Measuring tapes

11 Rubber bands

12 Money value pieces

13 Base ten plastic grid

14 Base ten linear pieces

15 Plastic coins

16 Literature

17 Supermagnets with hooks

18 Game markersNumber Corner includes a Quick Start Guide similar to this one. It is intended for Number Corner teachers in classrooms where Bridges is not the primary curriculum. Since Number Corner and Bridges share some materials, please follow the steps here.



BOX 3 NUMBER CORNER

Teachers Guides

Keep the Volume 1 binder handy, and store the other binders in your bookcase or cabinet for now. Add the Number Corner portion of the Assessment Guide to the Assessment Guide binder found in Bridges box 1.

The Teachers Guides and ancillary pages are also available for viewing and download on the Bridges Educator site.

Number Corner Components

You’ll need access to these materials throughout the year. Store them where you can retrieve them easily. Keep the calendar markers, mats, and cards, each in their own labeled bag, in a box or file drawer.

1 Word Resource Cards

2 Calendar markers

3 Card decks

4 Work mats

5 Display cards

If you are upgrading from Number Corner to Bridges, you will already have the items shown on these pages.



Number Corner Manipulatives

1 Calendar Grid pocket chart

2 Colored tiles

3 Pattern blocks

4 180° protractors

5 Measuring cups – 1 cup & 1 quart

6 Plastic coins

7 360° protractor

8 Spinner overlays

9 Dice

Store the manipulatives listed below with the markers, mats and cards for use during Number Corner:

❚ Colored tiles

❚ Spinner overlays

❚ Dice

❚ 180° protractors

❚ Plastic coins


your materials & classroom

Store the manipulatives listed below

in a single basket or shoebox:

❚ Plastic coins

❚ Measuring tapes

❚ Game markers

❚ Spinner overlays

❚ Dice

Store each larger manipulative

listed below in its own tub:

❚ Calculators*

❚ Modeling clay (keep in zip-top bag)*

❚ Pattern blocks

❚ Colored tiles

❚ Geoboards and geobands

❚ Plastic cubes

❚ Money value pieces

❚ Base ten pieces

Store these items where students

have easy access to them:

❚ Student whiteboards, pens, and erasers*

❚ Rulers*

❚ Protractors

Store these materials with your general

classroom supplies and equipment:

❚ Pan balance scale

❚ Platform scale

❚ Measuring cups

❚ Oral Syringe

❚ Adding machine tape

❚ Rubber bands

❚ Supermagnets with hooks

Store your three literature books with your

Teachers Guides so they don’t get mixed

in with your classroom book collection.

Post these wall charts in your

Number Corner display area:

❚ Calendar Grid pocket chart

* Please see the Bridges Educator site for a comprehensive list of required materials that are not included in your kit. Those mentioned here are marked with an asterisk.

There are many good ways to organize your materials. Begin with the recommendations here, and refine your system throughout the school year to better meet the unique circumstances of your classroom. You’ll find more detailed information—including photos from real Bridges classrooms—on the Bridges Educator site. If you have great organization tips you’d like to share, we’d love to pass them on to other Bridges users! You can email your ideas to [email protected].


The following steps will prepare you to teach Bridges and Number Corner on the first day of school.

1 BRIDGES Read “Introducing Bridges in Mathematics Grade 4,” found in the front of the Unit 1 Teachers Guide.

NUMBER CORNER Read “Introducing Grade 4 Number Corner,” found in the front of the Volume 1 Number Corner Teachers Guide.

Introducing Bridges in Mathematics

Grade 4Welcome to Bridges in Mathematics

Bridges in Mathematics, second edition, is a comprehensive K–5 mathematics curriculum that equips

teachers to fully implement the Common Core State Standards for Mathematics in a manner that is

rigorous, coherent, engaging, and accessible to all learners. The curriculum focuses on developing

students’ deep understandings of mathematical concepts, proficiency with key skills, and ability to

solve complex and novel problems. Bridges blends direct instruction, structured investigation, and

open exploration. The program taps into the intelligence strengths of all students by presenting mate-

rial that is as linguistically, visually, and kinesthetically rich as it is mathematically powerful.

Bridges ActivitiesA Bridges classroom features a combination of whole-group, small-group, and independent

activities that are problem centered. Fourth graders engage in five major kinds of activities:

Problems & Investigations, Work Places, Math Forums, Problem Strings, and Assessments.

Problems & Investigations

Problems & Investigations are whole-group activities that also incorporate periods of indepen-

dent and partner work. They often begin with a problem posed by the teacher, followed by time

for students to think independently, work for a period of time, and talk in pairs before reconven-

ing to share and compare strategies and solutions as a whole class.

Work PlacesWork Places are engaging, developmentally appropriate math stations that offer ongoing prac-

tice with key skills. Many Work Places are partner games, but some are independent activities

or more open-ended partner work. Work Places are always introduced and practiced as a whole

class, after which students have opportunities to repeat the Work Place over a period of weeks.

Work Places include suggestions that enable the teacher to differentiate each activity to address

students’ needs for additional support or challenge.

Math Forums

Students discuss their solutions to and strategies for solving problems in nearly every Bridges

lesson. Math forums, which occur a few times in most units, are a more formal and structured

time for students to share and discuss their work. Prior to conducting a forum, the teacher reviews

students’ written work on a particular problem and selects specific students to share during the

forum. She carefully plans the order in which students will share to help the rest of the class

develop a deeper understanding of the problem and the variety of strategies that can be applied

to solve it. Students who are not sharing their own work are expected to listen carefully, compare

their classmates’ work to their own, and ask questions to better understand each student’s ideas.

Topics Covered in

This Introduction

Bridges Activities

Problems & Investigations

Work Places

Math Forums

Problem Strings

Assessments

Number Corner

Mathematical Emphasis

Content

Practices

ModelsNumber Line

ArraysRatio Tables

Base Ten Area Pieces

Models for Fractions

Models for Geometry

Teacher Materials

Teachers GuideUnit Introductions

Module Introductions

Sessions (Daily Lesson Plans)

Ancillary Pages

Assessment Guide

Support & Intervention

Answer Keys

Student Materials

Bridges Student Book

Home Connections

Spanish-Language

Materials

Additional Materials

Technology

Vocabulary

© The Math Learning Center | mathlearningcenter.org

Bridges in Mathematics Grade 4 Teachers Guide

Introducing Grade 4 Number CornerWelcome to Number Corner!Number Corner, second edition, is a program of skills practice as well as ongoing encounters with broader mathematical concepts. Extensively revised to address the Common Core State Standards for Mathematics, Number Corner features daily 20-minute workouts that intro-duce, reinforce, and extend skills and concepts related to the critical areas of study at each grade level. Number Corner is an essential component of the Bridges in Mathematics curricu-lum, but it can be used to complement any K–5 curriculum, providing students and teachers with opportunities to apply Common Core skills in new settings and real-world contexts.The term Number Corner refers not only to the program as a whole but also to the physical bulletin board display. The display is the center of learning activities and the heart of a math-rich classroom environment. We strongly encourage leaving the display up in the room (rather than tucking it in an interactive whiteboard), so students can make use of the models throughout the day. The teacher and students add new pieces to the display each day, which offer starting points for discussions, problem solving, and short written exercises. Over the course of any given month, fourth graders predict and post new markers in the Calendar Grid pocket chart; collect and record a unit of measure or a small set of data each day and then make observations and draw conclusions about the collection; play games and participate in activities designed to improve computational fluency, including number line work; engage in problem strings—a focused whole-group activity designed to increase students’ understanding of mathematical operations and relationships between numbers; and solve prob-lems involving multiple steps, estimating, reasoning, fractions, and all four operations including division with remainders. Math becomes less abstract as students work with concrete and visual models related to multi-digit numbers; fractions; developing and using efficient strategies to add, subtract, multiply and divide; measurement quantities and measurement tools; and investigat-ing and analyzing two-dimensional shapes and their attributes.Many teachers use the quick-paced Number Corner workouts as a warm-up for their daily math time. Others incorporate a workout into their morning routine or as a whole-group time to gather, review, and reflect at the end of the day. The lively sessions feature creative, original activities that build from five predictable routines. Games and challenges are designed to engage young learners as they develop numerical literacy and proficiency. The rigor, focus and coher-ence in each workout promote conceptual understanding and procedural fluency. We hope you’ll enjoy guiding your students through Number Corner. We believe you’ll find that with daily, long-term opportunities to work and play with numbers and concepts, their growth in mathematical thinking, confidence, and enthusiasm will soar.

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Number Corner Grade 4 Teachers Guide© The Math Learning Center | mathlearningcenter.org

2 BRIDGES Read the Bridges Unit 1 Introduction, and review the organi-zational charts.

AssessmentsThere are three written assessments in Unit 1—a unit pre-assessment near the beginning of Module 1, a checkpoint near the beginning of Module 3, and a unit post-assessment at the end of Module 3. In addition to these, six Work Places introduced over the course of the unit offer teachers frequent opportunities to observe students’ skills in authentic settings. The following chart shows where and when assessment opportunities appear throughout the unit.Skills/Concepts Assessed Observational Assessments Written Assessments3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers

M3, S2 Multiplication & Division CheckpointSupports 3.OA Use and explain additive and multiplicative strategies to demonstrate an understanding of multiplication

M2, S5 Work Place 1C The Multiple Wheel

3.OA.5 Multiply using the commuta-tive property M2, S3 Work Place 1A Cover Up 3.OA.5 Multiply using the distributive property M2, S4 Work Place 1B Arrays to One Hundred 3.OA.6 Solve division problems by finding an unknown factor (e.g., Solve 32 ÷ 8 by finding the number that makes 32 when multiplied by 8)

M1, S3 Unit 1 Pre-AssessmentM3, S5 Unit 1 Post-Assessment3.OA.7 Fluently multiply with products to 100 using strategies

M2, S3 Work Place 1A Cover Up M2, S4 Work Place 1B Arrays to One HundredM2, S5 Work Place 1C The Multiple WheelM2, S6 Work Place 1D Spinning Around MultiplicationM3, S4 Work Place 1F Dragon’s GoldM3, S1 Work Place 1E Products Four in a Row

M1, S3 Unit 1 Pre-AssessmentM3, S2 Multiplication & Division CheckpointM3, S5 Unit 1 Post-Assessment

3.OA.9 Explain patterns among basic multiplication facts by referring to properties of the operation

M2, S3 Work Place 1A Cover Up M3, S2 Multiplication & Division Checkpoint3.NBT.3 Multiply whole numbers from 1–9 by multiples of 10 from 10–90 using strategies based on place value and properties of operations

M1, S3 Unit 1 Pre-AssessmentM3, S5 Unit 1 Post-Assessment3.MD.7b Find the area of a rectangle by multiplying its side lengths

M2, S3 Work Place 1A Cover UpM2, S4 Work Place 1B Arrays to One Hundred

M3, S2 Multiplication & Division Checkpoint3.MD.7c Use the area model for mul-tiplication to illustrate the distributive property (e.g., the area of a rectangle with side lengths a and b + c is equal to a × (b + c) or a × b + a × c)

M2, S3 Work Place 1A Cover Up

4.OA.1 Make a comparison statement to match a multiplication equation; write a multiplication equation to represent a verbal statement of a multiplicative comparison

M1, S3 Unit 1 Pre-AssessmentM3, S2 Multiplication & Division Checkpoint M3, S5 Unit 1 Post-Assessment4.OA.2 Solve story problems involving a multiplicative comparison using multiplication or division

M1, S3 Unit 1 Pre-AssessmentM3, S5 Unit 1 Post-Assessment4.OA.3 Solve multi-step story prob-lems involving only whole numbers, using addition, , multiplication, and division

M1, S3 Unit 1 Pre-AssessmentM3, S5 Unit 1 Post-Assessment

ix © The Math Learning Center | mathlearningcenter.org


Unit 1 Introduction

Skills Across the Grade LevelsThe table below shows the major skills and concepts addressed in Unit 1. It is meant to provide a

quick snapshot of the expectations for students’ learning during this unit, as well as information

about how these skills are addressed in Bridges Grade 3, elsewhere in Grade 4 including Number

Corner (NC), and also in Grade 5.

Major Skills/Concepts Addressed Gr. 3 Unit 1 Gr. 4 Elsewhere Gr. 5

3.OA.1 Interpret products of whole numbers M R/E N/A N/A

3.OA.3 Solve multiplication story problems with products to 100 involving situations of equal groups

M R/E N/A N/A

3.OA.4 Solve for the unknown in a multiplication equation involving 3 whole numbers

M R/E N/A N/A

3.OA.5 Multiply using the commutative and distribu-tive properties

M R/E N/A N/A

3.OA.7 Fluently multiply with products to 100 using strategies

M R/E N/A N/A

3.MD.7a Demonstrate that the area of a rectangle with whole-number side lengths can be found by multiply-ing the side lengths

M R/E N/A N/A

3.MD.7b Represent the product of two numbers as the area of a rectangle with side lengths equal to those two numbers

M R/E N/A N/A

3.MD.7c Use the area model for multiplication to illustrate the distributive property

M R/E N/A N/A

3.MD.7d Find the area of a figure that can be decom-posed into non-overlapping rectangles

M R/E N/A N/A

4.OA.1 Write a multiplication equation to represent a verbal statement of a multiplicative comparison

I M Unit 2NC Sep., Nov., Jan., Apr.

R/E

4.OA.2 Solve story problems involving a multiplicative comparison using multiplication or division

I M Units 2, 7NC Sep., Apr.

R/E

4.OA.4 Find all factor pairs for a whole number between 1 and 100

I M Unit 2NC Sep.–Dec.

R/E

4.OA.4 Demonstrate an understanding that a whole number is a multiple of each of its factors

I M Unit 2NC Sep.–Dec.

R/E

4.OA.4 Determine whether a whole number between 1 and 100 is prime or composite

N/A M Unit 2 R/E

4.MD.1 Identify the relative sizes of centimeters, meters, and kilometers; grams and kilograms; ounces and pounds; milliliters and liters; seconds minutes and hours

D D Units 4, 7, 8NC Sep., Nov., Apr., May

R/E

4.MD.1 Express a measurement in a larger unit in terms of a smaller unit within the same system of measurement

I D Units 4, 7, 8NC Sep., Nov., Apr., May

R/E

I – Skill or concept is introduced or reintroduced.D – Skill or concept is developed.M – Skill or concept is expected to be mastered.R/E – Skill or concept is reviewed, practiced, or extended to higher levels.

S – Support materials are provided for students who require intervention or additional practice.

N/A – Skill or concept is not addressed.

viii © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 4 Teachers Guide

Unit 1 Introduction

Unit 1

Multiplicative Thinking

Overview

Unit 1 begins the year with a study of multiplication and division, focusing in particular on models, strategies and multiplica-

tive comparisons. In Module 1, students use open number lines, arrays, and ratio tables. They also solve multiplication and

division story problems and participate in their first math forum. In Module 2, they use the area model to investigate factors

and multiples and prime and composite numbers. They also review strategies for finding single-digit multiplication facts.

Module 3 has them working with factors and products as well as multiplicative comparisons and equations. Module 4 extends

the idea of multiplicative comparison into the arena of measurement, as students develop deeper understandings of the relative

sizes of metric units for length, mass, and liquid volume.

Planner

ModuleDay Session & Work Places Introduced P&I PS MF WP A HC DP

Module 1 Models for Multiplication & Division

The teacher and class work together to build

community and set the tone for the year ahead.

In a multiday investigation, students use open

number lines, ratio tables, and arrays to deter-

mine the number of school supplies collected in

a fictional classroom.

1 Session 1 Setting Our Course for the Year

2 Session 2 Number Lines

3 Session 3 Unit 1 Pre-Assessment

4 Session 4 Methods & Models for Multiplication

5 Session 5 Models for Division

6 Session 6 Math Forum on Multiplication & Division

Module 2 Primes & Composites

Students use the area model to investigate fac-

tors of numbers and determine whether numbers

are prime or composite. They consider multiplica-

tion fact strategies introduced in third grade and

use open number lines, ratio tables, and the area

model to review them. The Work Place activities

introduced in this module also provide practice

with multiplication facts and strategies.

7 Session 1 Finding Factors of Numbers from 1 to 36

8 Session 2 Exploring Prime & Composite Numbers

9 Session 3 Reviewing Multiplication Strategies

Work Place 1A Cover Up

10 Session 4 Introducing Work Place 1B

Arrays to One Hundred

Work Place 1B Arrays to One Hundred

11 Session 5 Seeing Strategies, Part 1

Work Place 1C The Multiple Wheel

12 Session 6 Seeing Strategies, Part 2

Work Place 1D Spinning Around Multiplication

Module 3 Multiplicative Comparisons & Equations

This module focuses on factors, products, multi-

plication comparisons, and equations. Students

are introduced to two new Work Places. In

Products Four in a Row, they develop strategies

to choose factors that will give them the most

advantageous products. Then in Dragon’s Gold,

they learn to verbalize and record statements of

multiplicative comparison.

13 Session 1 Introducing Work Place 1E Products

Four in a Row

Work Place 1E Products Four in a Row

14 Session 2 Multiplication & Division Checkpoint

15 Session 3 Multiplicative Comparisons with a Giant

16 Session 4 Introducing Work Place 1F Dragon’s Gold

Work Place 1F Dragon’s Gold

17 Session 5 Unit 1 Post-Assessment

Module 4 Measurement Experiences

This module provides hands-on experience

with measurement as students explore linear

measurement, mass, weight, and liquid volume,

and review the definitions and units of measure

for each category. They use various measure-

ment tools and match the units of measure with

each tool. The investigations enable them to

better identify the relative sizes of various units

of measure.

18 Session 1 Linear Measurement

19 Session 2 Benchmarks for Standard Units:

Mass/Weight

20 Session 3 Volume & Capacity

P&I – Problems & Investigations, PS – Problem String, MF – Math Forum, WP – Work Place, A – Assessment, HC – Home Connection, DP – Daily Practice

Unit 1

i © The Math Learning Center | mathlearningcenter.org


to teach

Visit the Resources section of the Bridges Educator site to find online resources mapped to the units and modules of Bridges in Mathematics and months of Number Corner. It is designed to help teachers and students make the most of the many excellent free resources provided by educators, authors, universities, and organizations.



3 BRIDGES Review the Unit 1, Module 1 Introduction. (Each unit contains four modules.) The Planner shows what kinds of activities you’ll be doing in the first module. Use the Materials Chart as a checklist to prepare your materials before your first Number Corner session..

NUMBER CORNER Review the Introduction section of the September Number Corner Teachers Guide. The Sample Display shows how to set up your Number Corner display, and the Daily Planner gives you the month’s schedule at a glance. The Materials Chart shows everything you’ll need to prepare ahead of time. Use it as a checklist to get all the materials ready before the first day of school.

Number Corner SeptemberOverviewDuring this first month of school, students become familiar with the rhythms and routines of each Number Corner workout,

while reviewing, revisiting, and extending skills and concepts addressed in third grade and exploring those new to fourth

grade. While each workout stands alone, there are also connections among them that invite students to consider the material in

different contexts and that help solidify and deepen their understandings. The primary mathematical emphasis this month is

multiplication: students review multiplication facts, work with multiples of 10, think about factors and multiples, and work on

strategies for multiplication with larger numbers.ActivitiesWorkouts

Day ActivitiesD G SB

Calendar Grid Ancient Egyptian NumeralsThe calendar markers this month feature unfamiliar symbols, which students learn mid-month are ancient Egyptian numerals. Students search for patterns among the symbols to determine how the ancient Egyptian system of numeration works and how the markers are changing from day to day. This pattern provides a place value review that will help as they work with larger numbers and decimal numbers later in the year.

1 1 Introducing the Calendar Grid 4 2 Updating & Discussing the Calendar Grid 7 3 Revealing the Tenth Marker & Introducing the Observations Chart

10 4 Comparing Numeration Systems 12, 16 5 Completing a Student Book Page 20 6 Concluding the September Calendar Grid

Calendar Collector Six Inches a DayThe class collects a 6-inch strip of paper each day and glues it onto a yard-long strip marked at 1-foot incre-ments. Students keep a chart to show the growing collection of inches, feet, and yards. They make conver-sions from one unit to another that involve both whole numbers and fractions.

3 1 Introducing the October Calendar Collector 6 2 Introducing the Calendar Collector Record Sheet 14 3 Sharing Observations & Computing Total Inches, Feet & Yards 18 4 Completing the Inches, Feet & Yards Page

Computational Fluency The Number Line & Splat!Students identify and consider multiples of 2, 3, and 6 on a number line and and play a game called Splat! In the number line activities, students review factors and multiples, do count-arounds (i.e., count by a particular number), and record the multiples of 2, 3, and 6 on a number line. The game Splat! provides practice multiply-ing by 10 and by multiples of 10.

1, 7, 12 1 Marking Multiples of 2, 3 & 6 on the Number Line 4 2 Introducing Splat! 10, 16 3 Playing Splat! with a Partner 20 4 Looking Back at the Month

Problem Strings Multiplication ModelsStudents explore multiplication models and strategies as they review and solidify their understanding of how problem strings work.

11 1 Problem String 1 13 2 Problem String 2 19 3 Problem String 3

Solving Problems One-Step Multiplication ProblemsStudents solve problems and then discuss their solutions in pairs and as a class. For each problem, they paraphrase the question they are being asked to answer, identify the pertinent information in the problem, show their work, and state the answer in the form of a complete sentence. The mathematical content focuses mainly on one-step multiplication problems, including multiplication in the context of calculating area.

2 1 Introducing Solving Problems & Solving Megan’s Marbles Problem 5 2 Discussing Megan’s Marbles & Solving a Related Problem

15 3 Solving Xavier’s Garden Problem 17 4 Discussing Xavier’s Garden Problem

Assessment Baseline AssessmentStudents spend two periods completing a written assess-ment that provide teachers with information about some of the most critical skills students should have mastered in third grade.

8 Baseline Assessment, Part 1 Completing Pages 1–39 Baseline Assessment, Part 2 Completing Pages 4 & 5D – Discussion, G – Game, SB – Number Corner Student Book

September

Introduction

1



Bridges in Mathematics Grade 4 Teachers Guide1

Unit 1

Module 1

Models for Multiplication & Division

Overview

In Module 1, the teacher works to set the tone for the year and to build community within the class. Students brainstorm

what the class should look like and sound like in Session 1, extending and refining their list as the module continues. Also in

Session 1, the teacher launches a multi-day investigation in which students determine the number of school supplies collected

in a fictional fourth grade classroom. This context allows students to review and extend their understanding of multiplication

strategies, concepts, and models including open number lines, ratio tables, and arrays. Students take the Unit 1 Pre-Assessment

in Session 3 and reflect on their work in Session 4. They participate in the first math forum of the year in Session 6, sharing

their work on a variety of story problems from Session 5.

Planner

Session

P&I PS MF WP A HC DP

Session 1 Setting Our Course for the Year

Session 1 opens with a discussion about how the classroom should look and sound during math

period to ensure that everyone has a chance to be successful. Students’ ideas are recorded on a chart

to set the tone for the day’s work. Students listen to a story that launches them into an investigation

to determine quantities of school supplies to be used in a fictional fourth grade classroom. They solve

problems in pairs and share their strategies with the class. To close the session, the class makes a

poster about their Community of Learners to refer to for the rest of the year.

Session 2 Number Lines

This session opens with the first problem string of the year. Students set up their student journals and

work through the string to review using an open number line to represent multiplication problems.

Then the investigation into Mrs. Carter’s school supplies continues as they use a variety of strategies,

including the problem string, to find quantities of supplies in Mrs. Carter’s class. Students examine a

Number Line Puzzle and apply the strategies they are practicing.

Session 3 Unit 1 Pre-Assessment

This session begins with a short problem string in which students investigate ratio tables. Then

students complete the Unit 1 Pre-Assessment. They reflect on the assessment during the next session.

This session ends with a brief exploration of the math manipulatives and materials students will use

throughout the year.

Session 4 Methods & Models for Multiplication

After reviewing the pre-assessment given in Session 3, students solve several multiplication story

problems and the teacher models their strategies using open number lines, ratio tables, and rectan-

gular arrays. In the back of their math journals, students begin a handbook involving a collection of

mathematics vocabulary and strategies to use throughout the year.

Session 5 Models for Division

Students investigate the relationship between multiplication and division using open number lines,

ratio tables and the area model. After students collaborate to connect the three models to division,

they begin a set of multiplication and division story problems.

Session 6 Math Forum on Multiplication & Division

Students finish the Camping Story Problems Student Book page from Session 5. Then the teacher

leads the first math forum, a purposeful classroom discussion of students’ strategies. Today’s forum

focuses on grouping and sharing problems, using the array model to strengthen understanding. The

teacher asks intentionally selected students to share their strategies for solving two of the Camping

Story Problems. Throughout the forum, the teacher guides students’ understanding of the strategies

and how the strategies relate to each other.

P&I – Problems & Investigations, PS – Problem String, MF – Math Forum, WP – Work Place, A – Assessment, HC – Home Connection, DP – Daily Practice

Unit 1

Module 1

4 BRIDGES Read Unit 1, Module 1, Session 1.

NUMBER CORNER Read the first week’s featured workouts.

September Calendar Grid Ancient Egyptian NumeralsOverviewThe calendar markers this month feature unfamiliar symbols, which students learn mid-month

are ancient Egyptian numerals. Students search for patterns among the symbols to determine

how the ancient Egyptian system of numeration works and how the markers are changing

from day to day. This pattern provides a place value review that will help as they work with

larger numbers and decimal numbers later in the year. Skills & Concepts• Generate a number or shape pattern that follows a given rule and identify features of the

pattern that were not explicit in the rule used to generate it (4.OA.5)

• Demonstrate an understanding that in a multi-digit number, each digit represents ten

times what it represents in the place to its right (4.NBT.1)• Read and write multi-digit whole numbers represented with numerals, with words, and in

expanded form (4.NBT.2)• Write a simple expression to record calculations with numbers (5.OA.2)

• Construct viable arguments and critique the reasoning of others (4.MP.3)

• Look for and make use of structure (4.MP.7)MaterialsActivities

Day CopiesKit Materials Classroom Materials

Activity 1 Introducing the Calendar Grid

1• Calendar Grid pocket chart• Ancient Egyptian Numerals Calendar Markers• Month, Day, and Year Cards

Activity 2 Updating & Discussing the Calendar Grid

4

Activity 3 Revealing the Tenth Marker & Introducing the Observations Chart

7 TM T1 Ancient Egyptian Numeration Chart

• Calendar Grid Observations Chart (see Preparation)• 1 piece of lined chart paper (see Preparation)• erasable pen or dry-erase marker

Activity 4 Comparing Numeration Systems

10 NCSB 1* Comparing Numeration Systems

Activity 5 Completing a Number Corner Student Book Page

12, 16

NCSB 2* Expanded Form NCSB 3* Equations for Egyptian NumeralsActivity 6

Concluding the September Calendar Grid

20 NCSB 4* Cracking the Code

TM – Teacher Master, NCSB – Number Corner Student BookCopy instructions are located at the top of each teacher master.

* Run 1 copy of this page for display.

Vocabulary An asterisk [*] identifies those terms for which Word Resource Cards are available.

equation*numeral place valuepredict

September

CG

5

Number Corner Grade 4 Teachers Guide


September Calendar Collector

Six Inches a DayOverviewThe class collects a 6-inch strip of paper each day and glues it onto a yard-long strip marked at

1-foot increments. Students keep a chart to show the growing collection of inches, feet, and

yards. In the process, they make conversions from one unit to another, working in both whole

numbers and fractions through the month.

Skills & Concepts

• Recognize equivalent fractions (4.NF.1)

• Explain addition of fractions as joining parts referring to the same whole (4.NF.3a)

• Solve story problems involving addition of fractions referring to the same whole and with

like denominators (4.NF.3d)

• Multiply a fraction by a whole number (4.NF.4b)

• Express a measurement in a larger unit in terms of a smaller unit within the same system of

measurement (e.g., convert from feet to inches) (4.MD.1)

• Record equivalent measurements in different units from the same system of measurement

using a 2-column table (4.MD.1)

• Solve story problems involving distance using addition or multiplication of fractions (4.MD.2)

• Solve story problems that involve expressing measurements given in a larger unit in terms of

a smaller unit within the same system of measurement (4.MD.2)

• Reason abstractly and quantitatively (4.MP.2)

• Attend to precision (4.MP.6)

Materials

Activities Day Copies Kit Materials Classroom Materials

Activity 1 Introducing the October

Calendar Collector

3 TM T2 Six-Inch Strips

TM T3 Yard Strips

• glue stick

• calculators, optional

• yard stick, optional

Activity 2

Introducing the Calendar

Collector Record Sheet

6• Inches, Feet &

Yards Record Sheet

(see Preparation)

Activity 3

Sharing Observations &

Computing Total Inches,

Feet, & Yards

14

Activity 4

Completing the Inches,

Feet & Yards Page

18 NCSB 5* Inches, Feet & Yards

TM – Teacher Master, NCSB – Number Corner Student Book

Copy instructions are located at the top of each teacher master. *Run 1 copy of this page for display.

Preparation

Before the first Calendar Collector Activity this month, prepare all of the Six-Inch Strips and

one Yard Strip. Store the strips in a plastic bag or envelope and post near the display. Include

a glue stick in the bag or envelope. Post one Yard Strip before Activity 1 and add more Yard

Strips as needed through the month. Post the Inches, Feet & Yards Record Sheet on the

display before the second activity.

1 yard

1 foot

September

CC

15


© The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 4 Teachers Guide 3

Unit 1 Module 1

Session 1

Setting Our Course for the YearSummarySession 1 opens with a discussion about how the classroom should look and sound during

math period to ensure that everyone has a chance to be successful. Students’ ideas are

recorded on a chart to set the tone for the day’s work. Then the teacher tells a story to launch

an investigation in which students determine quantities of school supplies to be used in a

fictional fourth grade classroom. They solve problems in pairs and share their strategies with

the class. To close the session, the class makes a poster about their Community of Learners to

refer to for the rest of the year.

Skills & Concepts• Interpret products of whole numbers (3.OA.1)

• Make a comparison statement to match a multiplication equation (4.OA.1)

• Solve story problems involving a multiplicative comparison using multiplication or

division (4.OA.2)

• Make sense of problems and persevere in solving them (4.MP.1)

• Construct viable arguments and critique the reasoning of others (4.MP.3)

Materials

Copies Kit Materials Classroom Materials

Problems & Investigations Setting Our Course for the Year

TM T1 School Supplies

SB 1* More School Supplies

• 2 pieces of chart paper taped to

the wall in an easily accessible

location• marker

Daily Practice

SB 2 How Many Pencils?

HC – Home Connection, SB – Student Book, TM – Teacher Master

Copy instructions are located at the top of each teacher master. * Run 1 copy of this page for display.

Preparation• Prepare Student Books for use by writing students’ names on them.

• Create two charts for recording students’ thinking. On the first, make a T-chart with one

column labeled Looks Like and the other column labeled Sounds Like. On the second, write

Community of Learners at the top.

Vocabulary An asterisk [*] identifies

those terms for which Word

Resource Cards are available.

equation*

groups of

multiplication

multiplicative comparison

multiply*

strategy

unit*

Unit 1

Module 1

Session 1

START TEACHING, AND ENJOY!

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