## A blueprint for success

Bridges provides the guidance, materials, and tools for building mathematical thinkers.

Grades K–2 are available now. Grades 3–5 will be available in 2014.

## Kindergarten

### Overview

Students focus intensively on the two critical areas specified by the Common Core State Standards for Mathematics:

• Representing and comparing whole numbers
• Describing shapes and space

Six of eight units are devoted to number and operations. They help students learn to use numbers, including written numerals, to represent quantities and solve problems; count out a given number of objects; compare sets or numerals; and model simple joining and separating situations with objects, fingers, words, actions, drawings, numbers, and equations.

The remaining two units focus on geometry. They invite students to describe and analyze the attributes of shapes in the world around them; find, count, draw, build, and compare shapes; and fit shapes together to make other shapes and complete puzzles.

CCSS Correlations

Texas Correlations

### Content Outline

#### Unit 3 Bikes & Bugs: Double, Add & Subtract

• Bicycle Doubles
• Add, Subtract & Double It!
• Put Them in Order

#### Unit 5 Two-Dimensional Geometry

• Exploring Shapes
• Circles, Squares, Triangles & Rectangles
• Constructing & Drawing Shapes
• Sorting, Comparing, Composing & Decomposing Shapes

#### Unit 6 Three-Dimensional Shapes & Numbers Beyond Ten

• What Do You Know About Three-Dimensional Shapes?
• More Three-Dimensional Shapes
• Exploring the Teen Numbers
• Combinations to Ten

#### Unit 8 Computing & Measuring with Frogs & Bugs

• Catching, Counting & Comparing
• Frogs: Estimating & Measuring
• Tens & Ones

#### Number Corner

• Calendar Grid
• Calendar Collector
• Days in School
• Computational Fluency
• Number Line

### Sample Materials

Bridges Assessment Guide:

#### Manipulative Kit

See More Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image

#### Games & Activities

See More Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image

#### Number Corner Calendar Markers

Many students, especially my ELL students, are developing a stronger sense of number using the visual ten-frames and finger models from Bridges. These strategies are providing successful concrete to representational forms for students.

Kindergarten Teacher, Hood River, OR

### Overview

Students focus intensively on the four critical areas specified by the Common Core State Standards for Mathematics in Grade One:

• Addition and subtraction within 20
• Whole number relationships and place value
• Linear measurement in non-standard units
• Reasoning with shapes and their attributes

Four of eight units are devoted to addition and subtraction within 20. They help students gain fluency with facts to 10 and develop increasingly sophisticated strategies for solving addition and subtraction combinations to 20. During these units, students model, solve, and pose a wide variety of word problems to construct meaning for the operations of addition and subtraction, as well as an understanding of how the two are connected.

Two of the eight units focus on place value, extending the counting sequence to 120 as students learn to think of whole numbers between 10 and 100 in terms of tens and ones. Much of the work in these units engages first graders in developing, discussing, and using efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10.

The remaining two units revolve around geometry and measurement. The geometry unit challenges children to identify, describe, construct, draw, compare, compose, and sort shapes. Students also learn about fractions in the context of two-dimensional shapes. The measurement unit provides ample opportunity for students to develop an understanding of the meaning and processes of measuring time and length as they conduct duration experiments; construct, fly, and measure the flight distances of paper gliders; and investigate some of the many ways in which they have grown and changed since they were born.

CCSS Correlations

Texas Correlations

### Content Outline

#### Unit 1 Numbers All Around Us

• Counting & Data with Popsicles
• Meet the Number Rack
• Part-Part-Whole to Ten
• Adding & Subtracting to Ten with the Number Rack

#### Unit 4 Leapfrogs on the Number Line

• Adding & Subtracting on the Life-Sized Number Line
• Jumping by Fives & Tens
• Jumping by Fives & Tens on the Open Number Line
• Measuring, Comparing & Subtracting with Penguins

#### Unit 5 Geometry

• Introducing Two-Dimensional Shapes
• Introducing Three-Dimensional Shapes
• Putting Shapes Together & Taking Them Apart
• Sorting & Graphing Shapes

#### Unit 6 Figure the Facts with Penguins

• Story Problems for Basic Addition & Subtraction
• Combinations & Story Problems
• Solving for the Unknown in Penguin Stories
• Measuring & Comparing Emperor & Little Blue Penguins

#### Unit 8 Changes, Changes

• Time & Duration
• Patterns, Structure & Change
• Measurement & Data with Paper Gliders
• Measuring our Growth

#### Number Corner

• Calendar Grid
• Calendar Collector
• Days in School
• Computational Fluency
• Number Line

I have a very challenging group of kids, and we are having an outstanding year in math. The kids are so engaged and interested.

### Overview

Students focus intensively on the four critical areas specified by the Common Core State Standards for Mathematics in Grade Two:

• Extending understanding of base-ten notation
• Building fluency with addition and subtraction
• Using standard units of linear measurement
• Describing and analyzing shapes

The first unit revisits and extends addition and subtraction within 20, helping to ensure that second graders operate with understanding and fact fluency from the start of the school year.

Units 2, 3, 5, and parts of Unit 7, are devoted to place value and multi-digit addition and subtraction. During these units, students learn to count by fives, tens, and multiples of hundreds, tens and ones; read, write, and compare numbers to 1,000; and develop fluency with addition and subtraction to 100 as they solve and pose a wide variety of word problems. Later in the year, the children use concrete models and sketches, as well as strategies based on place value, properties of operations, and the relationship between addition and subtraction, to add and subtract to 1,000.

Unit 6 revolves around geometry, building foundations for understanding area, volume, congruence, similarity, and symmetry as students investigate, describe, build, draw, combine, decompose, and analyze two- and three-dimensional shapes.

Unit 4, and the first part of Unit 7, focus on linear measurement, as students construct their own rulers; estimate and measure in inches, feet, yards, centimeters, and meters; and solve problems that involve adding, subtracting, and comparing lengths.

Unit 8 revisits linear measurement in the context of science and engineering as students make and test cardboard ramps of different kinds to investigate some of the factors that cause marbles to roll farther and faster. In the process, they generate data by measuring marble roll distances multiple times, pool their data, and enter it on line plots to better see, understand, and analyze how manipulating the different variables affects the outcomes.

CCSS Correlations

Texas Correlations

### Content Outline

#### Unit 1 Figure the Facts

• Sorting & Graphing
• Number Facts with the Number Rack
• Introducing Addition & Subtraction Strategies
• Fluency with Addition Facts to Twenty

#### Unit 2 Place Value & Measurement with Jack's Beanstalks

• Counting & Modeling Two- & Three-Digit Numbers
• Measuring Jack’s Giant Beans with Tens
• Adding on the Open Number Line
• Thinking in Twos

#### Unit 4 Measurement

• Inches & Feet
• Inches, Feet & Yards
• Proportion & Fractions with a Giant
• Thinking in Threes

#### Unit 6 Geometry

• Attributes of Two-Dimensional Shapes
• Exploring Area & Arrays
• Composing & Decomposing Patchwork Shapes
• Patchwork Fractions

#### Number Corner

• Calendar Grid
• Calendar Collector
• Daily Rectangle
• Computational Fluency
• Number Line

### Sample Materials

Bridges Assessment Guide:

#### Manipulative Kit

See More Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image

#### Games & Activities

See More Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image

#### Number Corner Calendar Markers

View Product Catalog Page

As an experienced Bridges teacher, I have seen the power of the ten-frames visual model. The addition of the Number Rack in the second edition of Bridges provides a wonderful new tool for engaging learners with this model. I have been so impressed with how my students are confidently constructing number combinations and modeling equations efficiently.

### Overview

Students focus intensively on the four critical areas specified by the Common Core State Standards for Mathematics in Grade Three:

• Developing understanding of multiplication and division and strategies for multiplication and division within 100
• Developing understanding of fractions, especially unit fractions (fractions with numerator 1)
• Developing understanding of the structure of rectangular arrays and of area
• Describing and analyzing two-dimensional shapes

The first unit reviews and extends work with addition and subtraction as students review facts, look for patterns, and work with larger numbers. Unit 2 transitions to multiplication by having students use a variety of rich contexts (arrays of stamps, groups of windows, and a coral reef) to develop and refine multiplication strategies and models. Unit 3 returns to addition and subtraction, this time focusing on strategies for computing with larger numbers.

In Units 4 and 5, students explore measurement, fractions, division, and multiplication of larger numbers. Students estimate and make measurements in different units; explore unit fractions and equivalent fractions, and begin adding and subtracting fractions; and connect multiplication to division and extend multiplication strategies to larger numbers. Students develop a strong understanding of area through their work with multiplication.

Unit 6 focuses on geometry, as students investigate, draw, and build two-dimensional shapes, using their properties to classify and analyze these shapes. They also connect geometry to fractions as they express the area of a shape as a unit fraction of the whole. Unit 7 brings together and extends many of the skills and concepts addressed in earlier units as students solve challenging problems that involve calculating with multi-digit numbers. They explore algorithms for addition and subtraction and dig deeper into division. Students develop strategies and models for division, many of which are based on their work with multiplication.

Unit 8 integrates mathematics and science, with a primary focus on designing and building model bridges. Students test the strength of their model bridges in systematic ways to collect data. Then they graph and analyze the data, finding the range and mean, to make conjectures and draw conclusions about effective bridge design and construction.

### Content Outline

#### Unit 1 Addition & Subtraction Patterns

• Community Building & Addition Facts to Twenty
• Subtraction Facts to Twenty
• Story Problems & Strategies

#### Unit 3 Multi-Digit Addition & Subtraction

• Rounding &
• Multi-Digit Subtraction
& Subtract
• Exploring the Algorithms
& Subtraction

#### Unit 5 Multiplication & Division

• Multiplication & Division Patterns & Problems
• Multiplication & Division Families
• Larger Multiplication
• Area in Non-Standard Units

#### Unit 6 Geometry & Area

• Investigating Polygons
• Perimeter & Area
• Hexarights & Dream Houses

#### Unit 7 Computation, Division & Fractions

• Place Value & Multi-Digit Addition & Subtraction
• Division & Mixed Story Problems
• Fractions as Parts of a Whole & Parts of a Set
• Fractions & Liquid Volume

#### Unit 8 Bridge Design & Construction: Data Collection and Analysis

• Building Beam & Arch Bridges to Gather & Analyze Data
• Building Suspension Bridges to Gather & Analyze Data
• Using Data to Build Longer & Stronger Bridges
• Using Data, Measurement & Geometry to Talk About Bridges

#### Number Corner

• Calendar Grid
• Calendar Collector
• Computational Fluency
• Number Line
• Solving Problems

### Sample Materials

Lesson:

Manipulative Kit

See More Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image

See More Image

#### Number Corner Calendar Markers

View Product Catalog Page

### Overview

Students focus intensively on the three critical areas specified by the Common Core State Standards for Mathematics in Grade Four:

• Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends
• Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers
• Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry

The first two units focus on multiplication and multiplicative thinking. Unit 1 reviews and extends multiplication work from third grade and examines factors and products, as well as prime and composite numbers. Unit 2 delves deeper as students explore and extend strategies, concepts, and models related to multi-digit multiplication. Unit 3 uses measurement contexts to deepen students’ understanding of multi-digit addition and subtraction and measurement.

Units 4, 5, and 7 focus on fractions, decimals, division, and more multiplication. Various models help students understand more about operations with fractions and fraction equivalence, as well as the relationship between fractions and decimals. Students also discover the relationships between multiplication and division as they see that many multiplication strategies also apply to division problems. Students solve division problems with and without remainders and begin exploring multiplication and division of simple fractions.

Unit 6 focuses on geometry and extends students’ understandings of area, volume, and symmetry. Students investigate, draw, and build two-dimensional shapes and the properties of those shapes to classify and analyze them. Students also learn to use protractors to measure and construct angles.

Unit 8 integrates many key skills and concepts in the context of science and engineering by giving students the opportunity to design playgrounds. In the process, they generate and analyze data, and use a line plot to represent that data.

### Content Outline

#### Unit 4 Adding & Subtracting Whole Numbers & Fractions

• Measurement
• Measurement & Data Displays

#### Unit 5  Geometry & Measurement

• Angles
• Polygons & Symmetry
• Geometry Measurement Problems
• Measuring Length, Time, Mass, Weight & Liquid Volume

#### Unit 6 Multiplication & Division; Data & Fractions

• Multiplication & Division Strategies
• Revisiting Area & Perimeter
• Line Plots, Division & Fractions
• Solving Problems with Division

#### Unit 7 Patterns & Problems

• Number & Shape Patterns
• Expressions & Equations
• Exploring the Traditional Algorithm for Multiplication
• Using the Traditional Multiplication Algorithm

#### Unit 8 Playground Design: Measurement, Data & Geometry

• Planning Playgrounds with Geometry, Measurement
& Data
• Using Data to Make Decisions
• Using Scale Models for Our Playground & Field
• Building & Drawing Model Playgrounds to Scale

#### Number Corner

• Calendar Grid
• Calendar Collector
• Computational Fluency
• Problem Strings
• Solving Problems

### Sample Materials

Lesson:

Manipulative Kit

See More Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image Image

See More

#### Number Corner Calendar Markers

View Product Catalog Page

My students and I enjoyed using the "quick sketch" model for multiplication. It is so nice to be able to put a visual in students' hands to help them understand a normally complicated process.

Grade 4 Teacher, Ft. Bridger, WY

### Overview

Students focus intensively on the three critical areas specified by the Common Core State Standards for Mathematics in Grade Five:

• Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions)
• Extending division to 2-digit divisors, integrating decimal fractions into the place value system, developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations
• Developing understanding of volume

The first unit is focused on volume, and includes a review of multiplication facts and multi-digit multiplication strategies. In Unit 2, students use what they know about equivalent fractions to add and subtract fractions. Unit 3 extends students’ understandings of place value and the properties of operations to help students develop powerful strategies for computing fluently with decimals. In Unit 4 students study geometry and measurement by graphing ordered pairs, classifying 2-D figures within a hierarchy, and formalizing the formula for finding volume.

Unit 5 helps students refine powerful multiplication and division strategies, including the standard algorithm for multiplication. In Unit 6 students learn to multiply fractions. In Unit 7 students develop accurate and efficient strategies for dividing whole numbers, decimals, and fractions (unit fractions by whole numbers, and whole numbers by unit fractions).

Unit 8 integrates science, engineering and math. In this final unit, students apply the understandings and skills they have developed over the year while studying solar energy and designing solar homes.

### Content Outline

#### Unit 1 Expressions, Equations & Volume

• Multiplication & Volume
• Factors, Multiples, & the Associative Property
• Multiplication Strategies
• From Multiplication to Division

#### Unit 5 Multiplication

• Multiplication Strategies
• The Multiplication Algorithm
• Extending the Traditional Algorithms for Multiplication

#### Unit 6 Fraction Multiplication

• Multiplying Fractions by Whole Numbers
• Multiplying Fractions by Fractions
• Multiplying Mixed Numbers
• Fractions Review: How Do You Know What to Do?

#### Unit 7 Division

• Division of Fractions & Whole Numbers
• Partitive & Quotative Division
• Division Strategies
• The Standard Algorithm for Long Division

#### Unit 8 Solar Design

• Investigating Solar Energy
• Investigating Passive Solar Design
• Designing Solar Homes
• Finishing Our Models

#### Number Corner

• Calendar Grid
• Calendar Collector
• Computational Fluency
• Problem Strings
• Solving Problems

### Sample Materials

Lesson:

Manipulative Kit

See More Image Image Image Image Image Image Image Image Image Image Image Image

#### Number Corner Calendar Markers

View Product Catalog Page

I am so grateful to finally have a curriculum
that digs deep into the concepts!