Do the Math

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Discipline

Mathematics

Copyright

2021

Grade(s)

1 - 8

Delivery Method

Imprint

Heinemann

Author(s)

Marilyn Burns

Program Guide Sample

Math is about more than finding the correct answer. It's about using numerical reasoning to find the best strategy for solving a problem. Created by Marilyn Burns, one of North America's most trusted math educators, and a team of master educators, Do The Math® provides flexible, classroom-tested instruction for building numerical reasoning and confidence.

Whether used for core instruction in numerical reasoning, pull-out intervention, or summer school settings, Do The Math provides effective instruction at any elementary grade level.

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Overview

Build a solid mathematical foundation with classroom-tested lessons

"Classroom tested" means there's plenty of support in each module's 30 half-hour lessons. Teachers build capacity as students move from basic conceptual understanding to skills development in addition and subtraction, multiplication, division, and fractions.

Addition and Subtraction

DTM1 — **NUMBER CORE**
Supports the development of quantity by using benchmark numbers, thinking flexibly about composing and decomposing numbers, and building facility with figuring sums.

**A: ADDITION WITH SUMS UP TO 100**
Builds on the big idea that “10” is an organizer for our number system.

**B: SUBTRACTION WITH NUMBERS UP TO 100**
Reinforces addition and subtraction as inverse operations and teaches the three meanings of subtraction: take-away, missing parts, and comparison problems.

**C: NUMBERS GREATER THAN 100**
Applies these big ideas to calculations with greater numbers and provides strategies for solving word problems.

Multiplication

DTM2 — A: BASIC CONCEPTS
Provides visual and contextual models to help students understand the meaning of multiplication, supporting the shift from thinking additively to thinking multiplicatively.

B: FACTS THROUGH 12x12
Uses an array model to represent the basic facts and demonstrate key concepts and strategies for multiplication.

C: FACTORS GREATER THAN 12
Develops strategies for making estimates and computing products with two- and three-digit factors, using the distributive property and multiplying by multiples of 10.

Division

DTM3 — A: BASIC CONCEPTS
Builds upon the idea that division is inverse to multiplication and provides computational methods for solving division problems, using contextual and concrete methods to support the two meanings of division—sharing and ungrouping.

B: FACTS THROUGH 100÷10
Applies the inverse relationship between multiplication and division to make sense of divisibility and the concept of taking out a quantity by groups of 10.

C: DIVIDENDS TO 1000
Extends to dividing two- and three-digit dividends by two-digit divisors, engages students in exploring divisibility, and provides experiences with solving contextual problems involving greater numbers.

Fractions

DTM4 — A: BASIC CONCEPTS
Connects and builds upon the big ideas of whole numbers as they apply to fractions, using concrete materials to help students give meaning to the abstract idea of fractions.

B: EQUIVALENCE AND COMPARISON
Helps students learn key strategies for comparing and ordering fractions while keeping the instructional focus on the meaning of the fractions being compared.

C: ADDITION AND SUBTRACTION
Builds on what students have learned in order to develop the computational tools and strategies to add and subtract fractions, including improper fractions and mixed numbers with like and unlike denominators.

Do The Math Middle School

Do The Math Middle School is for older, striving learners. Research shows students with diverse needs succeed in learning mathematics through explicit, intentional teaching based on proven instructional strategies. Research-based instructional principles include: Scaffolded Content, Explicit Instruction, Multiple Strategies, Gradual Release, Meaningful Practice, "Think, Pair, Share, Vocabulary and Language, and Differentiation.

Along with Beginning-of-Unit and End-of-Unit Assessments that measure understanding, every fifth lesson is an assessment that provides an opportunity to monitor student progress. Teachers get the resources and direction to effectively prepare, teach the lesson, and assess student understanding. Teacher Guides include ten units with 15 lessons each.

Implementation Recommendations:

1. SMALL GROUP (For 1 teacher and 8 students)

1 Teacher Bookcase for each module, 8 Student WorkSpace Books, 1 Classroom Materials Box.

2. WHOLE CLASS (Serves 1 teacher and 24 students)

1 Teacher Bookcase for each module, 24 Student WorkSpace Books, 3 Classroom Material Boxes

Please note:

1. In order to implement the program successfully we strongly recommend purchasing the Classroom Materials in addition to the Teacher Bookcases and Student Workspace Books.

2. Digital components are not available for purchase in Canada at this time.

Do the Math Elementary Grades 1-5

Build a solid mathematical foundation with classroom-tested lessons

Addition and Subtraction

Multiplication

Division

Fractions

Do the Math Middle School Grades 6-8

Building the Foundations for Algebra

Trusted, respected intervention and education leadership that helps older, struggling students and their teachers in three important ways.

Focused & Coherent Content

Do The Math Middle School helps students build deep understanding, learn to reason mathematically, and make connections across operations. Students can apply their skills to higher-level mathematics, including critical foundations of algebra.

Teacher Support

Written and developed by Marilyn Burns, one of today’s most highly respected mathematics educators, the research-based lessons in Do The Math Middle School supports teachers in understanding and delivering effective math intervention.

Student Motivation & Support

Students experience success early with instruction organized into manageable chunks. Do The Math Middle School empowers students to think about math in new ways with sequenced and paced learning and teaching for improving achievement.

Multiplication & Division

Do-the-math-middle-school-TG-cover-multiplication — Develop visual representations and reasoning skills that strengthen students’ conceptual understanding and computational skills. At the foundation of the lessons are applying the place-value structure of our number system and properties of numbers.

**Unit 1: Build a Foundation for Multiplication**

Although students may have previous experience with multiplication, lessons take a step back in this unit to deepen students’ conceptual understanding of the meaning of multiplication by drawing on real-world contexts and rectangular arrays.

**Unit 2: Develop Multiplication Number Sense**

Students are actively engaged with the Commutative, Associative, and Distributive Properties of Multiplication. Students explore patterns on the multiplication chart and use visual models of rectangles to represent basic facts, deepening their understanding and number sense.

**Unit 3: Use Place-Value Strategies to Multiply**

Students learn the useful strategy of splitting factors into their place-value parts. They apply these strategies to estimate and solve multi-digit multiplication problems.

**Unit 4: Connect Multiplication and Division**

These lessons build on students’ understanding of multiplication to develop the relations between multiplication and division. Students solve division group problems, explore divisibility, and calculate quotients and remainders.

**Unit 5: Use Place-Value Strategies to Divide**

These lessons focus on deepening students’ understanding of the division process. Students solve three-digit dividend problems and extend their skills to the division of two-digit divisors.

Fraction Fundamentals

Do-the-math-middle-school-TG-cover-fractions — Strengthen students’ conceptual understanding of fractions by developing mental representations as students use number sense to compare, order, and explore equivalent fractions.

**Unit 6: Develop Understanding of Fractions**

Students investigate fractions by making fraction kits to model whole, halves, fourths, eighths, and sixteenths. They learn to identify equivalent fractions, compare and combine fractions, and represent fractions greater than a whole.

**Unit 7: Reason with Fractions**

Students extend their fraction kits to include thirds, sixths, and twelfths. They learn comparing strategies that help develop number sense and provide options rooted in understanding.

**Unit 8: Extend Fraction Concepts and Comparing Strategies**

Students are introduced to two more strategies while using cube trains to explore, compare, and identify fractions.

**Unit 9: Build on Equivalence to Estimate, Compare, Add, and Subtract**

Students learn to rename fractions to have a common denominator while deepening their understanding of equivalence, estimating sums and differences, and adding and subtracting fractions.

**Unit 10: Develop Fraction Number Sense**

Students learn to add and subtract fractions and mixed numbers mentally. They also play games with meaningful fraction practice to develop their fraction number sense.

Proven Instructional Strategies

Elevate learning with research-based intervention

Scaffolded Content: Scaffolding of the content makes the mathematics more accessible to students.
Explicit Instruction: Students benefit from instruction based on teaching for understanding.
Multiple Strategies: Multiple strategies for developing concepts and skills support student learning.
Gradual Release: Four-phased pedagogy built on gradual release prepares students for individual success.
Meaningful Practice: Assignments provide opportunities to practice, strengthen, and extend their learning.
"Think, Pair, Share": Research shows that student interaction such as “think, pair, share” deepens student understanding.
Vocabulary and Language: Intentional vocabulary instruction helps students develop effective communication about the math they are learning.
Differentiation: Ongoing assessment is built into the program to help teachers meet individual student needs.

Effective, Efficient Program Structure

Build confidence with insight from ongoing assessments.

Along with Beginning-of-Unit and End-of-Unit Assessments that measure understanding, every fifth lesson is an assessment that provides an opportunity to monitor student progress.

Teachers get the resources and direction to effectively prepare, teach the lesson, and assess student understanding. Teacher Guides include ten units with 15 lessons each. Instructional support for reach lesson includes:

Lesson Summary
Objectives
Materials
Teacher Display Tools
Preparation
Language Development
Step-by-Step Instruction

Core Subject

Specialized Program/Course

Resources

Do the Math

Overview

Build a solid mathematical foundation with classroom-tested lessons

Implementation Recommendations:

Do the Math Elementary Grades 1-5

Build a solid mathematical foundation with classroom-tested lessons

Do the Math Middle School Grades 6-8

Building the Foundations for Algebra

Focused & Coherent Content

Teacher Support

Student Motivation & Support

Proven Instructional Strategies

Elevate learning with research-based intervention

Effective, Efficient Program Structure

Samples

Do the Math

Implementation

Help & Support

Core Subject

Specialized Program/Course

Resources

Topic

Grade

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Core Subject

Specialized Program/Course

Resources

Do the Math

Overview

Build a solid mathematical foundation with classroom-tested lessons

Implementation Recommendations:

Discipline

Topic

Grade

Implementation

Help & Support

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