Build deep math reasoning

## Encourage deep math reasoning using rich, problem-solving tasks and common manipulatives.

Math Tasks uses open-ended tasks and manipulatives to apply deep conceptual understanding to real-life challenges and deepen math reasoning. Each Teacher Guide focuses on a single manipulative and offers countless ways to use them. Flexible activities can be fit into your math curriculum to preview, support, or reteach important concepts.

• Challenges students’ thinking while encouraging multiple solutions.
• Enables teachers to identify student thinking and
scaffold problems.
• Incorporates hands-on learning using common manipulatives and rich math tasks.

## How it Works

### Introduction

Present a possible scenario for introducing the students to the activity. The aim of this brief introduction is to help you give student the tools they will need to investigate independently and grow their own mathematical power.

### On Their Own

These hands-on explorations have the potential for bringing  new mathematical ideas to students and deepening skills as well as helping them make sense of problems
and persevere in
solving them.

### Math Talk

Several prompts are provided to promote discussion. Prompts are designed to encourage students to describe what they notice, tell how they found their results, and give the reasoning behind their answers.

### Extension

The Extension takes the essence of the main activity and either alters or extends its parameters. These activities are well used with a class that becomes deeply involved in the primary activity or for students who finish before the others.

## Libraries

Each Teacher Guide includes 18 lessons that incorporate the appropriate manipulative into math activities in meaningful ways that help students grasp concepts with greater ease and apply this conceptual understanding to real-world tasks and challenges. Lessons teach perseverance that will benefit K–8 students in solving other math problems using other manipulatives and connect to the core of mathematics learning that is important to every K–8 student.

## Base Ten Blocks

Base Ten Blocks provide students with ways to physically represent the concepts of place value and addition, subtraction, multiplication, and division of whole numbers. By building number combinations with Base Ten Blocks, students ease into the concept of regrouping, or trading, and are able to see the logical development of each operation. The blocks provide a visual foundation and understanding of the algorithms students use when doing paper-and-pencil computation. Older students can transfer their understanding of whole numbers and whole-number operations to an understanding of decimals and decimal operations.

## Cuisenaire® Rods

Cuisenaire Rods can be used to develop a wide variety of mathematical ideas at many different levels of complexity. Initially, students use the rods to explore spatial relationships. This introductory exploration will lead students to discover how some combinations of rods are equal in length to other, single rods. Older students who have no previous experience with Cuisenaire Rods may explore by comparing and ordering the lengths of the rods and then recording the results on grid paper to visualize the inherent “structure” of the design. In their early work with the rods, students have a context in which to develop their communication skills through the use of grade-appropriate arithmetic and geometric vocabulary.

## Pattern Blocks

Pattern Blocks help students explore many mathematical topics, including congruence, similarity, symmetry, area, perimeter, patterns, functions, fractions, and graphing. In the beginning students work with Pattern Blocks to explore spatial relations. Young students have an initial tendency to work with others and to copy one another’s designs. Yet even duplicating another’s pattern with blocks can expand students’ experience, help them develop the ability to recognize similarities and differences, and provide a context for developing language related to geometric ideas. Throughout their investigations, student should be encouraged to talk about their constructions. Expressing their thoughts out loud helps students clarify and extend their thinking.

## Color Tiles

Although Color Tiles are simple in concept, they can be used to develop a wide variety of mathematical ideas at many different levels of complexity. Young students who start using Color Tiles to make patterns may be likely to talk about numbers of different-colored tiles. Some students may even spontaneously begin to count and compare numbers. The fact that the tiles are squares means that they fit naturally into a grid pattern, so the tiles can be used to discover many number patterns.

### Standards Alignment

Snap Cubes are very suitable for developing understanding of the meaning of addition. The colors can also broaden students’ understanding of subtraction. Snap Cubes are also ideal for developing the concept of multiplication, both as equal grouping and as an array. In addition, Snap Cubes are suitable for exploring area, perimeter, volume, and surface area relations.

## Components and Configurations

### Teacher Guides

Feature 18 rich tasks that teach content and practice standards using the most common manipulatives.

### Libraries

Includes the grade-appropriate Teachers Guides for: Base Ten Blocks, Color Tiles, Cuisenaire® Rods, Pattern Blocks, Geoboards, and Snap Cubes®.