# Cutting Boards

Josh and Sam each have a board to cut. The boards are the same size and are in the shape of a rectangle. Josh cuts his board in thirds and uses two-thirds of the board. Sam cuts his board in sixths and uses four-sixths of the board. Do both boys use the same amount of their boards? Show all your mathematical thinking.

### More Accessible Version

Josh and Sam each have a board to cut. The boards are the same size and are in the shape of a rectangle. Josh cuts his board in halves and uses one-half of the board. Sam cuts his board in fourths and uses two-fourths of the board. Do both boys use the same amount of their boards? Show all your mathematical thinking.

### More Challenging Version

Josh and Sam each have a board to cut. The boards are the same size and are in the shape of a rectangle. Josh cuts his board in thirds and uses two-thirds of the board. Sam cuts his board in ninths and uses six-ninths of the board. Do both boys use the same amount of their boards? Show all your mathematical thinking.

## Plan

#### Underlying Mathematical Concepts

#### Possible Problem-Solving Strategies

#### Formal Mathematical Language and Symbolic Notation

A student may independently select a printed number line, number chart, ten frames, graph paper, etc. as they work on a task.

### Suggested materials

Engagement Image:

Teachers may project the image below to launch this task for their students, define nouns, promote discussion, access prior knowledge, and inspire engagement and problem solving.