Math Focus 3
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# Chapter 9: Division   Design a Group of Castles

## INTRODUCTION

Buildings aren’t just made of walls and a roof. They need at least one door so you can get in and out! Windows let you see outside and let light inside, too. And if the building happens to be a castle, you could climb high up in its towers.

## THE TASK

Imagine you are designing a group of castles for a family of princesses and princes. Each prince or princess will have his or her own castle, and each castle must look exactly the same. You need to decide how many princes and princesses are in the family (either 2, 3, or 4). You have only 12 doors, 16 windows, and 6 towers to build your castles with.

## THE PROCESS

1. Decide how many castles you need to build altogether (2, 3, or 4) for the princesses and princes.
2. Visit Castle Constructor to make the castle design. Draw rectangles for the other castles you are building on your paper. Remember that all of your castles must look the same, and that you have only 12 doors, 16 windows, and 6 towers to use. You do not need to use all of each type of material. Scroll down in the Castle Parts section to see the towers and different doors and windows to choose from.
3. As you add parts to your castle on the computer, add the same parts to your castles on your paper to make them look alike. Count the parts to make sure you don’t use more than you have.
4. Write a division sentence for the number of doors on each of your castles. Use counters or other manipulatives to help you. Make an array to model your division sentence.
5. Write a multiplication sentence for the number of windows on each of your castles. Use counters or other manipulatives to help you. Make an array to model your multiplication sentence.
6. Use repeated subtraction to show the number of towers. Write a division sentence and a multiplication sentence for the number of towers on each of your castles. Use counters or other manipulatives to help you.

## RESOURCES

Website:

Castle Constructor

Materials:

pencil

paper

counters, or other manipulatives

## ASSESSMENT

 Mathematical Processes Work meets standard of excellence Work meets standard of proficiency Work meets acceptable standard Work does not yet meet acceptable standard Problem Solving • develops a thorough plan for solving the problem • chooses an efficient and effective strategy: may demonstrate creativity and innovation in designing castles • develops a workable plan for solving the problem • chooses an appropriate and workable strategy to design castles • develops a basic plan for solving the problem • chooses a simplistic and/or routine strategy to design castles • develops a minimal and/or flawed plan for solving the problem • chooses an inappropriate or unworkable strategy to design castles Visualization • uses insightful visual representations to show an array • uses meaningful visual representations to show an array • uses simple visual representations to show an array • uses unclear visual representations to show an array Connections • makes insightful connections between division, multiplication, and arrays • makes meaningful connections between division, multiplication, and arrays • makes simple connections between division, multiplication, and arrays • makes minimal or weak connections between division, multiplication, and arrays Mental Mathematics and Estimation • demonstrates computational fluency that is efficient and flexible • demonstrates computational fluency that is workable and understood • demonstrates computational fluency that is routine and familiar • has difficulty in demonstrating computational fluency and must work through procedures