This page is an overview and menu page for all the information you need to do these Grade 3 activities.
About the Activities
In the activity Arranging Chairs in Rectangular Arrays students are challenged to find different ways to arrange rows of chairs for an audience by manipulating 12 cubes to see how many different rectangles they can make. They list the dimensions of these rectangles and the factors of 12. In the activity Arranging More Chairs students repeat this work with larger numbers of chairs. In these two activities students' work focuses on:
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making rectangles for quantities of 12 and other numbers
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finding factors of 12 and other numbers
To do these activities, you, the teacher, will need:
(These files are provided in Portable Document Format (PDF) and can be read using Adobe's free Acrobat Reader. If you don't have this application, you can download it at Adobe's web site.)
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Instructions for Arranging Chairs in Rectangular Arrays & Arranging More Chairs PDF
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Overhead projector (optional)
Your students will need:
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Interlocking cubes
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Half-inch graph paper (optional)
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Calculators
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The Arranging Chairs Puzzle PDF , 1 per student
About the Unit
Things That Come in Groups is the third grade unit on multiplication and division (the number strand) in the Investigations curriculum. In this unit students develop their own strategies for doing multiplication and division problems. They discover that both types of problems deal with equal groups. Students explore methods to help visualize relationships between numbers by: (1) using arrays; (2) skip counting on a 100 chart; and (3) identifying patterns in multiplication tables.
"The way I used to teach multiplication is probably the way most 3rd grade teachers teach multiplication. I would make flash cards, they would study them and rattle off the answers. I don't know if they knew what they were rattling off. I believe the difference is that they can carry it over, it's not just rattling off answers. I really believe they understand it. They can use what they know to carry over to other things. I never used multiplication to do division. Now as children are understanding what they are doing they naturally use multiplication to do division because they really have an understanding." -- Grade 3 Teacher
"Arrays help children learn multiplication and understand it because they have it in front of them. They can see 1 x 12, 2 x 6. They can see it right in front of them." -- Grade 3 Teacher
"It's visualizing and understanding. Arrays are a great way to teach multiplication--to see it, to understand it." -- Grade 3 Teacher
"When we memorize, we're guessing. Using arrays and understanding multiplication, I can look at a number and say, 'That doesn't look right.' My children are doing that too. They look and say, 'That doesn't look right.' If 2 into 10 goes 5 (times), what would 2 into 20 be? I'm able to check better too. I can ask the students to rethink what they did. I even look at my checkbook now, and say, 'This doesn't look right.' This is what I want children to do. I want them to look at an answer and say, 'This doesn't look right.'" -- Grade 3 Teacher
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