# Interpret area models to form rectangular arrays.

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Interpret area models to form rectangular arrays.
Module 4 Lesson 7 Interpret area models to form rectangular arrays.

Skip counting Let’s skip count by 3s to 30. 30 24 9 3 6 27 18 15 12 21

Skip counting Let’s skip count by 6s to 60. 60 48 18 6 12 54 36 30 24 42

Skip counting Let’s skip count by 7s to 70. 70 56 21 7 14 63 42 35 28 49

Skip counting Let’s skip count by 8s to 80. 80 64 24 8 16 72 48 40 32 56

Skip counting Let’s skip count by 9s to 90. 90 72 27 9 18 81 54 45 36 63

Draw Rectangles First of all, Make sure you have Grid Paper.
Draw a rectangle that has an area of 12 square units. Draw a rectangle that has an area of 6 square units. Thumbs up when you’re done! Draw a rectangle that has an area of 35 square units. Draw a rectangle that has an area of 10 square units. Draw a rectangle that has an area of 24 square units. Draw a rectangle that has an area of 16 square units.

Draw Rectangular Arrays
Draw a 4 x 2 rectangular array using the squares on your grid paper. How many square units are in your array? 8 square units.

Draw Rectangular Arrays
Draw a 6 x 2 rectangular array using the squares on your grid paper. How many square units are in your array? 12 square units.

Draw Rectangular Arrays
Draw a 4 x 3 rectangular array using the squares on your grid paper. How many square units are in your array? 12 square units.

Draw Rectangular Arrays
Draw a 6 x 4 rectangular array using the squares on your grid paper. How many square units are in your array? 24 square units.

Problem of the Day

Concept Development Work with people at your table (you can have a group size of 2 – 3) Make sure each group has equal amounts of centimeter tiles and square inch tiles. Decide with your partner (group) how to arrange your tiles to make the same shape rectangle. Then create those rectangles with your pieces (cm cubes, and square inch tiles) Trace or draw a picture of your rectangles. THUMBS UP WHEN YOU’RE FINISHED.

Time to think! You and your partner(s) made the same shape rectangle. Is there area also the same? Why or why not? Write the area of your rectangle on your board. I will show you 1 square meter on the board Suppose you used 12 square meter tiles to make your rectangle. Would this rectangle have a BIGGER area or a smaller area compared to your rectangle? BIGGER

Still thinking… Now I’m going to draw a square foot on the board. How would your rectangle compare if you make it from 12 square feet? It would be bigger than 12 square inches or centimeters, but smaller than 12 square meters. How about this pad of sticky notes? Still bigger than square inches or centimeters, but smaller than square feet or centimeters.

THE BIG QUESTION Why is it important to label the UNIT when you’re talking about area? The area changes if the unit is small or big If you do not know the unit then you really don’t know the size of the area.

Relate area to multiplication to draw rectangular arrays
We will draw a rectangular array with an area of 18 square centimeters. How might we find the side lengths? Work with your partner to make a list of multiplication facts that equal 18. (1x18, 18x1, 2x9, 9x2, 3x6, 6x3) Use a ruler to create a 3cm x 6cm rectangular array. After drawing your squares, check your work by skip-counting the rows to find the total number of tiles you drew. Thumbs up when you’re done.

DOES THE RECTANGLE STILL HAVE THE SAME AREA?
3 cm 6 cm 3 cm 6 cm DOES THE RECTANGLE STILL HAVE THE SAME AREA?

Erase the inside grid lines of your 3 x 6 rectangular array.
The empty rectangle with the labeled side lengths is called the area model. How can you find the total area just using the labeled side lengths? 6 cm 3cm What is the total area of this rectangle?

8 square inches Suppose the unit In this area model is in inches.
The side lengths of this Model are not labeled. Do we need to draw grid lines to find the area Of this rectangle? What is the area of this Area model? 8 square inches

PROBLEM SET!