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XY Encounter

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Teacher's Guide: Part 2: Conclusion

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Map of Teacher's Guide	Part 1	Part 2	Part 3	Part 4
	Introduction	Introduction	Introduction	Introduction
	Pause Point 1	Pause Point 1	Pause Point 1	Pause Point 1
	Pause Point 2	Conclusion	Pause Point 2	Conclusion
	Pause Point 3		Conclusion
	Conclusion

Related Activities and Extensions:

Rectangular Arrays

Another interesting activity is to have students, using square tiles or manipulatives, make all the possible rectangular arrays using first one tile, then two, then three, and so on, up to thirty (Figure 5). As they are making the arrays ask them to predict if any number from 1 to 30 will have more than one array. Will any have three or four arrays?

Have them copy the arrays on large grid paper and cut them out. Put the numerals from 1 to 30 on a wall and put the arrays under them.

1. Notice that some numbers have only one array but others have more than one. Why? [Those with only one array (except 1) are prime numbers. Those with more than one are composite numbers.]

2. How can the students describe the difference between even and odd numbers by looking at the array? [Group squares by 2’s. If there are none left over then it is even; if there is one leftover it is odd.]

3. If each array represents a product, how can we view the array to determine the set of factors? [If you look at the sides of the arrays, you will get all the factors for that number. For 8, the sides of the arrays are 1, 2, 4, and 8. Those are the factors of 8.]

4. If you need help with division, how can you use the arrays to visually get your answer? [In 12 ÷ 4, the students can look at the arrays for 12, find the one that has a side of 4 and see how many rows of 4 are in the array.]

5. How are 1, 4, and 9 special? [They all have a rectangular array that is a square so they are called square numbers.]

6. By looking at the arrays, can we find their common multiples? For example, what do you notice about 3, 6, and 9? [They all have an array with a side of 3; therefore, 3, 6, and 9 are all multiples of 3.]

Other Activities

1. Create arrays for the multiplication facts through the tens using concrete models.

2. Identify patterns in multiplication facts using concrete objects, pictorial models, or technology.

3. Use linear measure to find the perimeter of a shape.

4. Use square units to determine the area of shapes.

5. Measure to solve problems using length and area.

6. Identify prime factors of a whole number and common factors of a set of whole numbers.

7. Use concrete objects or pictures to make generalizations about determining all possible combinations of factors for a given number.

8. Use appropriate formulas to measure and to solve problems involving area.

9. Use tangrams to create different shapes that have the same area.