Frogs, Fleas and Painted Cubes - Investigation 2.2, Changing Dimensions
HW for Day 1 = None
HW for Day 2 – ACE #2 (2-31) – starts on page 38
In this Problem, you will explore what happens to the area of a square when
one or both of its dimensions change. You can use the Distributive Property
to write equivalent expressions for area in both factored from and expanded
form.
Problem 2.2 – The Distributive Property
A.
1.
2.
3.
4.
5.
6.
Each rectangle is the result of changing one or more dimensions of a
square. Each rectangle has been subdivided into two or four smaller
rectangles. Write two expressions for the area of the rectangle
outlined in red, one in factored form and one in expanded form.
B.
Use a rectangle model to write each expression in expanded form.
1.
(x + 3)(x + 5)
2.
(4 + x)(4 + x)
3.
3x(x + 1)
C.
Carminda says she doesn’t need a rectangle model to multiply (x + 3) by
(x + 5). She uses the Distributive Property.
1. Is Carminda correct? Explain what she did at each step.
2. Show how using the Distributive Property to multiply (x + 3) and (x + 5) is
the same as using a rectangle model.
F.
O.
I.
L.
D.
Use the Distributive Property to write each expression in expanded
form.
1. (x + 5)(x + 5)
2. (x - 4)(x + 3)
4. (2x + 1)(5 - x)
5. (n - 2)(n + 2)
E. Write each expression in expanded form.
1. (x + 7)2
2. (x – 7)2
3. (2n – 5)2
4. (2n + 5)2
5. After doing similar problems like these, Lydia claims that she sees a
pattern that would help her expand expression in less time. What
pattern do you think she observes?