Please do the following exercises, you should follow the instructions carefully. I have uploaded **12.1** and **12.2** for you but for **12.3** I haven’t upload it but you can find it from the textbook below.

12.1 #1 (a, b, c, d, g), #4 (a-d), #12 (a-e), #15 (a-b)

12.2 #1 (c, f, h), #4 (a-d), #14

12.3 #2 (a-d), #11 (a,b), #12 (c)

Name of the Textbook:

Reconceptualizing Mathematics for Elementary School Teachers, 3rd Edition

by Sowder, Sowder & Nickerson (2017). You should be able to find it online.

12.1

1. Evaluate and then express each of the following statements as a general property, using

variables. Give the name of the property.

a. (18 × 93) + (18 × 7) can be calculated mentally and exactly by 18 × (93 + 7).

b. 12 nickels plus 8 nickels has the same penny value as 20 nickels.

c. (231 + 198) + 2 can be calculated exactly by 231 + (198 + 2).

d. (17 × 25) × 4 can be calculated mentally and exactly by 17 × (25 × 4).

g. Each of 4 pockets has a dime and 7 pennies. Calculate the total value in two ways.

4. The following problems are typical of those asked in grade school. Express each one using

an equation with one variable:

a. Malia has $2.30 but wants to buy a movie ticket, which costs $4.00. How much more does

she need?

b. Leesha had 8 stuffed animals and received 3 more. How many does she have now?

c. Jeremy downloaded 6 songs from iTunes onto his iPod. He already had 360 songs on his

iPod. How many songs does he have on his iPod now?

d. Regis is a teacher. He bought 10 boxes of colored markers for his students. Each box has 12

markers. He packages them into bags for each of his 30 students. If each student gets the same

number of markers, how many markers are in each bag?

12. Use an array, a rectangular area, a number line, or base-ten blocks to model each of these

properties for a particular instance.

a. distributive property of multiplication over addition: 7 × (44 + 6) = 7 × 44 + 7 × 6

b. associative property of addition: 96 + 21 = 96 + (4 + 17) = (96 + 4) + 17

c. commutative property of multiplication: 17.4 × 3.5 = 3.5 × 17.4

d. associative property of multiplication: (4 × 3) × 6 = 4 × (3 × 6)

e. commutative property of addition: 314+838=838+314

15. Following is a child’s description of his or her computation of 21 × 15.

▶ To find twenty-one times fifteen, I multiply 20 × 15 because that is easy. Two times fifteen is

thirty, so for twenty I add a zero and get three hundred. But I need one more than twenty. Three

hundred and one! ◀

a. If the child is using correct logic, discuss what property he or she may be recognizing and

describing. If the child is making an error, describe what property he or she appears not to

understand.

b.Model the child’s correct thinking or use the model to show the correct thinking.

12.2

1. For each pattern, give the next four entries and any particular entry requested, as suggested

by the pattern. Assume that the patterns continue indefinitely.

c. 6.5, 7.3, 8.1, 8.9, ___, ___, ___, ___; the 20th entry is ____.

f. 5, 2.5, 1.25, 0.625, ___, ___, ___, ___

h. 12,23,34,45, ___, ___, ___, ___; the 100th entry is ____.

4. Use the equation (nth term) = a + (n − 1)d for an arithmetic sequence starting with a and

having a common difference d to find each of the following numbers:

a. the 500th number in the sequence, 10, 14, 18, 22, 26, . . .

b. the 25th number in the sequence, 634,712,814,9,…

c. the first number in an arithmetic sequence that has a common difference of 5 and 257 as its

51st term

d. the first number in an arithmetic sequence that has a common difference of 4.5 and 466 as

its 101st term

14. An investment increases at a rate of 1.03 each year. If the original investment is $500, what

is the investment worth after 10 years?

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