MATH​ ​(The Crow and the Pitcher and Review Problems) Just as you did with last summer’s homework, your first job is to skim through the entire assignment and make some decisions about how best to tackle it. We would certainly recommend splitting the work out over several sessions rather than tackling it all at once. Spend approximately two hours on Section 1 (The Crow and the Pitcher), following the instructions in that section. Spend about two to three hours working on the problems in Section 2. (Please call or email one of the math teachers if you have been working in a focused manner for more than three hours and are not finished.) Work neatly and carefully on graph paper, remembering to record the original problem in each case. Staple your work together, ​in order​ (if we have to tell you to write your name on the first page, we are going to weep). ​Check your work! Section 1: The Crow and the Pitcher “The Crow and the Pitcher” helps to make concrete the connections between the math we have been studying and what we will be exploring in greater depth. We will be using the following experiment to help guide us through our first days back in the fall. You should spend about two hours carefully setting up, conducting the experiment, cataloging and organizing your collected data, answering the questions, and displaying your information. Please do your work on graph paper, working neatly and labeling accurately. Optional work: You may choose to carefully and thoughtfully create a poster that clearly documents your experimentation. It should include (but is not limited to) a data table, a well-­crafted and labeled graph, and any conclusions you have made based on your results. If you wish to include photographs of your process and equipment, please do so. Section 2: Algebraic and Arithmetic Review
1. Write another expression equal to each of the following:
a.
𝑦 + 𝑦 + 𝑦 + 𝑦
b.
3𝑧 ∙ 3𝑧 ∙ 3𝑧
c.
(𝑥 − 7) + (𝑥 − 7) + (𝑥 − 7) + (𝑥 − 7)
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2. Simplify the following expressions. Remember the order of operations.
a.
(
b.
40 ÷ 2 − 2 × 5
c.
|
d.
72 ÷ 6 ÷ 4
e.
f.
)(
| |
(
(
)
|
)
)
+ ÷ −
3. Apply the distributive rule to the following expressions:
a.
3(𝑥 + 4)
b.
−𝑦(𝑥 − 5)
c.
(3z2 – z)z
d.
21𝑥 + 7
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4. Show the expressions that represent the area and the perimeter of each of the
following figures:
a.
y+4
y
b.
5x +3
3
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(Do problems 5 & 6 only if you have encountered these sorts of problems already in
Chapter 4 of Jousting Armadillos.)
5. Find the greatest common factor of 45, 72, & 10.
6. Find the least common multiple of 3x, 15x², & 21x³.
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7. Decimals:
a. 1.23 +3.14
b. 0.33 + 6.014 + 6.7
c. 5.47 − 3.26
d. 72.31 − 14.62
e. 302.4 − 6.91
f. 5.84 × 0.17
g. 75.15 ÷ 0.15
h. 36.08 ÷ 0.4
i.
0.7218 ÷ 0.009
j.
3.216 ÷ 0.04
k. 5.575 ÷ 0.025
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8. Fractions and Mixed Numbers. Express your answers in simplest form:
a.
2 +3
b.
1 +2
c.
5 +7
d.
3 −1
e.
4
f.
17
−2
−2
g.
×
h.
3 ×2
i.
j.
k.
÷6
÷
3 ÷1
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9. Percentages:
a.
Express 0.57 as a percentage.
b.
Express
c.
Express 0.78 as a percentage.
d.
Express 35% as a fraction in simplest form.
e.
What is 20% of 180?
f.
15 is what percent of 75?
as a percentage.
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10. Arithmetic word problems:
a.
A recipe calls for cups of raisins to make 2 dozen cookies. How many cups
of raisins are needed to make one dozen cookies?
b.
Greg spent 15% of his money on a new backpack. If the backpack cost $120,
how much money does he have left?
c.
Greg walks 3 miles on Saturday and 2 miles on Sunday. How much farther
did he walk on Saturday than on Sunday?
d.
Ren had $364.34 in her bank account. After she wrote checks to the electric
company for $48.19 and to the water company for $54.96, how much did
she have left in her account?
e.
Doreen is planning to put a fence around her rectangular garden. If she
knows the area is 816 square feet and one side measures 17 feet, how long
is the other side?
f.
Linus earned $1260 selling weasels at the fair. If he has to give 25% of his
earnings to fair owners, how much many does Linus get to take home?
g.
Doreen bought a box of donuts. of them were chocolate, were strawberry,
and of the remainder had sprinkles. If there were 25 donuts with sprinkles,
how many donuts were there altogether?
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