An Introduction to Proportion – Part 1, Easy
An Introduction to Proportionality – Part 1, Hard
1. Circle “Yes” or “No” for the following to show whether they are likely to be
1. Circle “Yes” or “No” for the following to show whether they are likely to be
proportional or not:
proportional or not:
The number of people and the amount of socks worn.
Yes
No
The amount of syrup and its total sugar content.
th
A man’s age and the number of ears he has.
Yes
No
The number of 7 grade students and noise emitted.
The number of sheep and amount of available wool.
Yes
No
The amount of teeth a woman has and her number of grey
The number of cats in a household and the amount of cat
Yes
food served every evening.
hairs.
No
A countries’ rainfall and the number of plants per square
2. Complete the tables below considering zero and the first six natural numbers for
each of the following:
kilometre.
Yes
No
Yes
No
Yes
No
Yes
No
2. Explain why an accurate table with specific values can’t be made for a boy’s height
a. Number of squares (not adjacently placed, separate to each other) and number
and his age.
of edges:
# of squares
3. Think of a pair of variables, 𝑥 and 𝑦 that the table below may consider. (A range
# of edges
of possible answers exists.)
b. Number of tricycles and number of wheels:
# of tricycles
𝒙
0
1
2
3
4
𝒚
0
6
12
18
24
# of wheels
c.
4. Give a reason as to why the two variables below are not proportional to one
If the squares in the question above were adjacently placed, give a general
another.
statement about the relationship between both variables.
3. Circle “Yes” or “No” for the following to show whether 𝑥 and 𝑦 are proportional
𝒙
0
1
2
3
4
𝒚
2
7
32
58
84
or not:
𝑦 = 5𝑥
Yes
No
𝑥+𝑥 = 𝑦
Yes
No
2𝑥 − 7 = 𝑦
Yes
No
𝑥 = 5(2 − 𝑦)
Yes
No
𝑦 2⁄
3
Yes
No
𝑥 = √𝑦 + 3
Yes
No
𝑥=
5. Does the equation 𝑥 = 2⁄𝑦 imply that 𝑥 and 𝑦 are proportional or not? Give a
reason as to how you know this.
An Introduction to Proportionality, Part 2
An Introduction to Proportionality, Part 2
1. Please answer the questions below and provide an assumption for each.
a. If two pencils cost 150 Yen, how much do six pencils cost?
1. Please answer the questions below and provide an assumption for each.
a. If two pencils cost 150 Yen, how much do six pencils cost?
Assumption:
Assumption:
b. Yuki ran 100 metres in 13 seconds. How long did it take Yuki to run 10 metres?
b. Yuki ran 100 metres in 13 seconds. How long did he take to run 10 metres?
Assumption:
c.
Assumption:
If a cat eats a 150g fish in 30 seconds, how long would it take to eat a 200g
c.
If a cat eats a 150g fish in 30 seconds, how long would it take to eat a 200g
fish?
fish?
Assumption:
Assumption:
d. Which of the statements above is the least realistic for the given answer to be
true?
true?
2. If two variables 𝑥 and 𝑦 have the relationship 𝑥 = 4𝑦 2, are 𝑥 and 𝑦 directly
proportional? Explain why or why not.
3. State whether 𝑥 and 𝑦 are directly proportional if 3𝑦 =
2. If two variables 𝑥 and 𝑦 have the relationship 𝑥 = 4𝑦 2, are 𝑥 and 𝑦 directly
proportional? Explain why or why not.
4𝑥
3
. Show how you know
this.
4. Let 𝑦 ∝ 𝑥. As 𝑦 increases by 24, 𝑥 increases by 6. Write down their relationship
by stating an equation in the form 𝑦 = 𝑘𝑥.
d. Which of the statements above is the least realistic for the given answer to be
3. State whether 𝑥 and 𝑦 are directly proportional if 3𝑦 =
4𝑥
3
. Show how you know
this.
4. Let 𝑦 ∝ 𝑥. As 𝑦 increases by 24, 𝑥 increases by 6. Write down their relationship
by stating an equation in the form 𝑦 = 𝑘𝑥.