Patters and Relations Review
1. The pattern rule that relates the input to the output is: Divide the input
by 3, then subtract 2
a. Check the data in the table. Identify any output numbers that are
incorrect. How do you know they are incorrect?
b. Write the Input Pattern Rule.
c. Write the Output Pattern Rule
d. Write the next 4 input and output numbers.
Input
6
9
12
30
45
51
Output
0
1
3
8
15
17
2. The table shows the input and output for this machine.
a. Write the pattern rule that relates the input to the output.
b. Choose 4 different input numbers that are not on the chart. Find
the output for each.
c. Predict the output when the input is 23. Check your prediction.
Input
3
5
7
9
11
13
15
Output
15
27
39
51
63
75
87
3. In a bobsled race, teams of 4 people race to the finish for the
best time.
a. Make a table to show the numbers of people in a race
when 2, 3, 4, 5 and 6 teams are entered.
b. Write a pattern rule that relates the number of people to
the number of teams entered.
c. Write an expression to represent this pattern.
d. Use the expression to find the number of people when 13 teams are entered. How can you
check your answer?
PR = divide by 4
Exp = P÷4
13= P÷4
13 x 4= 48 48÷4= 13
Teams
1
2
3
4
5
6
4. Label a coordinate grid. Plot each point on the grid. How do you decide which scale to use on
the axes? Describe how you move from R to S, T to U and V to R
R (20, 3)
S (5, 18)
T (25, 30)
U(35, 0)
V(10, 24)
People
4
8
12
16
20
24
5. a. Draw a pattern to model the data in the table. Extend the
pattern to Figure 10.
b. Graph the data in the table.
c. Describe the relationship shown on the graph.
d. Write an expression to represent the pattern.
e. Find the number of shapes in the 21st figure. Which strategy did
you use? Why?
6. Rewrite each expression using a commutative property.
a. 30 x 5
b. 87 + 35
c. 53 + 12
d. 7 x 14
7.
a.
b.
c.
d.
Input
1
2
3
4
5
6
7
e. 22 x 6
Output
0
5
10
15
20
25
30
f. 44 + 22
For each equation below:
Draw the equation using squares and rectangles
Show the preservation of equality. Make sure to use a different operation for each equation.
Draw the preservation of equality using squares and rectangles
15-3=12
5x2 = 12-2
4+4=8
48 ÷ 6 = 15-7
8. For each equation below:
- Apply the preservation of equality to write an equivalent for of the equation. Use a different
operation for each.
- Draw the equation to check.
a. 8b = 16
b. t = 7
c. 15 = 3r
d. 50 = 5q