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Maths · Grade 6 · Set A
When One Changes, So Does the Other
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A
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Goal: 15 min
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Remember: A table, a graph and an equation can all show the same steady change.

Tables, graphs and equations

1
Mia bikes at a steady speed. In the table, t is her hours and d is her miles. How many miles after 4 hours?
2
What equation gives d from t?
d = t + 6d = 6td = t ÷ 6
3
Mia's miles are d = 6t, with t in hours. How many miles after 5 hours?
4
In Mia's table, t is her hours and d is her miles. Which variable changes because the other one changes?
t, the hoursd, the miles
5
Tickets cost the same each. In the table, n is tickets and c is dollars. Which graph matches?
Graph 1
Graph 2
Graph 3
6
In d = 6t, when t goes up by 1, d goes up by 6.
TrueFalse
7
Leo's cost is c = 9n dollars for n tickets. Then 4 tickets cost 13 dollars.
TrueFalse
8
Leo's cost is c = 9n dollars. How many tickets cost 45 dollars?
9
Join each equation to its story. Ava earns p dollars for h hours.
  1. 1p = 2h
  2. 2p = 5h
  3. 3p = 2h + 6
  4. 4p = 5h + 2
  • A2 dollars for each hour
  • B5 dollars for each hour
  • C6 dollars at the start, then 2 each hour
  • D2 dollars at the start, then 5 each hour
10
Ava's pay is p = 2h + 6, with h in hours. How many dollars after 3 hours?
11
What equation gives p from h?
p = 6h + 2p = 2h + 6p = 8h
12
The graph shows Mia's ride, d = 2t. Across is hours t and up is miles d. What does point P tell us?
After 4 hours, she has gone 2 miles.After 2 hours, she has gone 4 miles.She bikes 6 miles in all.
13
Write how the table, the graph and the equation d = 6t tell the same story about Mia's ride.
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Answer key · Set A
When One Changes, So Does the Other
124 Each hour adds 6 miles: 6, 12, 18, 24.
2d = 6t Each row is 6 times t: 6 × 1, 6 × 2, 6 × 3, 6 × 4.
330 d = 6 × 5 = 30.
4d, the miles The miles depend on the hours, so d is the dependent variable. We choose t first.
5Graph 3 Across is n and up is c. The table says 1 ticket costs 3 and 2 tickets cost 6: the points (1, 3) and (2, 6).
6True Each extra hour adds 6 more miles.
7False c = 9 × 4 = 36 dollars, not 13.
85 9 × 5 = 45.
91-A, 2-B, 3-C, 4-D The number beside h is the change for each hour. The number added on is what she starts with.
1012 2 × 3 = 6, and 6 + 6 = 12.
11p = 2h + 6 At 0 hours she has 6, and each hour adds 2.
12After 2 hours, she has gone 4 miles. P is 2 across and 4 up: 2 hours and 4 miles.
13Your own words: a grown-up reads it.
Mark each answer, count the right ones and write the score on the sheet.