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Maths · Grade 6 · Set C
Two-Step Expressions
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C
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Goal: 15 min
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Remember: A letter holds the place of a number. Work out the brackets first, then multiply, then add.

Say it with a letter

1
Which one says: 3 more than twice a number n?
3n + 22n + 32(n + 3)
2
Which one says: twice the sum of a number n and 3?
2(n + 3)2n + 3n + 6
3
If n is 5, then 2n + 3 is .
4
If x is 4, then 3(x + 2) is .
5
A tape has three parts of x and one part of 5. Which expression gives the whole length?
3(x + 5)3 + x + 53x + 5

Tables, formulas and stories

6
What rule does the table follow?
x + 53x + 12x + 3
7
The table follows the rule 3x + 1. What number goes in the empty box?
8
2n + 3 and 5n are the same for every number n.
TrueFalse
9
Pizzas cost p dollars each. Join each story to its expression.
  1. 1Dad buys 3 pizzas and a drink for 2 dollars.
  2. 2Dad pays with a 20 dollar bill for 3 pizzas. How much change?
  3. 320 dollars is shared equally by p friends.
  4. 4Each pizza is cut into 8 slices. How many slices in p pizzas?
  • A3p + 2
  • B20 − 3p
  • C8p
  • D20 ÷ p
10
A rectangle is l long and 3 wide. Which expression gives the distance around it?
2l + 6l + 33l
11
Which pair of expressions are equal for every number n?
n + n and n²n + n and 2nn + 2 and 2n
12
Mia has 4 boxes with b stickers in each box and 7 loose stickers. If b is 6, how many stickers does she have?
13
Write a story that fits 5n + 2. Say what n stands for.
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Answer key · Set C
Two-Step Expressions
12n + 3 Twice n is 2n, and 3 more than that is 2n + 3. Try n = 5: twice 5 is 10, and 3 more is 13.
22(n + 3) The sum n + 3 comes first, so it goes inside the brackets, and then it is doubled.
313 2 × 5 = 10, and 10 + 3 = 13.
418 The brackets first: 4 + 2 = 6. Then 3 × 6 = 18.
53x + 5 Three parts of x is 3x, and then there is one part of 5: 3x + 5.
63x + 1 Try 3x + 1: 3 × 2 + 1 = 7, 3 × 4 + 1 = 13 and 3 × 6 + 1 = 19. The rule x + 5 fits 2 → 7 but not 4 → 13.
716 x is 5, so 3x + 1 is 3 × 5 + 1 = 16.
8False They match only for some numbers. For n = 2, 2n + 3 is 7 but 5n is 10.
91-A, 2-B, 3-D, 4-C Each story tells which operation to use with p.
102l + 6 The distance around is l + 3 + l + 3, which is 2l + 6.
11n + n and 2n n + n is two n's, which is 2n. But n² means n × n, and n + 2 is not 2n.
1231 4b + 7 with b = 6: 4 × 6 = 24, and 24 + 7 = 31.
13Your own words: a grown-up reads it.
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