Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 What is $10 halved twice?
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$2.50.
2 If 7 × □ = 84, write the value of the square, and then the value of the triangle if △ + □ = 30.
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□ = 12 and △ = 30 − 12 = 18.
3 A number is doubled and then 6 is added, giving 20. What was the number?
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7.
Level 2 · Core
4 Each star and each heart has a fixed value.What is the value of one star?
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20 − 13 = 7.
5 $1.25 is the result of halving an amount three times. Write the amount after one doubling, and the amount at the start.
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$2.50, then $5, then $10.
6 What is 117 ÷ 14, written as a whole number of groups? Give just the number of groups.
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8 groups, with 5 left over.
Level 3 · Challenge
7 Consider the sentence "117 shared between 14, with 5 left over".1 117 = 14 × 8 + 5 is correct.
2 117 = 14 × 7 + 19 gives the right total.
3 117 = 14 × 7 + 19 is a correct way to write the sharing.
Which statements are correct?
2 117 = 14 × 7 + 19 gives the right total.
3 117 = 14 × 7 + 19 is a correct way to write the sharing.
Which statements are correct?
Show worked solution
14 × 8 + 5 = 117 ✓ (1 ✓). 14 × 7 + 19 = 98 + 19 = 117, so the total is right (2 ✓). But a remainder of 19 is bigger than 14, so another group would fit — it does not describe the sharing (3 ✗). 1 and 2.
8 Each star and heart has a fixed value: ★ + ★ + ♥ = 20 and ★ + ♥ = 13. Write the value of a star and the value of a heart.
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A star is 7 and a heart is 6. Check: 7 + 7 + 6 = 20 ✓.
9 An amount of money is halved three times and $1.25 is left. How many dollars were there at the start?
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$1.25 → $2.50 → $5 → $10.