Test solutions with the detailed point scale. Add up your points and spot what to review.
1 Computations / 4 pts
- \( 6 \times 3 = 18 \) (1 pt)
- \( \dfrac{4}{5} \times \dfrac{1}{2} = \dfrac{2}{5} \) (1 pt)
- \( \dfrac{5}{8} \times \dfrac{12}{5} = \dfrac{12}{8} = \dfrac{3}{2} \) (1 pt)
- \( \dfrac{7}{3} \times \dfrac{6}{7} = 2 \) (1 pt)
2 Reciprocals / 3 pts
- \( \dfrac{4}{9} \) (1 pt)
- \( \dfrac{1}{6} \) (1 pt)
- False: dividing by 4 means multiplying by \( \dfrac{1}{4} \), so \( \dfrac{3}{5} \div 4 = \dfrac{3}{20} \). (1 pt)
3 Bar model / 3 pts
- \( \dfrac{5}{6} \div \dfrac{1}{12} \) (1 pt)
- \( \dfrac{5}{6} \times 12 = 10 \) (1 pt)
- \( 10 \times \dfrac{1}{12} = \dfrac{10}{12} = \dfrac{5}{6} \) (1 pt)
4 Soup for the class / 4 pts
- \( \dfrac{7}{2} \div \dfrac{1}{4} = \dfrac{7}{2} \times 4 = 14 \) (1 pt). She can fill 14 bowls (1 pt).
- \( \dfrac{3}{4} \div 3 = \dfrac{3}{4} \times \dfrac{1}{3} = \dfrac{1}{4} \) (1 pt). Each student gets \( \dfrac{1}{4} \) liter (1 pt).
5 Interpreting quotients / 3 pts
- Greater, because the divisor \( \dfrac{2}{5} \) is less than 1. (1 pt)
- Less, because the divisor \( \dfrac{9}{8} \) is greater than 1. (1 pt)
- \( \dfrac{3}{4} \times \dfrac{8}{9} = \dfrac{24}{36} = \dfrac{2}{3} \) (1 pt)
6 Slow snail / 3 pts
- \( \dfrac{3}{10} \div \dfrac{1}{4} = \dfrac{3}{10} \times 4 = \dfrac{12}{10} = \dfrac{6}{5} \) (1 pt). Speed: \( \dfrac{6}{5} \) m/h, that is 1.2 m/h (1 pt).
- \( 3 \div \dfrac{6}{5} = 3 \times \dfrac{5}{6} = \dfrac{15}{6} = \dfrac{5}{2} \), so 2.5 hours (1 pt).
Test yourself: quick challenge for Grade 6
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