Teaching and Group Activities for Understanding
Day 1 Teaching
Children enter 1 ÷ 3 = into a calculator. What’s the answer? What fraction is this decimal equivalent to? If we divide 1 into 3 equal parts, each is a one third; we write this as 0.333333; it repeats 3 forever. We call it a recurring decimal. Repeat for 2 ÷ 3 and 1 ÷ 7. Use a calculator to discover other unit fractions (denominator <10) that have recurring decimals.
-- Use a calculator to convert fractions to decimals by division; place the fractions on a 0–1 (or 0–2) line. Aim to get three fractions in a line without an opponent’s fraction in between.
Day 2 Teaching
Children enter 1 ÷ 3 into the calculator but don’t clear it. If you multiply this answer by 3, what should you get? Try it. What happens? The calculator is wrong! This is called a rounding error. Children predict whether the same thing will happen when dividing then multiplying by 4, 5 and 6.
-- Investigate divisors 2 to 10 (or 20) that will give rounding errors on the calculator.
-- Given the answer 1.181818 (13 ÷ 11), use a calculator to work out the mystery division. Set further similar problems for the group.
Day 3 Teaching
Write on the board the following questions: 675 + ☐ = 1000, 47.2 × ☐ = 283.2, 586.1 ÷ ☐ = 24.7, 84 ÷ ☐ = 7, ☐ − 6.795 = 4.615, 25 × ☐ = 1000; Find two consecutive numbers with a product of 2070; Find two numbers greater than 1000 with a difference of 75. Children discuss each question, in pairs, and decide whether or not they would use a calculator. Share reasoning. Set other problems.
-- Use a calculator to solve multiplication problems.
-- Use a calculator, trial and improvement and reasoning skills to aid problem solving.
Day 4 Teaching
Learn how to use the calculator’s memory button. Write the key sequence: 3 + 2 = M+ 3 × 4 = M+ MR. Children enter it. What did the calculator do? Did you notice the little M in the display? Repeat with similar key sequences, using the M+ and M− buttons to add and subtract to/from numbers in the calculator memory. How do we solve calculations with brackets?
-- Practise using the memory functions in multi-step calculations, including word problems.
-- Use the memory function to help solve a shopping-related multi-step calculation.
Day 5 Teaching
Write on the board this sequence of keys: 6 + 4 = M+ 4 + 2 = × MR = and ask children to work out what happens. Repeat with other sequences including division, e.g. 5 − 3 = M+ 6 + 4 ÷ MR =. Use the memory buttons to work out (32 + 35) ÷ (42 + 19).
-- Discuss given calculator key sequences. Compare estimates of answers with actual answers.
-- Use the memory function to help solve an area-related multi-step calculation.