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Multiplication and Division
Objectives
To calculate divisions using beaded lines.
To understand division as the inverse of multiplication.
Resources
Abacus Workbook 2 | 📄 0–30 beaded line | 📄 Division cards
Vocabulary
division | divide | inverse
Today's Lesson
What to Get Ready
Print and cut out the 📄 Division cards.
Introduction
Write: 20 ÷ 5 = ___ 
Ask:
- What does this number sentence ask us to do?
Agree that this is asking us to find how many lots of 5 there are in 20.
Using the 📄 0–30 beaded line, ring 20 and model drawing hops of 5 until you reach zero, so modelling division as repeated subtraction, the inverse of multiplication, which is repeated addition.
Count the hops to find that 20 ÷ 5 = 4, that is, there are four 5s in 20.
Ask your student to say the matching multiplication too: 4 × 5 = 20, four lots of five is 20.
Use objects to model and explain how these operations are the inverse of one another, that is, repeatedly add groups of 5 to an array until you reach 20 (5, 10, 15, 20: 4 lots of 5 is 20); then repeatedly subtract groups of 5 from an array until you reach 0 (15, 10, 5, 0: 20 divided into groups of 5 is 4 groups).
Repeat with 12 ÷ 2 and 25 ÷ 5, modelling and narrating saying, ‘I start at the ‘big’ number to be divided (the ‘dividend’), then draw hops back along the line in groups of the smaller number (the ‘divisor’) until I can’t make any more groups.’
Remind your student that multiplication and division are inverse operations: they are the opposite of one another. If we know one, it can help us remember the other.
Main Activity
Ask your student to pick a prepared card from the 📄 Division cards (dividing by 2, 5 or 10).
They should draw the hops onto a beaded line to find the answer: start with the ‘big’ number to be divided (the ‘dividend’), then draw hops back along the line in groups of the smaller number (the ‘divisor’) until you can’t make any more groups.
Write the inverse (matching) multiplication.
Workbook
To help your student build upon their learning from today, please ask them to complete the activities on page 57 of Abacus Workbook 2.