Divide and Conquer

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Purpose

This is a collection of activities to enhance and extend division skills and understanding.

Achievement Objectives
NA4-1: Use a range of multiplicative strategies when operating on whole numbers.
Specific Learning Outcomes

solve problems using multiplication and division facts
use divisibility rules
use place value strategies to solve division problems
use distributive property to solve equations
use rounding and compensating to solve division problems

Description of Mathematics

Basic Facts, AM (Stage 7)

Required Resource Materials
Practice exercises with answers (PDF or Word)
Activity

Prior Knowedge

Multiplication and division basic facts

Multiply by 10s and 100s

Background

This activity provides students with practise using their basic multiplicaiton and division facts.  It requires students to use their knowledge to explore a range of strategies to solve problems involving division.

Comments on the Exercises

Exercise 1: Lucky Dip

Asks students to work out which numbers from a set of numbers are divisible by 100, 10, 5, 2 and 3.

Exercise 2: Pick a Pair

Asks students need to select some numbers from a given list to complete ivision sentences. They are expected to do any working that is required to find the answer ‘in their head’.  It involves divsion with mutliples of 10 and 100, for example 560 ÷  = 80.
 

Exercise 3: Find the Family

Asks students are to write division facts from given sets of numbers.  They are required to create as many division equations as they can using these numbers

Exercise 4: Multiplication Squares

Asks students to use reversibility and recognise the factors of numbers up to 10 × 10 to complete the multiplication squares.

Exercise 5: Divadagons

Asks students to complete divadagons by recognising the factors of numbers up to 10 × 10.

Exercise 6: Multiples and Factors

Asks students to explore the divisibility patterns that result from comparing the multiples of sets two different numbers.
They are asked to find lowest common multiples and highest common factors of pairs of numbers and then use this knowledge to explore relationships between other pairs of numbers.
As an extension exercise a generalisation is sought.

Exercise 7: Fun with Factors

Asks students to solve problems that involve knowledge of factors, multiples and primes.

Exercise 8: Do it in your head

Asks students to practise their division skills by doing the calculations mentally and using a place value, for example 355 ÷ 5.

Exercise 9: Division by Partitioning

Asks students to work out the answer to a division problem by partitioning the number into multiples of the divisor that are easy to work with. For example, 72 ÷ 4 = (40 ÷ 4) + (32 ÷ 4) = 10 + 8 = 18

Exercise 10: Division Using Tidy Numbers

Asks students to round numbers to a tidy number and then compensatie to do division problems. For example, 114 ÷ 6 = (120 ÷ 6) - 1 = 19.

Exercise 11: Dividing and Dividing

These exercises enable students to practice doing division by dividing by a pair of factors of the divisor. For example, 72 ÷ 4 = 72 ÷ 2 ÷ 2. This strategy enables students to do many divisions easily in their heads.
Knowledge of halving is required including halving odd numbers.

  • Divide by 4 by halving and halving again.
    Verify this by paper folding. Fold a piece of paper into two equal pieces and then fold again into tow into pieces. The results I four equal pieces so dividing by 2 and dividing by 2 again is equivalent to dividing by 4.
  • Divide by 6 by dividing by 2 and then dividing by 3 or dividing by 3 and then dividing by 2.
    Once again this can be verified by paper folding.
  • Divide by 3 and then divide by 4 is the same as dividing by 12
  • Divide by x then divide by y is the same as dividing by xy

Exercise 12: Copymaster - Div4Grid

Asks students to match word problems to number sentences. There are 6 matching tasks based on Numeracy Project Book 6 (Revised Ed) page 5 and are designed to illustrate the different types of division problem.

  • Equal groups – division by sharing
  • Equal groups – division by measuring/grouping
  • Rate - division by sharing
  • Rate – division by measuring/grouping
  • Comparison - division by sharing
  • Comparison - division by measuring/grouping

The numbers used are straightforward as the tasks are intended to assist students in identifying the type of division problem involved.
Material can be copied on to light card and laminated before cutting out the 24 pieces.

Suggestions for using the “Div4Grid” cards:

  • Group cooperative activity
  • Individual self assessment task
  • Material for creating written “notes” on division

Exercise 13: If You Know …

Asks students to use a given division fact to work out the answer to a connected division fact.

Exercise 14: Target

Asks students to arrange the given numbers to form a division problem whose answer is as close as possible to the target number. Students need to recognise multiples of the target number.

Exercise 15: Number Squares

Asks students to practice recognising factors of numbers to complete the number squares. 1 – 5 involve factors of numbers below 100.

Related Activities

Game 1: Copymaster - Dominoes

This set of dominoes is designed to practise division strategies. Some of the numbers are quite difficult but students should be encouraged to work without a calculator and explore a range of mental strategies.

Game 2: Copymaster - Division Matching Cards

This game involves activities for students to use independently of the teacher to practice number properties

There are 20 “Matching Cards” each with 3 parts

  • statement of a division problem eg 80 / 10 = ?
  • equivalent multiplication problem eg 10 x ? = 80
  • solution eg ? = 8

The “Matching Cards” need to be photocopied on to light card and cut out.
Students could work in pairs or small groups to match the sets of 3 cards for each problem.

Game 3: Copymaster --4 in a Row

This game requires students to practise mental division and multiplication
Players select a pair of factors and calculate their product. A counter is placed on the resulting product on the game board.
Players alternate turns and the winner is the first player to have four counters in a row horizontally, vertically or diagonally.
Equipment required: 2 ten sided dice, counters, game board

Game 4: Copymaster - Remainders 4 in a Row

This game requires students to practise mental division and calculating remainders.
Players select a pair of factors and calculate their product. A counter is placed on the resulting product on the game board.
Players alternate turns and the winner is the first player to have four counters in a row horizontally, vertically or diagonally.
Equipment required: 2 ten sided dice, counters, game board

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Level Four