Adding in Parts

Purpose

These exercises and activities are designed for students to use independently to practise number properties.

Achievement Objectives
NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
NA4-2: Understand addition and subtraction of fractions, decimals, and integers.
NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
NA3-6: Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality.
NA4-2: Understand addition and subtraction of fractions, decimals, and integers.
Specific Learning Outcomes
solve addition problems with whole numbers by adding in parts
solve addition problems with decimnal numbers by adding in parts
use equal addition strategies to insert numbers to balance addition equations
use equal addition strategies to insert numbers and letter symbols to balance algebraic equations 
Description of Mathematics

Addition and Subtraction, AA and AM (Stages 6 & 7)

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

Prior knowledge

Split a whole number into parts eg. 8 = 5 + 3, 27 = 25 + 2
Make numbers up to a tidy number
Add and subtract tenths to make a decimals number into a whole number

Background

This activity uses partitioning to help solve addition problems.  One number is split or partitioned so one of its parts forms a tidy number with the number it is being added to e.g. 28 + 14 = 28 + 2 + 12 = 42.  The activity uses this strategy with whole numbers and decimal numbers.  The activity develops an understanding of equality in equations.  Using the equal additions strategy students are asked equations are true e.g. 68 + 34 = 70 + 32  and to complete equations so they are balanced.  Symbols are used in equations so students can generalise the equal additions strategy e.g. 38 +  = 36 + Δ,  the  is 2 less than Δ.
 

Comments on the Exercises

Exercise 1
Add on to a two digit number by splitting one number into parts.

Exercise 2
Add on to a three digit number by splitting one number into parts.
 
Exercise 3
Add tenths to get a whole number.

Exercise 4
Add decimal numbers with one decimal place by making one number into a whole number and adjusting the other number.

Exercise 5
Recognise true statements based on adjusting one number up and the other number down.

Exercise 6
Find the missing number to make a true statement based on adjusting one number up and the other number down.

Exercise 7
Write their own true statement and describe the relationship between the new numbers. For example 38 +  = 36 + Δ, what is the relationship between  and Δ.

Exercise 8
Asks students to decide if statements using <, >, and = are true or false.
 
Exercise 9
Generalise the relationship by using a variable with a number

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