Compatible numbers to 20

Purpose

These exercises and activities are for students to use independently of the teacher to practice number properties. Some of these activities would be suitable for homework. Others require follow-up during teaching sessions.

Specific Learning Outcomes
know compatible numbers to 20
use <, >, = symbols
solve addition problems using addition basic facts to 20
solve word problems using basic facts
Description of Mathematics
Basic Facts, AE (Stage 5) 
Addition and Subtraction, AE (Stage 5)

 

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

Prior knowledge

Recall the compatible numbers to 10
Solve problems with small numbers using a part-whole strategy
Recall "10 and" facts

Background

Many of these activities parallel those in “compatible numbers to 10”. They are designed for students who already have their facts to 10, but need to extend these to 20. However, these students may or may not have had exposure to the algebra aspects of those activities, so they have largely been repeated here. The teaching notes for “compatible numbers to 10” contain information about some significant teaching points embedded in both sets of exercises, so will not be repeated here, but should be accessed and read prior to using these activities.

Comments on the Exercises

Exercise 1
Asks students to identify equations that sum to 20. This exercise is split into 3 parts. The final part has sentences “written in reverse”. Students often think the equals sign means “work out the answer”, so this part is designed to help students realise that the equals sign means that the statements on either side are identical or balance. This understanding is essential for the development of algebra.
When reviewing this exercise with students it can be useful to ask students “why” some of the problems are false, or do not equal 20. For example, students may come up with reasons like “as both of the numbers are less than 10, then the total must also be less than 20”.
 
Exercise 2
Asks students to identify single digits additions are <. > or = to 20.
This exercise is in two parts, the second part again reverses the sense of the problems so the sum is on the right of the symbol. This is more challenging and will need to be discussed as part of relevant teaching before setting these problems. In this second set of problems students are doing the reverse of comparing a sum to 20. Rather, they are comparing 20 to the results of their calculation. This reverse sense can be problematic as the students are using inequalities, so may want to use the incorrect sign. Reading the sentence in reverse can alleviate this problem.
 
Exercise 3
Asks studetns to use compatible numbers to 20 to solve equations.This exercise looks to develop students’ understanding of algebraic notation.
 
Exercise 4
Asks students to solve problems involving algebraic notation.  Students are introduced to notation to show multiplication operations.  Examples use simple doubles e.g. 2  = 60.
 
Exercise 5
Asks students to solve equations using compatible numbrs to 20.
 
Exercise 6
Asks students to look at the links between addition and subtraction in a formal manner.  Before getting students to work on this exercise, it may pay to introduce a word problem or two, and explore students’ solution strategies, as this is likely to elicit both subtractions and additions. The formal use of notation to link these sentences can then be introduced and explored. A follow-up to this exercise is to pose the following question.Can any subtraction be changed into an addition, and can any addition be changed into a subtraction? Can you prove this? Your teacher will need to be convinced by any explanation or proof that you come up with.
 
Exercise 7
Asks students to solve word problems using compatible numbers to 20.

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