Stage 1 - addition and subtraction
Use a range of mental strategies including counting on from, counting back from, counting on and back, doubles, near doubles, bridging to ten; use a range of informal recording methods for addition and subtraction including jump and split strategies; record number sentences using drawings, numerals symbols and words; use the language of addition and subtraction.
- use a range of mental strategies including counting on from, counting back from, counting on and back, doubles, near doubles, bridging to ten
- use a range of informal recording methods for addition and subtraction including jump and split strategies
- record number sentences using drawings, numerals, symbols and words
- use the language of addition and subtraction.
Activities to support the strategy
Students need to recognise and use the terms ‘add’, ‘plus’, ‘is equal to’, ‘take away’, ‘minus’ and ‘the difference between’ to describe addition and subtraction. They also need to record number sentences using drawings, numerals, symbols and words. Students need opportunities to both pose and solve problems in addition and subtraction.
In Stage 1 the syllabus focuses on developing a range of mental strategies and informal recording methods for addition and subtraction. The following activities assist students in making connections between counting and addition and subtraction strategies and provide students with opportunities to demonstrate their understanding of place value and how numbers can be combined and partitioned.
It is important to present number sentence problems to students horizontally e.g. 34 + 49 =, this assists students in reading the numbers from left to right and will develop their understanding of place value and of how to read numbers. This will also provide students with opportunities to look at the whole number, not just the digits, assisting students with estimating the solution.
Activity 1 – language of mathematics
The Herrington Think Board is one way to organise and solve problems with students that also focuses on the language of mathematics.
- A process for understanding mathematics by Sue Gunningham (PDF 422.58KB) .
- For example, the teacher can supply the story “Mary had five oranges, Tom took two away, how many oranges does Mary have left?”
- Students can then draw a picture of the story, use objects such as counters or play dough to create and work out the problem, then record a number sentence that matches the story.
- To focus on the language, provide students with the number sentence and ask them to write a story to match.
Activity 2 – warm up activities
Short, focused, frequent activities are great ways to start or conclude a mathematics lesson. They are an opportunity to repeat skills that need to be practised.
Roll two dice and add
This is a whole class activity where students sit in a circle and two six-sided dice are thrown. Students share strategies for adding the numbers together. This activity can be played using subtraction and can be extended by changing the dice to eight- or ten-sided dice or by adding in a third dice. The third dice will provide opportunities for students to look for doubles, or friends of ten or to use known facts.
Students find today's date on the calendar, count how many days until the end of the month and work out the date 10 days later. Students explain strategies for their addition.
Hand addition pairs
Write a number on the board (less than 20). In pairs students make the number and record their combination. Ask how else they can make it.
Students are asked to come out the front and make a two-digit number e.g. 24 with their hands. Students soon realise they will need two others to help them. Do the same for another two-digit number e.g. 27. Students then discuss how to add the numbers e.g. grouping all the tens together then adding the ones, they will be able to make an extra ten from the 4 and 7, so the student with seven fingers up changes to ten (and joins the other tens) and the student with four changes to one. This activity assists students in understanding the place value of tens and ones and how to re-unitise numbers. You can record students’ strategies as they are explaining what they are doing. You can then move on to representing the numbers using unifix cubes in sticks as tens and loose blocks as ones. These strategies assist students in visualising the numbers.
Activity 3 – make 100
The teacher removes the picture cards (kings, queens, jacks) from a standard pack of playing cards. The Ace is used to represent one. In small groups, each student is dealt six cards. The aim of the activity is to add all six card numbers together to make the closest total to 100 (but no greater than 100). Each student can nominate one of their cards to be a 'tens' card.
For example, if the student was dealt
they could nominate the 7 card to have the value 70 and add the remaining cards for a total of 93. They should be encouraged to record their calculations and share their strategies.
Activity 4 – finding the difference
Students are given a number sentence with a missing element (using numbers less than 20) e.g.
Using unifix cubes, students work in pairs to make towers to represent the 13 and 5. They then compare the towers to work out the difference between the two towers. As a follow on activity, you can have students make the number differentiating between tens and ones using two colours. This will link to bridging to ten strategies.
- Developing efficient numeracy strategies Stage 1, 2003, 'Diffy Towers' pp. 119
Activity 5 – using a number line for difference
Use a 1 to 100 number line (commercially made, drawn on the board, created on the IWB or simply use a tape measure/one metre ruler). Mark the place of two numbers, for example 32 and 41 Have students come out and work out the difference between the two numbers. Be aware that although we generally relate difference to subtraction, some students will use a ‘count on’ not ‘count back’ strategy to solve the problem and therefore it can be related to addition as well. Have students write number sentence to match the working out.
- e.g. 41 – 32 = 9
Students can also write sentences using words to describe the working out. e.g. 'The difference between 32 and 42 is ten, so the difference between 32 and 41 must be nine.'
Linking to other strands
The concept of difference can also be explored when learning about length. Students can compare lengths and discuss the difference between the objects- either informally (for example, using paper clips) or formally (for example using centimetres).
“The ruler is longer than the pen. The rule is 12 cm and the pen is 9 cm. There is 3 cm difference between the objects.
ACMNA029: Explore the connection between addition and subtraction, ACMNA030: Solve simple addition and subtraction problems using a range of efficient mental and written strategies, ACMNA036: Solve problems by using number sentences for addition and subtraction.
MA1-5NA (+ & -) Uses a range of strategies and informal recording methods for addition and subtraction involving one – and two – digit numbers. MA1-8NA: P & A – Creates, represents and continues a variety of patterns with numbers and objects
NSW numeracy continuum
Aspect 2: EAS: Facile, Aspect 3: Pattern and Number Structure: Part whole to 10 and Part whole to 20, Aspect 4: Place Value: Ten as a unit; Tens and ones.
NSW literacy continuum
VOCC8M4: Vocabulary knowledge, Cluster 8, Marker 4: Recognises that different words can be used to describe similar concepts, e.g. everyday or technical language, synonyms.VOCC8M5: Vocabulary knowledge, Cluster 8, Marker 5: Shows evidence of capacity to improve vocabulary choices in response to purpose and audience when reviewing and editing writing.
Other literacy continuum markers
WRIC8M4 Aspects of writing, Cluster 8, Marker 4: Writes for a wider range of purposes, including to explain and to express an opinion.
Number Line Math: Practice addition and subtraction facts 1–10 using a number line as a tool for solving problems. Adjust the options to include any combination of Result, Change, or Start as the unknown quantity. Select the facts to practice.