Stage 3 - addition and subtraction
Use a range of mental strategies for addition and subtraction; round numbers to assist in estimating answers
- use a range of mental strategies for addition and subtraction
- round numbers to assist in estimating answers
Activities to support the strategy
Activity 1: addition strategies
1.Review some of the strategies that can be used when adding or subtracting numbers, e.g. split strategy, bridging to ten and jump method.
Work through examples of each strategy.
Pose this problem:
Tom’s house is 456 metres from his school. The shops are 560 metres beyond the school. How far is it from Tom’s house to the shops?
Present the following strategies that three different students used to solve the problem.
- explain each of these strategies by working through each step
- determine which strategy they would use to solve the problem.
2.Provide other examples of strategies used to solve addition problems and have students explain the strategy used, e.g.
4 210 + 432 = 4 210 + 400 + 30 + 2
= 4 610 + 30 + 2
= 4 640 + 2
= 4 772
3.Give students a copy of the grid below (or similar) which has a variety of numbers less than 100.
Students find all the groups of two or three numbers, side by side, across or down, which can be added together to total 100. Colour these groups, using a different colour for each group.
Encourage students to use a range of mental strategies to add the numbers, such as:
- adding the tens first, then the ones – split strategy
- bridging to ten
- adding the tens onto the first number, then the ones – jump method.
Students report back and identify some of the groups of numbers that added to 100 and the strategies they used.
Activity 2: estimation
When calculating, students should be encouraged to work out the approximate answer they should get.
Students brainstorm examples of when estimating an amount is recommended. Give details about two examples, e.g. estimating the cost of a holiday, estimating the total cost of the weekly food shopping at the supermarket.
1. Discuss strategies for estimating such as rounding off a number before adding or subtracting.
Work through this example of rounding to estimate an answer.
Say: The answer to 628 + 51 + 326 should be approximately 1010.
2. Have students work through other examples of rounding numbers when completing addition problems to estimate the answer. They can then check how accurate their estimate is by using a calculator or written strategies.
Activity 3: human society and its environment
Background learning: The Murray-Darling river system of Australia is one of the most important river systems of the world.
Students use the Murray-Darling Basin Authority website to research aspects of this river system and its commercial and environmental significance.
- use an atlas or web search to research the length of different rivers of the world.
- rank the rivers according to length.
- calculate the difference between the Murray-Darling river system and both the longest and shortest rivers on the list.
- pose other numeracy questions for the students to solve using the information contained in the table.
Future teaching point
The Murray-Darling basin provides a relevant topic for HSIE Stage 3 to locate and describe patterns of human involvement in an environmental area of Australia. Students may also identify how some aspects of religious and other belief systems can affect the way in which groups interact with the environment, e.g. the spiritual significance of the Ganges River in India.
ACMNA123: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers
MA3-5NA: Selects and applies appropriate strategies for addition and subtraction with counting numbers of any size.
NSW numeracy continuum
Aspect 4: Place Value – System Place Value.
NSW literacy continuum
VOCC12M2: Vocabulary knowledge, Cluster 12, Marker 2: Increasingly uses appropriate content vocabulary when creating spoken and written texts about specific topics.
Other literacy continuum markers
VOCC12M4: Vocabulary knowledge, Cluster 12, Marker 4: Draws on knowledge of word origins to work out meaning of new words.