Year Five - Estimating With Fractions
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About this Big Idea
In this Big Idea students develop their understanding of fractions by estimating the area of a shape that has been removed or is occupied by a particular feature in an image. Students use estimation and explore how this can be a powerful tool for mathematical understanding.
Understanding Goals:
Students will understand:
- the value of making informed estimates to mathematical reasoning.
- fractions, relationships between fractions and the size represented by fractions.
Background:
In Stage 3 Fractions and Decimals, students study fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12 and 100. Fractions may be interpreted in different ways depending on the context.
Core Content from the Syllabus:
Working Mathematically
Fractions
- model, compare and represent fractions with denominator of 2, 3, 4, 5, 6, 8, 10, 12 and 100 of a whole object, a whole shape and a collection of objects
- compare and order unit fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12 and 100
- compare the relative size of fractions drawn on the same diagram
- compare and order simple fractions with related denominators using strategies such as diagrams
- compare the relative value of unit fractions (Communicating, Reasoning)
- investigate and explain the relationship between the value of a unit fraction and its denominator (Communicating, Reasoning)
Area
- establish the relationship between the lengths, widths and areas of rectangles (including squares)
Language:
- whole, equal parts, half, quarter, eighth, third, sixth, twelfth, fifth, tenth, hundredth, thousandth, one-thousandth, fraction, numerator, denominator, mixed numeral, whole number, proper fraction, improper fraction
Connected to:
Mindset Mathematics Learning Activities
Visualise
Students begin to think about estimating with fractions by making paper snowflakes and developing strategies for estimating the portion of paper they have cut away. - See page 55
Questions for reflection:
- How close do you think your estimates are? Why? Do you think your estimates are over or under the actual fraction that is missing?
- How could you check your estimate or make it more precise?
- What do you think was the most effective (or interesting) strategy for estimating the fraction of paper that was cut away? Why?
Play
Students extend their work with snowflakes to develop strategies for cutting away a specific fraction of the paper. The class creates a snowflake display they can use to discuss fraction estimation strategies and patterns. - See page 61
Questions for reflection:
- What strategies did you come up with for making a snowflake with a target fraction of paper removed?
- Which fractions were harder or easier? Why?
- What was hard about targeting an estimate?
- What makes a fraction easier or harder to estimate?
Investigate
Students pose fraction estimation questions using photographs of collections and aerial images. Partners investigate their questions and develop strategies for fraction estimation. - See page 67
Questions for reflection:
- What strategies did you invent? What strategies would you like to hear more about?
- What connections do you notice between the different strategies that we used?
- Did you find yourself using different strategies for different questions? When were different strategies useful?
- How were these strategies similar to or different from the strategies we used with snowflakes?
- What fraction questions are you wondering about now? What kinds of questions would you want to investigate if you could ask questions outside your school?
Above and Below: Suggested images for this investigation. Students could estimate what fraction of the image is a particular colour or shape and then develop strategies to improve the accuracy of their estimate.
Image 1, 2 & 3 - Floor tiles from Duomo di San Martino in Lucca (Photo by Nigel Coutts) Image 4 - Sheep dog - shared from Twitter (Photo by Unknown)
Left Image: Braided River in Iceland (Photo by Andre Ermolaev)- Middle Image: Drone photo of Mumbai (Blue roofs are tarpaulins) - (Photo by Johnny Miller) Right Image: - Centre Pivot Irrigation (Source - Unknown)
Credit:
Boaler, Munson & Williams (2018) - Mindset Mathematics: Visualizing and investigating big ideas Grade 5
NESA - Mathematics K-10 - 2012
