Year Four - Modeling with Unit Fractions
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About this Big Idea
In this Big Idea students explore fractions as numbers and use a number line to locate fractions in reference to other numbers. Students are invited to play with fractions to see that they represent one number, not two as is often misconceived.
Understanding Goals:
Students will understand:
- that fractions represent a number and a relationship between numerator and denominator
- the need for fractions of units in measurement and other practical situations
- the mathematical concept of area
Background:
Fractions are used in different ways: to describe equal parts of a whole; to describe equal parts of a collection of objects; to denote numbers (eg is midway between 0 and 1 on the number line); and as operators related to division.
Core Content from the Syllabus:
Working Mathematically
Fractions
- model fractions with denominators of 2, 3, 4, 5 and 8 of whole objects, shapes and collections using concrete materials and diagrams
- count by quarters, halves and thirds, including with mixed numerals; locate and represent these fractions on a number line
- recognise that as the number of parts that a whole is divided into becomes larger, the size of each part becomes smaller (Reasoning)
Language:
- whole, part, equal parts, half, quarter, eighth, third, sixth, fifth, tenth, hundredth, one-sixth, one-tenth, one- hundredth, fraction, numerator, denominator, whole number, number line, length, area
Connected to:
Mindset Mathematics Learning Activities
Visualise
In this activity, students build a number line of fractional values as their own unit of measure. Students will measure objects and use fractions as values on a number line. - See page 118
Questions for reflection:
- What challenged you in this activity? How did you respond to that challenge?
- We all measured and used the same process to develop our measuring strip. If we measure the same object with two different measuring strips, will the measurements be the same?
- Did the items you measured match your measuring tape exactly? If not, what did you do?
Play
In this activity, students use tangrams to build fractions less than, equal to, and greater than a whole in different ways. Students discuss how determining what fraction each piece of the tangram set represents helps them build larger fractions. - See page 124
Questins for reflection:
- What do you notice? How did you go about generating squares? What strategies did you develop?
- How did the fractions help you build the squares?
- How did you modify your solutions to create new squares? (Students might have used equivalence to swap pieces out. Be sure to highlight this kind of thinking.)
- What was the most creative or interesting square you made? Why? What is the most creative or interesting square someone else made? Why?
- What makes a fraction easier or harder to build? Share some examples to support your thinking.
Investigate
In this investigation, students work on puzzles that relate fractions and area. Students look for unit fractions inside a grid where the fractional parts are shaded squares of a picture. They will form rectangles to break the picture into smaller pieces where the shaded squares represent the unit fractions they are looking for. - See Page 132
- What strategies did you use to solve the puzzle?
- Did your strategies change as you solved more puzzles?
- Were some puzzles more challenging? Why?
- What do you need to do to prove you have a solution?
- What strategies did you find helpful when solving these fraction puzzles?
Credit:
Boaler, Munson & Williams (2018) - Mindset Mathematics: Visualizing and investigating big ideas Grade 5
NESA - Mathematics K-10 - 2012
