Reasoning
Fractions - Sharing Brownies
Element
Reasoning
e
The learner
Demonstrates understanding
that the greater the number of
portions of a whole, the smaller the size of each equal share.
f
The learner
Justifies the ordering of fractions and whole numbers along a number line.
04.
g
The learner
Explains the role of the numerator and denominator.
Compares and orders unit fractions with the different
denominators.
h
The learner
Compares fractions, including equivalent
fractions, [proper, and mixed numbers]
and orders them on a number line.
i
The learner
Compares and orders fractions including
equivalent fractions, with different denominators and numerators on a number line.
J
The learner
Explains how the value of a fraction relates to the value/ size of the whole unit.
Language
Bigger, More, Smaller, Less than, The same as, Fewer
On Monday afternoon, you have some friends coming round. You have bought brownies for them to eat.
On Thursday, you have more friends round than you had on Monday, but you have the same number of brownies.
More or less brownies on Thursday compared to Monday?
Would your friends get more or less brownies on Thursday compared to Monday?
Agree with a partner
Lamon, S.J. (1999). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Lawrence Erlbaum Associates.
Click on the image to print
Brownie Thinking
Use ‘brownie’ thinking to solve other problems
Introducing notation
4 brownies between 6 friends: 4/6
4 brownies between 7 friends: 4/7
So which is bigger: 4/6 or 4/7?
Behr, M. J., Lesh, R., Post, T. R., & Silver, E. A. (1983). Rational-number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 91-126). New York, NY: Academic Press.
More Brownie Thinking.....
What kinds of brownie /people numbers give people 1 full brownie each?
3 brownies shared between 3 people, 4 brownies, 4 people, 15 brownies, 15 people, 89 brownies, 89 people
What kinds of brownie/people numbers give people half a brownie each?
With 4 brownies, how many people would you give each person half a brownie?
8 people, so 4/8 = 1/2
Mason, J.H. (1988). Specializing and generalizing together. In John Healey Mason (Ed.) Learning and Doing Mathematics (pp.22-37). Palgrave, London. https://doi.org/10.1007/978-1-349-09782-1_3
Watson, A., & Mason, J. (2002). Student‐generated examples in the learning of mathematics. Canadian Journal of Science, Mathematics and Technology Education, 2(2), 237–249. https://doi.org/10.1080/14926150209556516
Say it with brownies thinking.....
Put in order of size:
What kind of number of people would you give each person a really small bit of brownie?
Duval, R. (2017). Understanding the mathematical way of thinking – The registers of semiotic representations. https://doi.org/10.1007/978-3-319-56910-9
Tasks
1. What can you say about these six fractions
1/6, 1/25, 3/5, 3/20, 4/15, 5/8
2. Can you decide which fraction is largest and which is smallest?
3. Pick two fractions and say which one is larger.
4. Tell me another fraction that is equal to 3/5. And another?
5. Tell me another fraction that is equal to 5/8. And another?
6. Is the answer to 3/5 + 5/8 less than 1 or more than 1?
7. How can we work out the answer to 3/5 + 5/8?
Foster, C. (2014, 19 September). Lesson plan: KS4 Maths – Adding and subtracting fractions. https://www.teachsecondary.com/maths-and-science/view/lesson-plan-ks4-maths-adding-and-subtracting-fractions
