(Approximately: 3- 60 minute lessons)
NOTE: This lesson focuses primarily on the concept of "fair sharing". If students have a fragile understanding of comparing and ordering fractions, begin with this set of lessons :
https://docs.google.com/document/d/1CpPmrohuL4jE6x1pjVO8UQIaCKHj1fOh0ZWGHxUGgi0/edit?usp=sharing
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Number Sense:
B1.5 use drawings and models to represent, compare, and order fractions representing the individual portions that result from two different fair-share scenarios involving any combination of 2, 3, 4, 5, 6, 8, and 10 sharers
Partitioning to make equal-sized areas is a fundamental skill students need to build their understanding of fractions and area models. In this task, rather than use a ruler, students must find other ways to determine equal partitions and may discover paper folding is a key strategy. The ability to fold and consider both the number of folds as well as the regions created involves spatial reasoning and making predictions – both of which help students better understand fractions, proportions and how to equally partition area models.
develop understanding of fractions by sharing a pan of brownies with friends, where the whole is the pan of brownies and the fractional amounts are equal-sized regions of the whole;
develop understanding that the number of shares affects the size of the portions – i.e., a larger number of shares results in a larger digit in the denominator which corresponds with a smaller equal-sized region.
I use a range of paper folding strategies (horizontal, vertical, diagonal folds or a combination of these);
I double-check to be sure the regions are equal sized areas;
I predict what the next number might be, such as sixteenths;
I can use a halving strategy to get eights from fourths;
I persist with developing the partitions for tenths by further partitioning the eighths;
I use creative strategies for sharing portions which may include cutting off and redistributing regions.
If students have a fragile understanding of comparing and ordering fractions, begin with this set of lessons :https://docs.google.com/document/d/1CpPmrohuL4jE6x1pjVO8UQIaCKHj1fOh0ZWGHxUGgi0/edit?usp=sharing
In this lesson, students use paper folding to partition a pan of brownies (a sheet of rectangular paper) into equal portions (first four, then eight, then ten) through a simple story line told by the teacher.
Explain to students: “Here is your pan of brownies (outline of brownie pan on chart paper) and here is your brownie (show construction paper rectangle). You need to share the pan of brownies among yourself and three other friends (four people all together).”
Give students time to paper fold, or partition the brownie into four equal portions. Ask students to describe how they folded the paper to get four equal portions
Ask the group to pause: “Oh no! The doorbell rang and now four more friends have shown up. They want some brownie too. Use the same size pan of brownies and share equally among eight people.” Let them know that there are extra brownie sheets if the students wish to start fresh.
Give students time to paper fold or partition the brownie into eight equal portions. Then ask the group to share how they partitioned the pan of brownies to get eight equal portions.
State the next scenario: “Oh no! Two more friends arrived, now you need to partition the pan of brownies into ten equal portions.” Remind the students that there are extra brownie sheets if they wish to start fresh. Allow them to paper fold or partition the brownies into ten equal portions. Students may need to attempt several different strategies before arriving at an appropriate solution.
To consolidate, ask students “What fraction of the whole pan does each person get?” and discuss how this can be counted (e.g., 1 one-tenth, 2 one-tenths, 3 one-tenths, etc. arriving at 10 one-tenths).
How did you partition your brownies?
How do you know everyone got the same amount?
What fraction of the whole pan does each person get? What happens to the size of the brownie portions as more people arrive at the party?
