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##### Ontario Alignment By Overall Expectation

## Solving Equations to Find Radius Given Area of a Circle

As Justin Levack (LearnBlended.com) and I were planning for our GECDSB Middle Years Collaborative Inquiry Learning Fair recently, we realized that we were missing a math related activity that could model a simple real world situation and how it relates to mathematics from grade 7 to 9. With both of us learning more each day about serving up a well-designed 3 act math task, we came up with an idea in about 15 minutes even though we didn’t have a particular learning goal in mind.

## Act 1: Introducing The Problem

### Snipping the Straws

The first act of this task shows me cutting straws on camera at random lengths and in no particular order.

After giving some time for a chat with a partner/group, have students share out their thoughts in regards to where we might go with this question.

Some of the responses we received from teachers at the Middle Years Collaborative Inquiry Learning Fair included:

- Fractions and percents
- Proportions and ratios
- What’s the length of the straw?
- Why are we doing this???
- Grouping like lengths
- Who’s got the other half of my straw?
- Fractions and representing a whole
- Addition statements for fractions
- Geometric shapes
- Angles
- Patterning
- Percentages, fractions, decimals
- Ratios and rates
- Division of Fractions
- How many straws would it take to cover the table?
- What is the radius of the table?
- How can we use the straws to make art?

The next time I use this task in a professional development session for teachers, I intend to be more clear asking for teachers to state specific questions rather than just topics. I may have left the question too open for teachers to give “topics” rather than particular questions. By giving specific questions, I think this forces one to think deeper about the situation and the topic as it relates to math.

## Act 2: Reveal Some Information

### Revealing the Direction of the Task

After a good chat and share-out with the group, you can reveal the question to be explored in this case with some important information:

At this point, I hand out a piece of a “snipped straw” to each participant.

Given the length of a straw (20 cm) and the area of the circular banquet tables at the Ciocairo Club where we hold our board Professional Development sessions, the students (or teachers, in this case) must determine:

What is the length of your snipped straw?

## Act 3: Reveal the Answer

### Show the Diameter / Radius of the Table

In our case, the diameter of the table was 72 inches or 182.88 cm. Working on grabbing a photo of the table with the measuring tape. However, it is impossible to show each participant their solution as each straw cut is different.

## Sequels: Extending the Problem

### Other Questions to Answer

- Can you find your partner?
- Could you find your partner without using any math?

If you have participants match up with their partner, they can then check to see if they are correct by using an “uncut” straw to see if their two pieces equal an uncut straw.

Have you tried the problem? How did it go? How did you change it? Let us know in the comments section.

Here are some photos of teachers trying the problem at our Middle Years Collaborative Inquiry Learning Fair:

## New to Using 3 Act Math Tasks?

Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

## Share With Your Learning Community:

## About Kyle Pearce

I’m Kyle Pearce and I am a former high school math teacher. I’m now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.

Access Other Real World Math Tasks

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Grade 3 [3.B1.5, 3.B2.1, 3.B2.3, 3.B2.7, Measurement - M1, Number Sense and Numeration - NS1, Number Sense and Numeration - NS3]

Grade 4 [4.B2.1, 4.B2.4, 4.E2.5, 4.E2.6, Measurement - M1, Number Sense and Numeration - NS1, Number Sense and Numeration - NS3, Patterning and Algebra - PA2]

Grade 5 [5.B1.7, 5.B2.9, 5.D1.3, 5.D1.6, 5.E2.6, 5.F1.2, 5.F1.5, Measurement - M1, Measurement - M2, Number Sense and Numeration - NS1, Number Sense and Numeration - NS3, Patterning and Algebra - PA2]

Grade 6 [6.B2.12, 6.B2.9, Data Management and Probability - DP3, Measurement - M1, Measurement - M2, Number Sense and Numeration - NS1, Number Sense and Numeration - NS2, Number Sense and Numeration - NS3, Patterning and Algebra - PA1, Patterning and Algebra - PA2]

Grade 7 [7.B1.3, 7.B1.4, 7.B1.7, 7.B2.2, 7.B2.3, 7.C1.1, 7.C1.2, 7.C1.3, 7.C1.4, 7.D1.6, Data Management and Probability - DP3, Geometry and Spatial Sense - GS1, Measurement - M1, Measurement - M2, Number Sense and Numeration - NS1, Number Sense and Numeration - NS2, Number Sense and Numeration - NS3, Patterning and Algebra - PA1, Patterning and Algebra - PA2]

Grade 8 [8.B1.4, 8.B2.5, 8.C1.1, 8.C1.2, 8.C1.3, 8.C1.4, Data Management and Probability - DP1, Data Management and Probability - DP3, Geometry and Spatial Sense - GS2, Measurement - M1, Measurement - M2, Number Sense and Numeration - NS1, Number Sense and Numeration - NS2, Number Sense and Numeration - NS3, Patterning and Algebra - PA1, Patterning and Algebra - PA2]

Grade 9 [9.B3.5, 9.C3.1, 9.C3.2, 9.C3.3]

Kindergarten [k.15.1, k.15.10, k.15.2]

MAP4C [Mathematical Models - MM1, Mathematical Models - MM2, Mathematical Models - MM3]

MAT1LMAT2LMBF3C [Data Management - DM1, Data Management - DM2, Geometry and Trigonometry - GT1, Geometry and Trigonometry - GT2, Mathematical Models - MM1, Mathematical Models - MM2, Mathematical Models - MM3]

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MHF4U [Characteristics of Functions - CF3, Exponential and Logarithmic Functions - EL2, Exponential and Logarithmic Functions - EL3]

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MPM2D [AG1, AG2, AG3, QR2, Quadratic Relations - QR3, Quadratic Relations - QR4, T2, T3]

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Geometry [G-C.5, G-C.8, G-C.9, G-GMD.3, G-GMD.4, G-GPE.4, G-GPE.5, G-GPE.7, G-MG.1, G-MG.2, G-SRT.11]

Grade 1 [1.NBT.4, 1.OA.1, 1.OA.6, 1.OA.A.1, 1.OA.B.3, 1.OA.B.4, 1.OA.C.5, 1.OA.C.6]

Grade 2 [2.NBT.5, 2.NBT.B.5, 2.NBT.B.8, 2.NBT.B.9, 2.OA.2, 2.OA.A.1, 2.OA.B.2]

Grade 3 [3.MD.C.5, 3.NBT.2, 3.NF.1, 3.NF.2, 3.NF.3, 3.NF.A.1, 3.OA.1, 3.OA.5, 3.OA.9]

Grade 4 [4-MD.3, 4.MD.1, 4.MD.2, 4.NBT.6, 4.NF.3, 4.NF.5, 4.NF.6, 4.OA.1, 4.OA.5]

Grade 5 [5.B1.7, 5.D1.3, 5.D1.6, 5.MD.1, 5.MD.3, 5.MD.4, 5.MD.5, 5.NBT.2, 5.NBT.3, 5.NBT.6, 5.NBT.7, 5.NF.1, 5.NF.2, 5.NF.3, 5.NF.4, 5.NF.5, 5.OA.1, 5.OA.2, 5.OA.3]

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