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Does that make sense in the story? Front-loading formative assessment during problem solving

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Frog Farming Farmer Mead would like to raise frogs. She wants to build a rectangular pen for them and has found 36 meters of fencing in her barn that she’d like to use. 1.Design at least four different rectangular pens that she could build. Each pen must use all 36 meters of fence. Give the length and width for each of the pens. 2.If each frog needs one square meter of area (1 m 2 ), how many frogs will each of your four pens hold?

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Notes:

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Notes:

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One Implementation Kids notice and wonder about scenario on projector: Think-Write-Share Reveal the question & pass out copies Teacher calls on one student to review what we are being asked to find Students work in their usual small groups to solve the problem

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Frog Farming Farmer Mead would like to raise frogs. She wants to build a rectangular pen for them and has found 36 meters of fencing in her barn that she’d like to use. She knows each frog needs one square meter of area (1 m 2 ).

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They noticed & wondered We notice…We wonder… Farmer Mead would like to raise frogs Why does she want to raise frogs? She wants to build a penWhat is a frog farmer? She has 36 meters of fencingHow big is the pen? Each frog needs one square meter of area Why do frogs need one square meter of area? The frog is greenHow many frogs does she have? Farmer Mead is a girl The fencing is in her barn The pen is rectangular

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What do we anticipate?

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The ones who were stuck Student Situation: Some students couldn’t get started – they could identify one fact “She used 36 meters of fence.” Teacher Action: Tell students, “Right, that means the perimeter is 36 meters.”

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The ones who were stuck Student Response: When 36 meters of fence was changed to “the perimeter is 36 meters” the students stayed stuck and didn’t use any strategies for finding side lengths give perimeter

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The ones who took forever Student Situation: Some students used guess and check drawing different rectangles to find ones that used 36 meters of fencing. It was taking forever… Teacher Action: Remind students of a hint: “The first step is to divide it [the perimeter] in half. What is half of 36? Can you find two numbers that add to 18?”

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The ones who took forever Student Response: When given the hint to “divide it in half” students start looking for four numbers that add to 18 because they look at their picture and remember rectangles have 4 sides.

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Those who couldn’t do Part 2 Student Situation: Some students couldn’t start Part 2. They could identify one fact “Each frog needs 1 square meter of area.” Teacher Action: Say, “Great, what do square meters measure? Area? Yes! Now you need to find the area of each pen you came up with in Part 1.”

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Those who couldn’t do Part 2 Student Response: When told to find area to solve Part 2, the students stop working and raise their hands to get more help: “I know how to find area but I don’t get what that has to do with how many frogs can fit in the pen.”

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How would you coach the teacher?

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What we tried next period Student Situation: only knew “she uses 36 meters of fence” Teacher Action: Confirm that matches the story, ask them to find a way she might have used the fence. Student Response: draw rectangles and triangles and label them so they add up to 36 (or did with some adjustment).

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What we tried next period Student Situation: guessed and checked inefficiently Teacher Action: We got the group back together to list possibilities in an organized way – LW 108 99 810 711 Student Response: the whole class almost instantly started yelling out all the other possibilities as soon as they saw our organization

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What we tried next period Student Situation: only knew “each frog needs 1 square meter of space” Teacher Action: Ask for guesses and reasons about how many frogs could fit in this pen. Student Response: Make guesses that all show wrong thinking – 36 frogs fit in each pen, 9 frogs fit in each pen since each frog “takes up” 4 meters of perimeter.

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What we tried next period Teacher Follow-Up: Invite students to use a drawing to show how many frogs will fit. Initial Response:

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What we tried next period But then… “I did it this way but I wasn’t supposed to. It should be 45 frogs but I drew the boxes too small. All I had to do was multiply.” “I can just multiply these! 6 rows and 12 columns of frogs is 72 frogs!”

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Reflections? Questions?

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Growing Worms [#5143] In the land of Trianglia, the worms are made of isosceles right triangles – and they grow fast! As you can see above, a worm that is 1 day old is made of 4 of these triangles. You can also see worms that are 2 days old and 3 days old. If that growth rate remains constant, how many triangles will be needed for a 4-day-old worm? a 10-day-old worm? a 63-day-old worm?

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How will you know they’re ready? What do you hope they notice? Hard words? What questions do you want them focused on? Thorny points they may disagree on?

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Watching Tasks What activities or general questions does Val use to get students sense-making and telling her about their thinking? What are you learning about the students? What else do you want to know about them to help them get ready? Reflections? Predictions? Tweet #ncsm163 to share as you watch, if you want!

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See Webpage for Video http://mathforum.org/nctm/2014/session163.html

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Final Reflections Something you saw that you’d like to implement or support a teacher to implement An insight into good questions or techniques for learning about students’ thinking while keeping them moving forward Other take-aways? Questions?

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Activities for sense-making Can you draw a picture? Pen vs. Pen Can you act it out with materials? What materials would you need? http://mathfour.com/general/10-questions-to- ask-about-a-math-problem http://mathfour.com/general/10-questions-to- ask-about-a-math-problem Pick one to do with your group!

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More activities for sense- making Students paraphrase the problem Students use guessing to show what they already know Ask questions like, “What’s the story about?” “What’s the action in the story?” “Does that make sense in the story?” “Can you check if that matches what it says in the story?”

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