Does that make sense in the story?

Does that make sense

in the story?

Front-loading formative assessment

during problem solving

Frog Farming

Farmer Mead would like to raise frogs. She wants to Farmer Mead would like to raise frogs. She wants to build a rectangular pen for them and has found 36 build a rectangular pen for them and has found 36 meters of fencing in her barn that she’d like to use.meters of fencing in her barn that she’d like to use.

1.1.Design at least four different rectangular pens that Design at least four different rectangular pens that she could build. Each pen must use all 36 meters of she could build. Each pen must use all 36 meters of fence. Give the length and width for each of the fence. Give the length and width for each of the pens.pens.

2.2.If each frog needs one square meter of area (1 mIf each frog needs one square meter of area (1 m22), ), how many frogs will each of your four pens hold?how many frogs will each of your four pens hold?

Notes: Notes:

Notes: Notes:

One Implementation

Kids notice and wonder about scenario on Kids notice and wonder about scenario on projector: Think-Write-Shareprojector: Think-Write-Share

Reveal the question & pass out copiesReveal the question & pass out copies

Teacher calls on one student to review what Teacher calls on one student to review what we are being asked to findwe are being asked to find

Students work in their usual small groups to Students work in their usual small groups to solve the problemsolve the problem

Frog Farming

Farmer Mead would like to raise frogs. Farmer Mead would like to raise frogs.

She wants to build a rectangular pen for them She wants to build a rectangular pen for them and has found 36 meters of fencing in her barn and has found 36 meters of fencing in her barn that she’d like to use.that she’d like to use.

She knows each frog needs one square meter of She knows each frog needs one square meter of area (1 marea (1 m22).).

They noticed & wonderedWe notice… We wonder…

Farmer Mead would like to raise frogs

Why does she want to raise frogs?

She wants to build a pen What is a frog farmer?

She has 36 meters of fencing How big is the pen?

Each frog needs one square meter of area

Why do frogs need one square meter of area?

The frog is green How many frogs does she have?

Farmer Mead is a girl

The fencing is in her barn

The pen is rectangular

What do we anticipate?

The ones who were stuck

Student Situation: Student Situation: Some students couldn’t get Some students couldn’t get started – they could identify one fact “She started – they could identify one fact “She used 36 meters of fence.”used 36 meters of fence.”

Teacher Action:Teacher Action: Tell students, “Right, that Tell students, “Right, that means the perimeter is 36 meters.”means the perimeter is 36 meters.”

The ones who were stuck

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

The ones who took forever

Student Situation: Student Situation: Some students used guess Some students used guess and check drawing different rectangles to find and check drawing different rectangles to find ones that used 36 meters of fencing. It was ones that used 36 meters of fencing. It was taking forever…taking forever…

Teacher Action: Teacher Action: Remind students of a hint: Remind students of a hint: “The first step is to divide it [the perimeter] in “The first step is to divide it [the perimeter] in half. What is half of 36? Can you find two half. What is half of 36? Can you find two numbers that add to 18?”numbers that add to 18?”

The ones who took forever

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

Those who couldn’t do Part 2

Student Situation: Student Situation: Some students couldn’t Some students couldn’t start Part 2. They could identify one fact “Each start Part 2. They could identify one fact “Each frog needs 1 square meter of area.”frog needs 1 square meter of area.”

Teacher Action: Teacher Action: Say, “Great, what do square Say, “Great, what do square meters measure? Area? Yes! Now you need to meters measure? Area? Yes! Now you need to find the area of each pen you came up with in find the area of each pen you came up with in Part 1.”Part 1.”

Those who couldn’t do Part 2

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

How would you coach the

teacher?

What we tried next period

Student Situation:Student Situation: only knew “she uses 36 only knew “she uses 36 meters of fence”meters of fence”

Teacher Action:Teacher Action: Confirm that matches the Confirm that matches the story, ask them to find a way she might have story, ask them to find a way she might have used the fence. used the fence.

Student Response:Student Response: draw rectangles and draw rectangles and triangles and label them so they add up to 36 triangles and label them so they add up to 36 (or did with some adjustment). (or did with some adjustment).


Student Situation: Student Situation: guessed and checked inefficiently guessed and checked inefficiently

Teacher Action:Teacher Action: We got the group back together to list We got the group back together to list possibilities in an organized way – possibilities in an organized way –

LL WW1010 8899 9988 101077 1111Student Response: Student Response: the whole class almost instantly the whole class almost instantly started yelling out all the other possibilities as soon as started yelling out all the other possibilities as soon as they saw our organizationthey saw our organization


Student Situation: Student Situation: only knew “each frog needs only knew “each frog needs 1 square meter of space”1 square meter of space”

Teacher Action: Teacher Action: Ask for guesses and reasons Ask for guesses and reasons about how many frogs could fit in this pen. about how many frogs could fit in this pen.

Student Response: Student Response: Make guesses that all show Make guesses that all show wrong thinking – 36 frogs fit in each pen, 9 wrong thinking – 36 frogs fit in each pen, 9 frogs fit in each pen since each frog “takes frogs fit in each pen since each frog “takes up” 4 meters of perimeter. up” 4 meters of perimeter.


Teacher Follow-Up: Teacher Follow-Up: Invite students to use a Invite students to use a drawing to show how many frogs will fit. drawing to show how many frogs will fit.

Initial Response:Initial Response:


But then…But then…

““I did it this way but I wasn’t supposed to. It I did it this way but I wasn’t supposed to. It should be 45 frogs but I drew the boxes too should be 45 frogs but I drew the boxes too small. All I had to do was multiply.” small. All I had to do was multiply.”

““I can just multiply these! 6 rows and 12 I can just multiply these! 6 rows and 12 columns of frogs is 72 frogs!”columns of frogs is 72 frogs!”

Reflections? Questions?

Growing Worms [#5143]

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

How will you know they’re

ready?What do you hope they notice?What do you hope they notice?

Hard words?Hard words?

What questions do you want them focused on?What questions do you want them focused on?

Thorny points they may disagree on?Thorny points they may disagree on?

Watching Tasks

What activities or general questions does Val use What activities or general questions does Val use to get students sense-making and telling her about to get students sense-making and telling her about their thinking?their thinking?

What are you learning about the students? What What are you learning about the students? What else do you want to know about them to help them else do you want to know about them to help them get ready?get ready?

Reflections? Predictions?Reflections? Predictions?

Tweet Tweet #ncsm163#ncsm163 to share as you watch, if you to share as you watch, if you want!want!

See Webpage for Video

http://mathforum.org/nctm/2014/http://mathforum.org/nctm/2014/session163.htmlsession163.html

Final Reflections

Something you saw that you’d like to Something you saw that you’d like to implement or support a teacher to implementimplement or support a teacher to implement

An insight into good questions or techniques An insight into good questions or techniques for learning about students’ thinking while for learning about students’ thinking while keeping them moving forwardkeeping them moving forward

Other take-aways?Other take-aways?

Questions?Questions?

Activities for sense-making

Can you draw a picture?Can you draw a picture?

Pen vs. PenPen vs. Pen

Can you act it out with materials? What Can you act it out with materials? What materials would you need?materials would you need?

http://mathfour.com/general/10-questions-to-ask-about-a-math-problem

Pick one to do with your group!Pick one to do with your group!

More activities for sense-making

Students paraphrase the problemStudents paraphrase the problem

Students use guessing to show what they Students use guessing to show what they already knowalready know

Ask questions like, “What’s the story about?” Ask questions like, “What’s the story about?” “What’s the action in the story?” “Does that “What’s the action in the story?” “Does that make sense in the story?” “Can you check if make sense in the story?” “Can you check if that matches what it says in the story?”that matches what it says in the story?”

Documents

Does that make sense in the story?