Three-act math tasks
Tips to be successful:
How Many Cookies Will Fit?
Day 1 Time: 35 minutes
Overview
For this activity we will be watching the beginning of a video clip, day one. Students will use special reasoning, and arrays to estimate ‘How many cookies will fit?’ Introduce the context of the conflict visually, then ask the central question
and collect estimates.
Materials
Math journals, pencil, or pen
Key Words
Estimating, think time, planning, research
Teaching Plans
Introduction
WATCH
Dane Ehlert's When Math Happens blog:
Watch Day 1:
https://whenmathhappens.com/2014/03/04/cookies/
ASK
DISTRIBUTE
Recording sheet:
this handout or
https://gfletchy.files.wordpress.com/2013/09/3-act-recording-sheet1.pdf
OPTION
Students might do research at home, there are multiple directions students could extend this.
Task
ASK
1. How many cookies will fit?
2. Write down a guess.
INDEPENDENTLY
Students will write down and document all the observations and questions.
SHARE
Students can share their results and wonderings.
Wrap Up
REFLECT
What questions do you still have about this problem?
What would happen if you changed the size of the pan?
Boaler, Jo (2015). Mathematical Mindsets.
Day 2 Time: 35 minutes
Overview
Common Core Standards 3.MD.C
Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Students will continue to estimate and plan their solution, creating think time. It is likely that some students did ‘research’ at home, including asking their parents to bake cookies.
Materials
SMARTboard to view the video and their math notebooks. Some students will request more materials: rulers, the measurement of the cookie sheet, directions for the cookie
Key Words
Estimating, think time, planning, research, spacing, spread, recipe, directions
Teaching Plans
Introduction
WATCH
ACT 2- https://whenmathhappens.com/2014/03/04/cookies/
REVIEW
Yesterday’s predictions. Watch the video again, stopping a few seconds in.
ASK
· What information would be useful to figure this out?
· Write down some questions you have in your head right now.
DISTRIBUTE
Math journals, (and rulers, recipe, measurements and photo of cookie sheet, if requested,) and/or this handout
OPTION
Students are welcome to do research at home
Task
SURVEY
Ask how many cookies do you think will fit.
TOGETHER
Talk about results of the survey.
Students collaborate to list necessary resources and ask questions.
Student should chart their results.
SHARE
Share findings and next steps
OPTION
Students can continue to do research prior to Act 3.
Wrap Up
SHARE
Collaborate and discuss how this kind of problem happens in the real-word.
DISCUSS
Day 3 Time: 35 minutes
Overview
This is Act-3 and the day of the reveal, students will get to see the entire video and see that 16 cookies (4 x 4) fit on the cookie sheet. On the third day students will confirm their results against the actual video and talk about why they were accurate or not, and talk about what surprised them and think critically as to how their solution compares to the real-world scenario, and account for the disparities. Give theories and explantions for how and why 16 fit on the tray, and all the variables for making it that way.
Materials
SMARTboard (video), paper, pencil
Key Words
Estimating, think time, planning, research, spacing, spread, recipe, directions
Teaching Plans
Introduction
WATCH
Final video:
https://whenmathhappens.com/2014/03/04/cookies/
REVIEW
Review the results and compare the results with what happened.
DISTRIBUTE
Paper or this handout
Task
INDEPENDENTLY
Students should compare their results with the actual results. They will begin theorizing how they got their answer and how it compares.
TOGETHER SHARE
Students will collaborate and share results and theories. Using and adding to their papers students will defend and ammend their work. They will begin to reflect on what helped them solve, and what information that wouldn've been helpful that they hadn't accounted for.
OPTION
What size box would you need for the cookies?
Wrap Up
REFLECT
What did you learn from these three-acts?
Day 1 Time: 35 minutes
Overview
For this activity we will be watching the beginning of a video clip, day one. Students will use special reasoning, and arrays to estimate ‘How many cookies will fit?’ Introduce the context of the conflict visually, then ask the central question
and collect estimates.
Materials
Math journals, pencil, or pen
Key Words
Estimating, think time, planning, research
Teaching Plans
Introduction
WATCH
Dane Ehlert's When Math Happens blog:
Watch Day 1:
https://whenmathhappens.com/2014/03/04/cookies/
ASK
- “What do you notice?”
- “What do you wonder?”
DISTRIBUTE
Recording sheet:
this handout or
https://gfletchy.files.wordpress.com/2013/09/3-act-recording-sheet1.pdf
OPTION
Students might do research at home, there are multiple directions students could extend this.
Task
ASK
1. How many cookies will fit?
2. Write down a guess.
INDEPENDENTLY
Students will write down and document all the observations and questions.
SHARE
Students can share their results and wonderings.
Wrap Up
REFLECT
What questions do you still have about this problem?
What would happen if you changed the size of the pan?
Boaler, Jo (2015). Mathematical Mindsets.
Day 2 Time: 35 minutes
Overview
Common Core Standards 3.MD.C
Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Students will continue to estimate and plan their solution, creating think time. It is likely that some students did ‘research’ at home, including asking their parents to bake cookies.
Materials
SMARTboard to view the video and their math notebooks. Some students will request more materials: rulers, the measurement of the cookie sheet, directions for the cookie
Key Words
Estimating, think time, planning, research, spacing, spread, recipe, directions
Teaching Plans
Introduction
WATCH
ACT 2- https://whenmathhappens.com/2014/03/04/cookies/
REVIEW
Yesterday’s predictions. Watch the video again, stopping a few seconds in.
ASK
· What information would be useful to figure this out?
· Write down some questions you have in your head right now.
DISTRIBUTE
Math journals, (and rulers, recipe, measurements and photo of cookie sheet, if requested,) and/or this handout
OPTION
Students are welcome to do research at home
Task
SURVEY
Ask how many cookies do you think will fit.
TOGETHER
Talk about results of the survey.
Students collaborate to list necessary resources and ask questions.
Student should chart their results.
SHARE
Share findings and next steps
OPTION
Students can continue to do research prior to Act 3.
Wrap Up
SHARE
Collaborate and discuss how this kind of problem happens in the real-word.
DISCUSS
Day 3 Time: 35 minutes
Overview
This is Act-3 and the day of the reveal, students will get to see the entire video and see that 16 cookies (4 x 4) fit on the cookie sheet. On the third day students will confirm their results against the actual video and talk about why they were accurate or not, and talk about what surprised them and think critically as to how their solution compares to the real-world scenario, and account for the disparities. Give theories and explantions for how and why 16 fit on the tray, and all the variables for making it that way.
Materials
SMARTboard (video), paper, pencil
Key Words
Estimating, think time, planning, research, spacing, spread, recipe, directions
Teaching Plans
Introduction
WATCH
Final video:
https://whenmathhappens.com/2014/03/04/cookies/
REVIEW
Review the results and compare the results with what happened.
DISTRIBUTE
Paper or this handout
Task
INDEPENDENTLY
Students should compare their results with the actual results. They will begin theorizing how they got their answer and how it compares.
TOGETHER SHARE
Students will collaborate and share results and theories. Using and adding to their papers students will defend and ammend their work. They will begin to reflect on what helped them solve, and what information that wouldn've been helpful that they hadn't accounted for.
OPTION
What size box would you need for the cookies?
Wrap Up
REFLECT
What did you learn from these three-acts?
3-act math resources
- Useful templates: http://www.mathedleadership.org/resources/threeacts/
- Dan Meyer (Upper) http://threeacts.mrmeyer.com/
- Dane Ehlert (K-8) http://wmh3acts.weebly.com/3-act-math.html
- Robert Kaplinsky (K-8) http://robertkaplinsky.com/lessons/
- Graham Fletcher (K-8) http://gfletchy.com/3-act-lessons/
- Mike Wiernicki (K-8) https://mikewiernicki.com/3-act-tasks/