Keith Devlin, Stanford Mathematician, wrote a book called: The Science of Patterns, in which he talks about mathematics being, at its heart, about pattern-seeking. In this activity students are invited to be mathematicians and to find and study patterns in the world's most famous triangle that has fascinated people for centuries ...
Jo Boaler’s Week of Inspirational Math Grades 3 – 4 For the first five days of the new school year, every math class in Grades 3-12 across the district is encouraged to participate in Jo Boaler’s Week of Inspirational Math. This week is about “inspiring students through open, beautiful and creative math”. The different tasks have been chosen so that students see math as a broad, interesting, and visual subject that involves deep thinking. Students will learn important growth mindset messages that will help them feel confident, try harder all year, persist with open and difficult problems and embrace mistakes and challenges. All tasks are low floor and high ceiling—they are accessible to all students and they extend to high levels. Lessons and resources have been pulled from and are freely available at www.youcubed.org. Necessary materials for Week 1 Instruction: online videos (links included)
PowerPoint files (included)
coloring supplies
chart paper
paper
pens/pencils
Revised 8/2015
handouts
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Day 1: Four 4’s Description In Day 1, the lesson includes a video and 2 activities. The first activity helps students practice working in groups, which is an important skill to carry throughout the year. The second is an inquiry task that helps to set norms on the first day of the year. The timing for the lesson is given after a description of the tasks. Video The main message of the video is that everyone can learn math—the video explains important brain and mindset evidence that will encourage students to persevere in math. It would be good if teachers structure time to discuss the video, after playing it or at the end of the lesson. Another option would be to ask the students to reflect on the ideas in writing later. Standards
SMP.1: Make sense of problems and persevere in solving them.
SMP.6: Attend to precision.
Learning Intentions
We are learning that when we work together, we can discover more diverse solutions to problems.
We are successful when we develop group norms/rules and follow those rules to solve math problems.
Vocabulary
square root
squared numbers
order of operations
cubed numbers
Differentiation
Students can use all numbers 0-9 and all four operations to come up with the numbers 1-20.
Students must use only square root numbers to find every number 1-20.
Use teacher discretion to decide what vocabulary terms are appropriate for grade level.
Lesson Materials Lesson Plan (NOTE: The video link in the lesson plan is NOT Day 1’s video; use the video link below.) Video (optional): Day 1 – Mindset paper, pencil/pen 2-4 pieces of large poster/chart paper to collect students’ ideas
Revised 8/2015
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Day 2: Number Visuals Description In Day 2, the lesson includes a video and an activity. The activity invites students to investigate a really interesting representation of numbers, created by Stephen Von Worley, that fascinates children and adults alike and gives students an important opportunity to understand numbers and to think visually about them. Video The video shares some important new research on the power of engaging with numbers and symbols visually, which involves brain crossing. Some people have been given unhelpful ideas that they are visual learners or not visual learners. The video explains that it is helpful for all students to think visually about mathematics, and today’s activity is a perfect opportunity for this. Standards
Learning Intentions
SMP.7: Look for and make use of structure.
SMP.8: Look for and express regularity in repeated reasoning.
We are learning that it can be helpful to represent mathematics visually.
We are successful when we represent numbers visually and interpret visual patterns.
Vocabulary
factors
prime Numbers
consecutive Numbers
adjacent
diagonals
Differentiation
The pattern relates to factors and multiples, these new concepts may need explicit instruction.
Use the Extension activity, Consecutive Numbers—students will rewrite number sentences into expression and equation form.
Use teacher discretion to decide what vocabulary terms are appropriate for grade level.
Lesson Materials
Lesson Plan
PowerPoint
Video (optional): Day 2 – Brain Crossing
Paper, pencil/pen
Colored pencils/markers
Number Visual handout, page 3
Number Visual Activity handout, page 4
Revised 8/2015
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Day 3: Paper Folding Description In Day 3, the lesson includes an activity that encourages students and teachers to engage in visual, creative thinking. The activity is coupled with a strategy for teaching students to reason and be convincing, two important mathematical practices. The lesson also includes a dot card number talk, which can be used at any point in the lesson. Click here to see Jo Boaler engaging in the number talk with a group of 6th grade students. Video The video explains to students that depth is more important than speed in math, and shares the story of a famous mathematician. This video really encourages learners who may have a negative attitude about math. Standards
Learning Intentions
SMP.1: Make sense of problems and persevere in solving them.
SMP.3: Construct viable arguments and critique the reasoning of others.
We are learning that reasoning and justifying are important mathematical practices.
We are successful when we convince others our argument is valid.
SMP.4: Model with mathematics. Vocabulary
area
fractions
estimation
Differentiation
Students can work at their own pace rather than completing the activity as a group.
Use teacher discretion to decide what vocabulary terms are appropriate for grade level.
Lesson Materials
Lesson Plan
PowerPoint
Video (optional): Day 3 – Speed
paper, pencil/pen
paper folding handout, page 5
one square piece of paper for each student—8.5” x 8.5” is a good size since this is made from a piece of 8.5” x 11” piece of paper; origami paper is also a widely available option
1 copy of the dot card visual for display, page 6
Revised 8/2015
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Day 4: Pascal’s Triangle Description Many school children, when asked to describe math, will say it is all about rules and procedures. But most mathematicians will tell you that math is about the study of patterns. Keith Devlin, Stanford Mathematician, wrote a book called: The Science of Patterns, in which he talks about mathematics being, at its heart, about pattern-seeking. In this activity students are invited to be mathematicians and to find and study patterns in the world’s most famous triangle that has fascinated people for centuries. Video The message of the video is that math is about the study of patterns. Students learn about Fibonacci’s sequence and where it exists in nature. Standards
Learning Intentions
SMP.1: Make sense of problems and persevere in solving them.
Learning Intention: We are learning that mathematics is about the study of patterns.
SMP.7: Look for and make use of structure.
SMP.8: Look for and express regularity in repeated reasoning.
Success Criteria: We are successful when we recognize and describe/articulate patterns.
Vocabulary
patterns
triangular numbers
Pascal’s Triangle
Differentiation
Students can use Cuisenaire Rods to help make the activity more concrete and visual to increase their understanding of the activity.
Lesson Materials
Lesson Plan
PowerPoint
Video (optional): Day 4 – Patterns
paper, pencil/pen
coloring supplies
Pascal’s Triangle handout, page 4
Pascal’s Investigation handout, page 3
Rod Trains, page 5 (optional)
Lattice Task, page 6 (optional)
Pascal’s Triangle with empty rows, page 7 (optional)
Revised 8/2015
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Day 5: Growing Shapes Description This lesson includes a video and a task about a growing pattern that you may want to extend into Day 6! Video This may be your students’ favorite video! It gives new research evidence on the importance of mistakes for brain growth and the need for challenge and thinking differently. Standards
Learning Intentions
SMP.1: Make sense of problems and persevere in solving them.
Learning Intention: We are learning that patterns can be represented many ways.
SMP.2: Reason abstractly and quantitatively.
SMP.7: Look for and make use of structure.
Success Criteria: We are successful when we can use representations and words to describe patterns.
Vocabulary
algebraic expression
variables
Differentiation
Use teacher discretion to decide what vocabulary terms are appropriate for grade level.
Have students find the pattern and expand the table to case #10.
Have students find the equation using the pattern and numbers on the table.
Lesson Materials
Lesson Plan
PowerPoint
Video (optional): Day 5 – Mistakes
paper, pencil/pen
coloring supplies
Shapes Task, page 4—one copy per student
Shapes Task for display, page 5—one copy
one page of chart paper per group if you want to have classroom posters
Revised 8/2015
page 6 of 6
