Lesson 1
Visual Thinking in Math
Overview
Math is visual and conceptual. One can express their thinking in creative ways expressing what you know number relationships visually. There is a video to acclimate the students into this idea that when you think of numbers as symbols and contrast that with visual representations of numbers students are brain crossing and creating pathways in their brains which can increase the number relationships and compositions of numbers. Students can color code number relationships they see.
Materials
Key Words
Visualize, math, number relationships, brain crossing, pathways, estimating, number symbols
Teaching Plans
Introduction
WATCH
Video by Jo Boaler about flexible, slow thinking: https://www.youcubed.org/wim-day-2/
REVIEW
Visual thinking routine, What do you see, what do you notice?
DISTRIBUTE
Handout of visual numbers
OPTION
Illustrate number 30 and share with classmates
Task
INDEPENDENTLY
Students study the sheet looking for patterns and number relationships. Students can color it if they like for 3-5 minutes.
TOGETHER After 3-5 quiet minutes have assed and students have had time to accquaint themselves, they can then share findings, extend to number 30 how would they draw that
OPTION
Students can continue to draw the numbers at home for homework 30 and beyond or draw their own numbers beginning from 1 or any number they choose.
Wrap Up
SHARE
Findings and patterns and relationships they saw on the handout and chart findings.
DISCUSS
What other ways could we draw (30, 36, 42)?
Reflection
EXIT TICKET / formative assessment
On a half-sheet of paper, ask:
Overview
Math is visual and conceptual. One can express their thinking in creative ways expressing what you know number relationships visually. There is a video to acclimate the students into this idea that when you think of numbers as symbols and contrast that with visual representations of numbers students are brain crossing and creating pathways in their brains which can increase the number relationships and compositions of numbers. Students can color code number relationships they see.
Materials
- From Jo Boaler’s YouCubed Website, Week of Inspirational Math 1 (you must subscribe) I am referring to the resources on week 1, day 2. https://www.youcubed.org/wim-day-2/
Key Words
Visualize, math, number relationships, brain crossing, pathways, estimating, number symbols
Teaching Plans
Introduction
WATCH
Video by Jo Boaler about flexible, slow thinking: https://www.youcubed.org/wim-day-2/
REVIEW
Visual thinking routine, What do you see, what do you notice?
DISTRIBUTE
Handout of visual numbers
OPTION
Illustrate number 30 and share with classmates
Task
INDEPENDENTLY
Students study the sheet looking for patterns and number relationships. Students can color it if they like for 3-5 minutes.
TOGETHER After 3-5 quiet minutes have assed and students have had time to accquaint themselves, they can then share findings, extend to number 30 how would they draw that
OPTION
Students can continue to draw the numbers at home for homework 30 and beyond or draw their own numbers beginning from 1 or any number they choose.
Wrap Up
SHARE
Findings and patterns and relationships they saw on the handout and chart findings.
DISCUSS
What other ways could we draw (30, 36, 42)?
Reflection
EXIT TICKET / formative assessment
On a half-sheet of paper, ask:
- How is drawing/visually representing a number the same as the symbol?
- What can you learn from showing a number visually?
Lesson 2
(Sketchnoting = Symbols + Pictures + Words Time: 45 min. - 1 hour
Overview
For this lesson students will review skills previously taught after learning the basics of sketchnoting. Using what students know about numbers, facts, pictures and symbols students will represent their math facts. Focusing on multiplication and division,
Materials
SMARTboard for a quick video, paper, pencil
Key Words
Sketchnote, containers, fonts, visual thinking, math facts, arrays, product, quotient
Teaching Plans
Introduction
WATCH
Sketchnote tutorial: https://www.youtube.com/watch?v=HhG94YjhXGc basics and containers
REVIEW
Brain crossing concept and talk about the benefits of looking at number relationships
Visually in picture and with symbols
DISTRIBUTE
Paper and give students an option of numbers and facts
OPTION
students can make as many facts as they wish, but they need to have at least six ways.
Task
TOGETHER
At their tables, students can compare solutions and get inspired by multiple strategies and representations of their math facts.
How many ways can we make 48? Model.
INDEPENDENTLY
Students will construct their drawings and understandings of the factors within their number.
OPTION
Pick a math fact they have trouble with (8 x 7 = 56, so 56) and work backwards from that number.
Wrap Up
SHARE
Results and final products at their tables. (formative assessment)
DISCUSS
How number relationships noticed today?
Resource: https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna-ssl.com/wp-content/uploads/2015/03/FluencyWithoutFear-2015.pdf
Overview
For this lesson students will review skills previously taught after learning the basics of sketchnoting. Using what students know about numbers, facts, pictures and symbols students will represent their math facts. Focusing on multiplication and division,
Materials
SMARTboard for a quick video, paper, pencil
Key Words
Sketchnote, containers, fonts, visual thinking, math facts, arrays, product, quotient
Teaching Plans
Introduction
WATCH
Sketchnote tutorial: https://www.youtube.com/watch?v=HhG94YjhXGc basics and containers
REVIEW
Brain crossing concept and talk about the benefits of looking at number relationships
Visually in picture and with symbols
DISTRIBUTE
Paper and give students an option of numbers and facts
OPTION
students can make as many facts as they wish, but they need to have at least six ways.
Task
TOGETHER
At their tables, students can compare solutions and get inspired by multiple strategies and representations of their math facts.
How many ways can we make 48? Model.
INDEPENDENTLY
Students will construct their drawings and understandings of the factors within their number.
OPTION
Pick a math fact they have trouble with (8 x 7 = 56, so 56) and work backwards from that number.
Wrap Up
SHARE
Results and final products at their tables. (formative assessment)
DISCUSS
How number relationships noticed today?
Resource: https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna-ssl.com/wp-content/uploads/2015/03/FluencyWithoutFear-2015.pdf
lesson 3
Sketchnoting Categories Time: 45 min. - 1 hour
Overview
For this lesson students will review skills previously taught after learning the basics of sketchnoting. And work on the structure of Categorizing and giving examples on one page. Students will review and 'show what they know' about the four critical areas they are responsible for in math.
Materials
SMARTboard for a quick video, paper, pencil, markers
Key Words
Sketchnote, containers, categories, separators, fonts, visual thinking, math facts, arrays, product, quotient
Teaching Plans
Introduction
WATCH
Sketchnote tutorial: https://www.youtube.com/watch?v=HhG94YjhXGc basics and containers
Sketchnote tutorial: categorizing (handout)
REVIEW
When we sort and separate things, we call this categorizing. What we are going to categorize today is all math, but there will be four areas of math
DISTRIBUTE
Paper and give students their heading:
Math
OPTION
students can make as many facts as they wish, but they need to have at least six ways.
Task
TOGETHER
Start to plan their papers to include an overarching theme and the four headings.
Math
INDEPENDENTLY
Students will complete their sketchnotes
OPTION
Students can categorize any of the previous categories (shapes: quadrilataterals, triangles...)
Wrap Up
SHARE
Results and final products on the rug
REFLECT
Exit ticket: What did you learn or relearn when categorizing today?
Overview
For this lesson students will review skills previously taught after learning the basics of sketchnoting. And work on the structure of Categorizing and giving examples on one page. Students will review and 'show what they know' about the four critical areas they are responsible for in math.
Materials
SMARTboard for a quick video, paper, pencil, markers
Key Words
Sketchnote, containers, categories, separators, fonts, visual thinking, math facts, arrays, product, quotient
Teaching Plans
Introduction
WATCH
Sketchnote tutorial: https://www.youtube.com/watch?v=HhG94YjhXGc basics and containers
Sketchnote tutorial: categorizing (handout)
REVIEW
When we sort and separate things, we call this categorizing. What we are going to categorize today is all math, but there will be four areas of math
DISTRIBUTE
Paper and give students their heading:
Math
- multiplication and division and strategies for multiplication and division within 100
- fractions
- rectangular arrays and of area
- two-dimensional shapes
OPTION
students can make as many facts as they wish, but they need to have at least six ways.
Task
TOGETHER
Start to plan their papers to include an overarching theme and the four headings.
Math
- multiplication and division and strategies for multiplication and division within 100
- fractions
- rectangular arrays and of area
- two-dimensional shapes
INDEPENDENTLY
Students will complete their sketchnotes
OPTION
Students can categorize any of the previous categories (shapes: quadrilataterals, triangles...)
Wrap Up
SHARE
Results and final products on the rug
REFLECT
Exit ticket: What did you learn or relearn when categorizing today?
lesson 4
Slowing Down and Trying it Out: Sketchnotes & Hailstones
Overview
Visual recording helps you understand and remember information and ideas. As you are watching a video or listening to your teacher you can visually record memory cues to help synthesize information and map concepts. This practice assists recall and remember information. Students will be invited to take sketchnotes on the video and the introduction to the lesson, reminding them that is a learning tool that is unique to them. Students will watch a brief video about depth is more important than speed in math. This lesson focuses on one of the world’s unsolved problems in mathematics, which we have found students get very excited about. It involves Hailstone sequences (Collatz Conjecture) and invites students to make their own conjectures. Students will heavily refer to their notes to retell the video and the rules and conjectures regarding Hailstone Sequences. -Youcubed, Jo Boaler Take notes on whether students are able to calculate number strings starting at more than one number.
Materials
Math notebooks, pencil, pens
Key Words
Unsolved, problem, number strings, hailstones, estimation, conjectures, divide, division, multiply, multiplication, add, addition
Teaching Plans
Introduction
WATCH
Speed is Not Important, Jo Boaler https://www.youcubed.org/wim2-day-4/
OPTION
Use this handout about the Hailstone Sequence
Task
INDEPENDENTLY
Explore the Hailstone Sequence starting with any number? (I retouched an example of student work here and here) (original student work)
TOGETHER
Share results and postulate conjectures.
SHARE
Did they go slow, think deeply?
Did they try to make a conjecture?
Did their work help them to figure out a conjecture?
Did they have a growth mindset as they worked?
Wrap Up
DISCUSS
What did they notice?
What questions do they still have?
Overview
Visual recording helps you understand and remember information and ideas. As you are watching a video or listening to your teacher you can visually record memory cues to help synthesize information and map concepts. This practice assists recall and remember information. Students will be invited to take sketchnotes on the video and the introduction to the lesson, reminding them that is a learning tool that is unique to them. Students will watch a brief video about depth is more important than speed in math. This lesson focuses on one of the world’s unsolved problems in mathematics, which we have found students get very excited about. It involves Hailstone sequences (Collatz Conjecture) and invites students to make their own conjectures. Students will heavily refer to their notes to retell the video and the rules and conjectures regarding Hailstone Sequences. -Youcubed, Jo Boaler Take notes on whether students are able to calculate number strings starting at more than one number.
Materials
Math notebooks, pencil, pens
Key Words
Unsolved, problem, number strings, hailstones, estimation, conjectures, divide, division, multiply, multiplication, add, addition
Teaching Plans
Introduction
WATCH
Speed is Not Important, Jo Boaler https://www.youcubed.org/wim2-day-4/
OPTION
Use this handout about the Hailstone Sequence
Task
INDEPENDENTLY
Explore the Hailstone Sequence starting with any number? (I retouched an example of student work here and here) (original student work)
TOGETHER
Share results and postulate conjectures.
SHARE
Did they go slow, think deeply?
Did they try to make a conjecture?
Did their work help them to figure out a conjecture?
Did they have a growth mindset as they worked?
Wrap Up
DISCUSS
What did they notice?
What questions do they still have?
lesson 5
Four 4’s (Collaborating and Revising)
Overview
Everyone can be a math communicator. In this lesson, students will work together and share ideas and revise their work to clearly show ways for make four 4’s. Mathematicians need to crunch numbers, and their work can get messy. Sometimes it’s good to have drafts in math, just like in writing. You can get all your ideas out and revise your work to communicate your mathematical thinking. For this lesson students will explore “Four 4’s” from Jo Boaler’s YouCubed.org website revise their findings to show how to get numbers 1-20 using four 4’s and for operations: + - x ÷ (i.e. 4/4 + 4 – 4 = 1). Notice how kids are working and take notes on their mindset and ability to communicate ideas verbally/written.
Materials
Key Words
Collaboration, operations, calculations, growth mindset, self-belief, revise, edit
Teaching Plans
Introduction
WATCH
Jo Boaler’s video on mindset is the topic, which is review and gets students ready to tackle something that sounds easy, but can be challenging. https://www.youcubed.org/wim-day-1
REVIEW
OPTION
Teach Factorials to add to their solutions 2! = 2 x 1, 3! = 3 x 2 x 1
Task
TOGETHER
Share findings from their first draft on a poster paper, listing multiple solutions for totals 1-20
INDEPENDENTLY
Revise and represent your thinking of all the ways to find Four 4’s on their individual paper
OPTION
Wrap Up
SHARE
DISCUSS
REFLECTION
Pick two of the questions below and write a reflection on today's work:
Overview
Everyone can be a math communicator. In this lesson, students will work together and share ideas and revise their work to clearly show ways for make four 4’s. Mathematicians need to crunch numbers, and their work can get messy. Sometimes it’s good to have drafts in math, just like in writing. You can get all your ideas out and revise your work to communicate your mathematical thinking. For this lesson students will explore “Four 4’s” from Jo Boaler’s YouCubed.org website revise their findings to show how to get numbers 1-20 using four 4’s and for operations: + - x ÷ (i.e. 4/4 + 4 – 4 = 1). Notice how kids are working and take notes on their mindset and ability to communicate ideas verbally/written.
Materials
- Dry-erase board
- Two sheets of paper per student
- Large poster paper- 1 per group
Key Words
Collaboration, operations, calculations, growth mindset, self-belief, revise, edit
Teaching Plans
Introduction
WATCH
Jo Boaler’s video on mindset is the topic, which is review and gets students ready to tackle something that sounds easy, but can be challenging. https://www.youcubed.org/wim-day-1
REVIEW
- Operations + - x ÷
- What makes good collaborative group work, and list these norms
- Show your work in pictures and in words
- Post-its for norms
- Paper for the Four 4’s (my sketchnote)
- Poster paper for collaborative work
OPTION
Teach Factorials to add to their solutions 2! = 2 x 1, 3! = 3 x 2 x 1
Task
TOGETHER
Share findings from their first draft on a poster paper, listing multiple solutions for totals 1-20
INDEPENDENTLY
Revise and represent your thinking of all the ways to find Four 4’s on their individual paper
OPTION
- Can you continue using Four 4’s to make numbers greater than 20?
Wrap Up
SHARE
- Do a gallery walk to:
- observe individual documentations
- Display group findings
DISCUSS
- Were you able to keep a growth mindset throughout this activity?
- Did it help to have self-belief?
- Was it easier collaborating in a group?
- How did revising your work to show your solutions help you understand today's math?
REFLECTION
Pick two of the questions below and write a reflection on today's work:
- Were you able to keep a growth mindset throughout this activity?
- Did it help to have self-belief?
- Was it easier collaborating in a group?
- How did revising your work to show your solutions help you understand today's math?