lesson 6
What is a Third?
Overview
Students will explore equal parts of a whole, fractions, and model one third in as many ways as they can. One half is so simple for them, quarters too, but thirds, sixths, are a little trickier to draw and this exercise will give them the practice that they need.
Materials
SMARTboard, Pencil, math notebooks
Key Words
Number sense, fractions, equal parts of a whole, triangle, hexagon, number line, numerator, denominator
Teaching Plans
Introduction
WATCH
Quick video of ways to draw and document fractions www.youtube.com/watch?v=6FTvSjGRheY
REVIEW
What do we know about fractions (equal sharing/equal parts/draw them equally)
WARM-UP
Which one doesn't belong (see photo below with for shapes, 3 triangles and a hexagon)
DISTRIBUTE
Math notebooks and have students
OPTION
Students can illustrate this problem:
I put my hand in a bag of m&m's. One-third of them were yellow. How many m&m's might you have had?
This will work on equivalent fractions
Task
INDEPENDENTLY
Sketch and write everything they know about the fraction 1/3. Label and use tools they've learned in earlier sketchnoting tutorials.
SHARE
Students will share any surprises that they learned through today's work.
We will show exemplary examples the
REFLECTION
Homework reflection half-sheet (2 per page) Reflection homework c. Jo Boaler
Overview
Students will explore equal parts of a whole, fractions, and model one third in as many ways as they can. One half is so simple for them, quarters too, but thirds, sixths, are a little trickier to draw and this exercise will give them the practice that they need.
Materials
SMARTboard, Pencil, math notebooks
Key Words
Number sense, fractions, equal parts of a whole, triangle, hexagon, number line, numerator, denominator
Teaching Plans
Introduction
WATCH
Quick video of ways to draw and document fractions www.youtube.com/watch?v=6FTvSjGRheY
REVIEW
What do we know about fractions (equal sharing/equal parts/draw them equally)
WARM-UP
Which one doesn't belong (see photo below with for shapes, 3 triangles and a hexagon)
DISTRIBUTE
Math notebooks and have students
OPTION
Students can illustrate this problem:
I put my hand in a bag of m&m's. One-third of them were yellow. How many m&m's might you have had?
This will work on equivalent fractions
Task
INDEPENDENTLY
Sketch and write everything they know about the fraction 1/3. Label and use tools they've learned in earlier sketchnoting tutorials.
SHARE
Students will share any surprises that they learned through today's work.
We will show exemplary examples the
REFLECTION
Homework reflection half-sheet (2 per page) Reflection homework c. Jo Boaler
lesson 7
Let's Share CANDY
Overview
Students will have an opportunity to think and draw something they have been doing for years, sharing candy (or coveted food items).
Materials
Pencil, handout
Key Words
Number sense, numerator, denominator,
Teaching Plans
Introduction
WARM-UP
Look at the image what doesn't belong, day 2, (see below)
REVIEW
I good example of student work surrounding fractions.
DISTRIBUTE
Handout with questions:
OPTION
What if the amount of candy bars doubled, how would that change how much each child would get?
Task
TOGETHER
In
INDEPENDENTLY
Sketch
SHARE
St
OPTION
They
Wrap Up
SKETCH RESULTS
x
REFLECTION
W
Overview
Students will have an opportunity to think and draw something they have been doing for years, sharing candy (or coveted food items).
Materials
Pencil, handout
Key Words
Number sense, numerator, denominator,
Teaching Plans
Introduction
WARM-UP
Look at the image what doesn't belong, day 2, (see below)
REVIEW
I good example of student work surrounding fractions.
DISTRIBUTE
Handout with questions:
- 4 children want to share 5 candy bars so that everyone gets the same amount. How much would each child get?
- 4 children want to share 11 candy bars so that everyone gets the same amount. How much would each child get?
- 3 children want to share 4 candy bars so that everyone gets the same amount. How much would each child get?
OPTION
What if the amount of candy bars doubled, how would that change how much each child would get?
Task
TOGETHER
In
INDEPENDENTLY
Sketch
SHARE
St
OPTION
They
Wrap Up
SKETCH RESULTS
x
REFLECTION
W
Lesson 8
Hands-on then Draw : Clothesline Fraction Math
Overview
Students have a difficult time with number sense in general, but with fractions it’s even more difficult. For example, 1/4th might seem larger that 1/3rd because ‘it has a four in it’, but when students actually cut a cookie into fourths or thirds and compare the delicious pieces that way, they often can begin to understand what a larger denominator means. This clothesline math activity can, “provide math communities with visual, dynamic, and student-centered activities that build number sense, conceptual understanding and procedural fluency,” all with a hand out and some string.
Materials
Clotheslines/string, fraction cards, scissors, paper, pencil, SMARTboard for warm-up, ruler (optional)
Fraction cards: http://www.estimation180.com/clothesline.html
‘fraction talks’ from Andrew Stadel's Estimation 180's website.
Key Words
Number sense, fractions, numerator, denominator, greater than, less than
Teaching Plans
Introduction
WATCH
Quick sketch of a fraction numberline: https://youtu.be/E4DVqnyfmUg
REVIEW
Open number line. Place 2/3, place ½
DISTRIBUTE
Fraction cards: https://drive.google.com/file/d/0B0Lk45wwjYBuR3RtWGFmNDJCcUU/view
OPTION
blank cards or the pictorial fraction cards to add to placing fractions in their correct spots on a numberline.
Task
TOGETHER
In groups of 3 or 4 students will make their number lines. Students will have a set of fraction cards and will place them along the number line in relationship to zero and one. They need to prove to themselves and their group that they think they got the right answer.
INDEPENDENTLY
Sketch the clothesline. Students should pay attention to where they are placing things spacially, and accurately. They might need to try more than once.
SHARE
Students should share throughout and collaborate on the placements of the cards until there is consensus.
OPTION
They can check and see if there results are similar.
Wrap Up
SKETCH RESULTS
Sample drawing
REFLECTION
Ask them to think about "Was there anything that surprised you about this exercise?"
Rate yourself on a numberline how you think you did. Print reflection labels for half-sheets/index cards
Overview
Students have a difficult time with number sense in general, but with fractions it’s even more difficult. For example, 1/4th might seem larger that 1/3rd because ‘it has a four in it’, but when students actually cut a cookie into fourths or thirds and compare the delicious pieces that way, they often can begin to understand what a larger denominator means. This clothesline math activity can, “provide math communities with visual, dynamic, and student-centered activities that build number sense, conceptual understanding and procedural fluency,” all with a hand out and some string.
Materials
Clotheslines/string, fraction cards, scissors, paper, pencil, SMARTboard for warm-up, ruler (optional)
Fraction cards: http://www.estimation180.com/clothesline.html
‘fraction talks’ from Andrew Stadel's Estimation 180's website.
Key Words
Number sense, fractions, numerator, denominator, greater than, less than
Teaching Plans
Introduction
WATCH
Quick sketch of a fraction numberline: https://youtu.be/E4DVqnyfmUg
REVIEW
Open number line. Place 2/3, place ½
DISTRIBUTE
Fraction cards: https://drive.google.com/file/d/0B0Lk45wwjYBuR3RtWGFmNDJCcUU/view
OPTION
blank cards or the pictorial fraction cards to add to placing fractions in their correct spots on a numberline.
Task
TOGETHER
In groups of 3 or 4 students will make their number lines. Students will have a set of fraction cards and will place them along the number line in relationship to zero and one. They need to prove to themselves and their group that they think they got the right answer.
INDEPENDENTLY
Sketch the clothesline. Students should pay attention to where they are placing things spacially, and accurately. They might need to try more than once.
SHARE
Students should share throughout and collaborate on the placements of the cards until there is consensus.
OPTION
They can check and see if there results are similar.
Wrap Up
SKETCH RESULTS
Sample drawing
REFLECTION
Ask them to think about "Was there anything that surprised you about this exercise?"
Rate yourself on a numberline how you think you did. Print reflection labels for half-sheets/index cards
lesson 9
Will we have enough?
Overview
Students will work on a real-life scenario. Sometimes we need to divide things equally and see if there is enough for everyone to have the same amount. In this problem the remainder will vary depending on how many students are present, but there will not be enough for everyone to have a half unless there are a lot of students absent.
Materials
Pencil, handout, SMARTboard for warm-up and student example, dry erase boards and markers.
Key Words
Fractions, numerator, denominator, fractional part, divide, equal sharing, parts of a whole
Teaching Plans
Introduction
Introduce the concept of getting something that you don't have enough to go around, like at a party, how do we solve this problem?
REVIEW
Representing simple fractional parts of objects and naming the fractional parts. What do we know? How do we do it? Reviewing denominator is the number of parts of the whole, reminding them that these are equal parts.
WARM-UP
True or False
DISTRIBUTE
Handout: There are eight sandwiches. If everyone gets a ¼ of a sandwich do we have enough for our classroom?
OPTION
Challenge: Could everyone get a ½ a sandwich?
Task
TOGETHER +INDEPENDENTLY
Students will sketch and plan their answer. There is usually some collaboration among students at their desks as they check their work and compare strategies.
SHARE
In small groups at their tables students will share their results.
OPTION
Are there enough for the teachers too?
Wrap Up
SKETCH RESULTS
On dry erase boards and share out answers.
REFLECTION
In a thought bubble, students will sketchnote their reflection: Here are my ideas about what I learned today.
Overview
Students will work on a real-life scenario. Sometimes we need to divide things equally and see if there is enough for everyone to have the same amount. In this problem the remainder will vary depending on how many students are present, but there will not be enough for everyone to have a half unless there are a lot of students absent.
Materials
Pencil, handout, SMARTboard for warm-up and student example, dry erase boards and markers.
Key Words
Fractions, numerator, denominator, fractional part, divide, equal sharing, parts of a whole
Teaching Plans
Introduction
Introduce the concept of getting something that you don't have enough to go around, like at a party, how do we solve this problem?
REVIEW
Representing simple fractional parts of objects and naming the fractional parts. What do we know? How do we do it? Reviewing denominator is the number of parts of the whole, reminding them that these are equal parts.
WARM-UP
True or False
- ¾ + ¼ = 1
- 2/3 + 2/3 = 1
- 2/4 + ½ = 1
DISTRIBUTE
Handout: There are eight sandwiches. If everyone gets a ¼ of a sandwich do we have enough for our classroom?
OPTION
Challenge: Could everyone get a ½ a sandwich?
Task
TOGETHER +INDEPENDENTLY
Students will sketch and plan their answer. There is usually some collaboration among students at their desks as they check their work and compare strategies.
SHARE
In small groups at their tables students will share their results.
OPTION
Are there enough for the teachers too?
Wrap Up
SKETCH RESULTS
On dry erase boards and share out answers.
REFLECTION
In a thought bubble, students will sketchnote their reflection: Here are my ideas about what I learned today.
lesson 10
Fraction Designs
Overview
Students have had an opportunity to think about many fractions as things you can represent, eat, put in order, today students will see how fractions can be seen in patterns. Patterns can be simple and complex.
Materials
Paper cut into squares, scissors, glue, paper, pencil, SMARTboard for warm-up, plain paper for wrap-up and reflection
Key Words
Number sense, fractions, patterns, designs, repetition
Teaching Plans
Introduction
WARM-UP
Look at the slides of the fractions below. Ask students what they notice, what they wonder.
REVIEW
How can you divide a square into quarters? If you wanted to have 1/4 of your square to be blue is there more than one way you could represent that?
DISTRIBUTE
Paper, scissors are rulers and let kids begin to plan squares
Task
INDEPENDENTLY
Students will fold paper and plan on coloring 1/4 of the area blue (or a color of your/their choice)
SHARE
Students will do a gallery walk and see the variety in such a simple activity.
OPTION
Students can make multiples of the same type of square and repeat it, or they can assemble two types of squares, or every square can be different, and then they can compare the results
Wrap Up
SKETCH
After the gallery walk, students will try to do a quick sketch of a pattern they found interesting.
REFLECTION
Sketchnote your reflection:
What surprised you about doing this activity using squares that are 3/4 white and 1/4 blue?
If we did something like this again, what would you want to try next?
Overview
Students have had an opportunity to think about many fractions as things you can represent, eat, put in order, today students will see how fractions can be seen in patterns. Patterns can be simple and complex.
Materials
Paper cut into squares, scissors, glue, paper, pencil, SMARTboard for warm-up, plain paper for wrap-up and reflection
Key Words
Number sense, fractions, patterns, designs, repetition
Teaching Plans
Introduction
WARM-UP
Look at the slides of the fractions below. Ask students what they notice, what they wonder.
REVIEW
How can you divide a square into quarters? If you wanted to have 1/4 of your square to be blue is there more than one way you could represent that?
DISTRIBUTE
Paper, scissors are rulers and let kids begin to plan squares
Task
INDEPENDENTLY
Students will fold paper and plan on coloring 1/4 of the area blue (or a color of your/their choice)
SHARE
Students will do a gallery walk and see the variety in such a simple activity.
OPTION
Students can make multiples of the same type of square and repeat it, or they can assemble two types of squares, or every square can be different, and then they can compare the results
Wrap Up
SKETCH
After the gallery walk, students will try to do a quick sketch of a pattern they found interesting.
REFLECTION
Sketchnote your reflection:
What surprised you about doing this activity using squares that are 3/4 white and 1/4 blue?
If we did something like this again, what would you want to try next?