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Grade 1-3 PLC

Math

Day 2: November 15, 2023

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“Children do not come into the world with the capacity for abstract thought. Instead, children must construct abstract concepts through their interactions with concrete objects in the environment.”

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(McNeil & Jarvin, 2007)

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Introducing Manipulatives

When you are introducing, or reintroducing manipulatives, what is the first thing you have students do?

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“Play time” vs “Purposeful time”

If we give students “play time” to work with manipulatives, they will see them as toys rather than as manipulatives.

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There are many ways we can explore manipulatives with “purpose”.

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Cuisenaire Rods

1 bag for every 3 adults

ARPDC’s Videos:

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Virtual Manipulatives:

  • NRICH

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Why Cuisenaire Rods

Adding & Subtracting

Multiplication & Division

Fractions

Place Value

Counting

Geometry & Measurement

Ratio & Area

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Caution

Do not rush to labelling the rods with numbers!

Give them time to

  • find relationships between the rods.
  • explore how they can mix and match them, compose and decompose them.

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Caution

Once you do give values to the manipulatives, make sure that students understand, you are choosing to give them that value. Value can change!

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Most people give the white one a value of 1. However, it can have a value of 5 or 1 billion or 0.01.

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Purposeful Introduction

  • Find one of every color and organize them however you want.
  • What colors do you see?

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Spatial Awareness

Use one of each of the rods to create the picture

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Source

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Compare and contrast

  • Grab one orange and one dark green.
  • What do you see? What do you notice?
    • Possible answers:
      • Orange is longer. Dark green is shorter.
      • Ends are the same (both 1 cm x 1 cm)
  • Can you find a rod that
    • Is shorter than the green one?
    • Is in between the orange and dark green?

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Compose

  • Grab an orange rod.
  • What rods could you use to make that orange rod?

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Compose

Create more layers that match up to the length of orange.

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Compose

Is one white and one blue the same as one blue and one white?

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Compose

They create the same total length but are not “the same”.

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However, they can be seen as ONE unique train.

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Why the distinguishment?

In Math 30-1, cuisenaire rods can be used to introduce Pascal’s triangle.

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In this case, students will need to build both trains.

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Labelling

Notice the labelling.

We have not yet assigned�numbers to this.

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w

r

g

p

y

d (dark green)

k (black)

n (brown)

e (blue)

o

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Labelling

Grab a green.

w

r

g

p

y

d (dark green)

k (black)

n (brown)

e (blue)

o

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Labelling

Compose green in different�ways.

w

r

g

p

y

d (dark green)

k (black)

n (brown)

e (blue)

o

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Labelling

What parts did you put together to create the whole I gave you?Label what you built, starting with green:

w

r

g

p

y

d (dark green)

k (black)

n (brown)

e (blue)

o

g

rw

wr

www

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Labelling

Eventually, add in operations:

g

r+w

w+r

w+w+w

w

r

g

p

y

d (dark green)

k (black)

n (brown)

e (blue)

o

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Parts and Wholes

If I gave you a yellow and a red, what would be your “whole” rod?

Whole

Part

Part

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Parts and Wholes

If I gave you a red and a yellow, what would be your “whole” rod?

Whole

Part

Part

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Parts and Wholes

Lots of focus needs to be on:

  • __= Red + Yellow
  • Red + Yellow = __
  • Yellow + Red = __
  • Black = Red + __
  • Black = __ + Yellow
  • Red + __ = Black
  • __ + Yellow = Black

Whole

Part

Part

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Values

Place an orange on your grid paper.

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Source

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Values

How long is it? How long are all the other colors?

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Values

If your parts are red and dark green, what is your whole?

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Compose larger numbers

Place an orange on your grid paper. Show me what 16 would look like. Be efficient.

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Source

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Compose larger numbers

Add 2 more.

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Connect to Number Lines

Start at 16. Add 2 more.

16

18

+2

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Subtraction

Let’s subtract 9 from 16.

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Source

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Subtraction

Put your finger on 24.

Subtract 5.

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Subtraction

Put your finger on 24.

Subtract 5.

-5

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Connect to Number Lines

Start at 24.

Subtract 5.

24

19

-5

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Skip Counting ⇒ Multiplication

Start with an orange.

Build a train that consists of only one color.

How many trains can you build?

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Skip Counting ⇒ Multiplication

1+1+1+1+1+1+1+1+1+1

2+2+2+2+2

5+5

10

Ten 1’s

Five 2’s

Two 5’s

One 10

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Skip Counting ⇒ Multiplication

10 divided into 5’s ⇒

⇐Ten divided into 2’s

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Build 5 x 2 as a rectangular array

1

2

3

4

5

2

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Build 2 x 5 as a rectangular array

1

2

5

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Build the following:

5 x 1

5

5 x 3

5 x 2

5 x 5

5 x 4

5 x 6

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15

20

25

30

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How are 5x2 and 5x4 connected to 5x6?

5 x 1

5

5 x 3

5 x 2

5 x 5

5 x 4

5 x 6

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15

20

25

30

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How are 5x2 and 5x4 connected to 5x6?

5 x 2

5 x 4

5 x 6

10

20

30

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How are 5x2 and 5x4 connected to 5x6?

5 x 2

5 x 4

5 x 6

10

20

30

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Review, Takeaways, and To Do’s

  • Today we focused on Cuisenaire Rods!
  • Show today’s slideshow to your staff!
  • Introducing manipulatives through purposeful guided activities helps students see them as tools for visualizing the mathematics.
  • Connection from concrete to pictorial to abstract must be done thoughtfully and carefully.

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Work Time!

With the remainder of our Math time together:

  • Think about how you can share this information with your staff.
  • Fill out this Google Form to identify Gr 1-3 teachers.
  • How might you introduce other manipulatives within your classroom?