# Cuisenaire Rods Topics

## Topics and Suggestions how to Represent those Math concepts

• Patterns make patterns, arithmetic and geometric progression
• Even numbers any train represented by a train of red rods
• Odd numbers any number which can not be made by a train of red rods
• Sequence stair cases
• Inequalities collections, trains, Venn diagrams, sets, groups
• Equalities collections, trains,
• Venn diagrams, sets, groups
• Addition trains, regrouping with mats
• Subtraction what's missing?, take away, regrouping with mats
• Associative property
• Commutative property
• Multiplication repeated addition, squares and rectangles, towers, place mat
• Distributive property
• Division repeated subtraction (How many can be taken away?) How many groups? How big of groups? Tear down a tower. Place mat division.
• Place value grouping game, trading game, place mats with rods, squares and cubes, towers *see exponents to do decimal numbers with towers.
• Fractions If then equations, puzzles, guess my mind (if red is 2/3 what is one?)
• Addition of fractions
• Subtraction of fractions
• Multiplication of fractions repeated addition, of, four ways,
• Division of fractions How many in? How many groups can be taken away? (repeated subtraction) How big of groups? 1/3 divided into three equal groups is 1/9? 4 divided into equal groups of 2/3 = 6 (make train of four light green rods and put red rods(2/3) under to match (6). 7/8 divided by 3/4 use eighths, 7/8 and 6/8, how many 6/8 in 7/8? one and one part of the 6 = 1 1/6.
• Decimals If then equations, puzzles Fractional equalities rectangles
• Primes A number that can not be formed by a train of any one color except white
• Composite Any number that can be formed by a tower of factors
• Greatest common factor Candy sacks
• Least common multiple candy sacks
• Exponents towers, for positive use white base and for negative put white on top of tower to show negative (3 - 1=1/3, 3 - 2=1/9)
• Mean, median, mode Line up rods to represent data, locate, count, move to balance.
• Introduction Cuisenaire Rods

## Number Sense, Number systems, Place Value Activities

### 1. General Concept: Whole numbers and place value.

Activity: Use a white cube to measure how many whites are in sets of orange rods, orange squares, and orange cubes. COG ( ) AFF ( )

Solve problems like the following:

5 orange cubes + 2 orange squares + 4 orange rods + 1 dark green

4 orange cubes + 7 orange rods + 4 light green

1 orange cube + 4 orange rods

3 light green + 4 orange squares + 2 orange cubes + 4 orange rods

### 2. General Concept: Volume of cubes

Activity: Measure the volume of larger cubes using white cubes.

COG ( ) AFF ( )

Solve problems like the following:

How many white cubes in each of the following?

red cube light green cube

purple square purple cube

yellow square yellow cube

orange square orange cube

brown cube

### 3. General Concept: Whole numbers and fractional value of one - half

Activity: Measure with whole and half units.

COG ( ) AFF ( )

Solve problems like the following:

How many red rods in each of the following?

Make red 1. If red = 1, then red =

Make red 1. If red = 1, then brown =

Make red 1. If red = 1, then orange rod + red rod =

Make red 1. If red = 1, then white =

Make red 1. If red = 1, then yellow =

Make red 1. If red = 1, then light green square =

Make red 1. If red = 1, then orange rod + yellow rod =

Make red 1. If red = 1, then 3 orange rods =

### 4. General Concept: Whole numbers and fractional values

Activity: Measure with whole and fractional units.

COG ( ) AFF ( )

Solve problems like the following:

Make light green 1. If light green = 1, then black =

Make red 1. If red = 1, then yellow =

Make yellow 1. If yellow = 1, then orange + yellow =

Make red 1. If red = 1, then brown =

Make white 1. If w = 1, then orange =

Make dark green 1. If dark green = 1, then orange + yellow =

Make dark green 1. If dark green = 1, then orange + dark green =

Make black 1. If black = 1, then orange + white =

Make light green 1. If light green = 1, then black =

### 5. General Concept: Equivalent parts as fractional values of whole numbers

Activity: Find units of measure.

COG ( ) AFF ( )

Solve problems like the following:

More IF then Puzzles with a Different Twist:

If O = 2, then what is one?

If O = 5, then what is one?

If O = 10, then what is one?

If E = 3, then what is one?

If O + R = 2, then what is one?

If O + O = 2, then what is one?

If N = 2, then what is one?

If O + O = 4, then what is one?

If 3Y = 3, then what is one?

If O + O + O + G = 11, then what is one?

If O + O + O + O + N = 8, then what is one?

### 6. General Concept: Place value of decimal numbers

Activity: Demonstrate how to solve for decimal values for squares and cubes with an orange rod as the unit.

COG ( ) AFF ( )

Solve problems like the following:

Let one orange rod = 1

If an orange rod = 1, then one white cube =

If an orange rod = 1, then one orange square =

If one orange rod = 1, then what is the value of each of the following sets?

Let one orange squeare = 1

1 orange square, 2 orange rods, and 4 white cubes

8 orange squares and 3 white cubes

2 orange rods, and 8 white cubes

5 orange cube, 2 orange rods, and 4 white cubes

7 white cubes

1 orange square, 3 orange rods, and 2 white cubes

5 orange cubes, 4 orange squares, 6 white rods, and 3 white cubes

How many cubes, squares, and rods are needed to represent the following numerals?

.1, .3, 1.5, 1.4, .4, .7, 12.6, 2.5

### 7. General Concept: Place value of decimal numbers

Activity: Discover decimal values for orange cubes with the orange rod as the unit.

COG ( ) AFF ( )

Let one orange square = 1

If an orange square = 1, then one orange rod =

If an orange square = 1, then one white cube =

Solve problems like the following:
If one orange square = 1, then what is the value of each of the following sets?

2 orange rods and 3 white cubes

1 orange rod, and 2 white cubes

3 white cubes

9 orange squares, 4 orange rods, and 5 white cubes

5 orange squares and 7 white cubes

2 orange cubes, 3 orange rods, and 8 white cubes

How many cubes, squares, and rods are needed to represent the following numerals?

1.05, 4.01, 3.6, 10.12, 7.13, 5

### 8. General Concept: Place value of decimal numbers

Activity: Discover decimal values for squares and cubes with an orange rod as the unit.

COG ( ) AFF ( )

Let one orange cube = 1

If an orange cube = 1, then one square =

If an orange cube = 1, then one orange rod =

If an orange cube = 1, then one white cube =

Solve problems like the following:

8 orange squares, 3 orange rods, and 4 white cubes

3 orange cubes and 2 white cubes

3 orange cubes, 2 oranges squares, 6 orange rods, and 5 white cubes

8 orange squares, 5 orange rods, and 6 white cubes

6 orange squares and 7 white cubes

9 white cubes

4 orange cubes, 2 white rods, and 5 white cubes

How many cubes, squares, and rods are needed to represent the following numerals?

1.23, 1.25, .789, 1.05, .001

### 9. General Concept: Equivalent parts as decimal values of whole numbers

Activity: Discover decimal values using different units.

COG ( ) AFF ( )

Solve problems like the following:

If an orange rod = .1, then .......... = 1.

If an orange square = .1, then .......... = 1.

If a white cube = .01, then .......... = 1.

If a white cube = .001, then .......... = 1.

If an orange rod = .01, then .......... = 1.

## Multiplication of Fractional Numbers Activities

### 1. General concept: multiplication of fractional numbers can be represented as repeated addition.

Background information: A numeral like 1/5 is a fraction. It can be thought of as one out of a group of five. 1/5 of the class has red hair, or one person out of every five has red hair.

Represented with Cuisenaire rods:

If Yellow = one,

then 3 x 1/5 =

1/5 + 1/5 + 1/5 or 3/5

Activity: Illustrate multiplication of a whole number and fractional number by joining the number of fractional parts.

COG ( ) AFF ( )

Solve problems like the following:

If you have three opened packs of chewing gum and each has one stick out of five left, then you have 1/5 + 1/5 + 1/5 or 3/5.

Therefore 3 x 1/5 = 1/5 + 1/5 + 1/5 or 3/5

Illustrate solutions for problems like the following.

 3 x 1/4 2 x 1/5 4 x 1/6 3 x 1/4 7 x 1/3 5 x 2/3 3 x 4/5

### 2. General concept: multiplication of fractional numbers can be represented as parts of a group.

Background information: Multiplication of a fractional number with a whole number, may be thought of as a fractional part OF a group. 3/5 OF 10 Can be thought of as how much would be in THREE small groups, if the ten were divided into five equal groups. 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = ONE GROUP (of ten).

3/5 OF 10 represented with Cuisenaire rods:

If white = one, then orange = 10

Think what rod could be used five times to match an orange?

Use this rod to be 1/5 of ten and then use repeated addition and add two more red rods.

Place them on top of the orange rod to compare them.

These three red rods represent 3/5 of orange (10) or 6 (white).

Activity: Illustrate multiplication of a fractional number and whole number by dividing a group into equal parts and select the fractional number of parts. COG ( ) AFF ( )

Solve problems like the following:

 1/3 x 9 1/4 x 12 1/3 x 12 1/5 x 15 2/5 x 10 3/4 x 12 3/5 x 15 1/5 x 5 1/5 x 20 3/5 x 10 1/4 x 12 2/3 x 18 3/4 x 12 3/4 x 16 2/3 x 12 2/3 x 21

 1/2 x 2/5 1/5 x 5/8 1/2 x 4/5 1/7 x 7/8 1/3 x 3/5Y 1/5 x 5/6

### 4. General concept: multiplication of fractional numbers and fractional numbers.

Activity: Illustrate multiplication of a fractional number and fractional number by dividing a group into equal parts, selecting the fractional number of parts, repeatedly add the fractional part, and equate it to a fractional number. COG ( ) AFF ( )

Students will solve problems like the following:

 2/3 x 3/5 3/4 x 4/5 3/4 x 8/10 2/3 x 3/4 2/3 x 3/5 3/5 x 5/6 2/3 x 3/7 4/5 x 5/8 2/3 x 1/2 2/3 x 4/5 3/4 x 3/5 3/4 x 1/5