Math Topics and Suggestions on their representation with Cuisenaire rods

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Franklin

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.

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:

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:

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