Number Rods consist of 10 colored rods that each corresponds to a different length from 1 to 10. These manipulatives were created by the Belgium schoolteacher Georges Cuisenaire and are therefore often called Cuisenaire® Rods. The name Cuisenaire® Rods is trademarked by ETA hand2mind and refers to a set of rods with a very specific color sequence: white, red, light green, purple, yellow, dark green, black, brown, blue, and orange.
Number Rods, or Cuisenaire® Rods, are tactile and visual educational tools for learning counting, addition, subtraction, multiplication, division, fractions, factor, ratios and proportions.
Virtual manipulatives, such as Brainingcamp's Number Rods, have built-in alignment and snapping features to make work fast and easy. The virtual manipulative includes a custom rod that can be set to sizes greater than 10. Users can turn on helpful grid or number line backgrounds. Special modes display integer, decimal, or fraction values directly on the rods. The fraction mode even lets users define which rod length constitutes the whole. Users can customize default rod colors to their own preference.
This activity works best with a number line that has intervals equal in size to the smallest number rod. To skip count by 3's, create a train of 3-unit long rods. Observe the numbers on which the edges of the rods fall to skip count (3, 6, 9, ...).
To add 3 and 2, combine a 3-unit long rod and a 2-unit long rod. The train has the same length as a 5-unit long rod, so 3 + 2 = 5. Explore other ways to make a sum of 5.
To subtract 5 from 9, start by placing a horizontal 9 unit long rod and then place a horizontal 5 unit long rod below it. 9 – 5 is the amount of empty space below the 9 unit long rod. A 4 unit long rod fits in the empty space below the 9 unit long rod, so 9 – 5 = 4.
Multiplication can be thought of as the first number telling how much to take of the second number. To model 3 × 4, place three 4-unit long rods one below the other. The results is an area that covers 12 unit squares, so 3 × 4 = 12. Explore other ways to make a product of 12.
Division is the inverse of multiplication, so 12 ÷ 3 is like finding how many rods of 3 can be made from 12. . Place 3-unit long rods below each other until the rectangular area covers 12 unit squares. There are 4 rods of 3, so 12 ÷ 3 = 4.
Dividing Integers with Remainders
Dividing 12 by 5 is like finding how many 5’s fit in 12. Start by placing a rod (or rods) 12 units long. Next place 5 unit long rods and see how many fit into the rod (or rods) of length 12. The 5-unit long rods fit into the 12-unit long rod (rods) two full times with some amount left over. The amount left over is two units long, so 12 ÷ 5 equals 2 remainder 2. The amount left over is equal to 2/5 of a 5 unit long rod, so we can also say that 12 ÷ 5 equals 2 and 2/5.
A fraction is a number that names a part of a whole. If a 6-unit long rod represents a whole, notice that it takes three 2-unit long rods to make a 6-unit long rod. The top number in a fraction is called the numerator and the bottom number is called the denominator. The denominator represents the number of equal-sized pieces in a whole unit. The numerator represents the number of pieces made by the part. So the 2-unit long rods model the fraction 3/3. Now remove one 2-unit long rod to model the fraction 2/3. Remove another 2-unit long rod to model the fraction 1/3. Remove one more 2-unit long rod to model the fraction 0/3.
To find which fraction is greater, 2/3 or 3/4, start by writing the fractions as equivalent fractions with a common denominator. The fractions 2/3 and 3/4 can be written as equivalent fractions 8/12 and 9/12. When fractions have the same denominator, the greater the numerator the greater the fraction. So 3/4 is greater than 2/3.
If an 8-unit long rod represents a whole, then two 1-unit long rods represents the fraction 2/8. A 2-unit long rod represents the fraction 1/4. Since the two fractions represent the same comparison, 1/2 and 2/4 are equivalent.
To find the least common denominator for the fractions 1/2 and 1/3, use 2-unit long rods and 3-unit long rods to represent the denominators 2 and 3. Create a train of each rod type by placing rod multiples beside each other. When the trains are the same length, the length of the train is a common multiple of the two denominators. The first common denominator of 1/2 and 1/3 is 6. Notice that 12 is also a common denominator of the fractions 1/2 and 1/3. Because 6 is the smallest number that is a multiple of the denominators, 6 is the least common denominator.
To add the fractions 1/2 and 1/3, model the fraction 1/2 using a 1-unit long rod over a 2-unit long rod and the fraction 1/3 using a 1-unit long rod over a 3-unit long rod. To find a common denominator, create a train of 2-unit long rods and a train of 3-unit long rods until both are the same length. Both trains have the same length when they are 6 units long, so 6 is a common denominator. The fractions 3/6 and 2/6 have a common denominator. Because the denominator represents the number of equal parts in a whole and the numerator represents the actual amount of parts in the quantity, add the numerators together. There are 5 parts in total, so 1/2 + 1/3 equals 5/6.
To perform the subtraction 2/3 – 1/4, model the fraction 2/3 using a 2-unit long rod over a 3-unit long rod and the fraction 1/4 using a 1-unit long rod over a 4-unit long rod. To find a common denominator, create a train of 3-unit long rods and a train of 4-unit long rods until both are the same length. Both trains have the same length when they are 12 units long, so 12 is a common denominator. The fractions 8/12 and 3/12 have a common denominator. Because the denominator represents the number of equal parts in a whole and the numerator represents the actual amount of parts in the quantity, subtract the numerator 3 from the numerator 8. There are 5 parts remaining, so 2/3 - 1/4 equals 5/12.
To find the factors of 12, place a rod (or rods) that is 12 units long. For each rod smaller than 12, see if you can make a train of length 12 using only that rod type. The factors of 12 are 1, 2, 3, 4, 6, and 12.
Ratios and Proportions
A ratio is a comparison of two numbers. Place a 5-unit long rod and a 6-unit long rod on the workspace. The length of the 5-unit long rod to the length of the 6-unit long rod can be written as the ratio 5:6. Next double the number of rods to create the ratio 10:12. A proportion is an equation that shows that two ratios are equal. The ratios 5:6 and 10:12 form a proportion because their ratios are equivalent. The cross products of proportions are equal.