What are relational rods?
Relational rods are rectangular solids with related lengths. A set usually contains between 70 and 80 rods. In a set, all rods of the same length are the same colour. The smallest rod is a 1 cm3 cube. The largest of the 10 rods has a volume of 10 cm3 , it is ten times as long as the small cube. The lengths of the different coloured rods increase incrementally from the smallest size to the largest size.

Why use relational rods?
Relational rods help students visualize mathematical concepts. They can be used in all of the math strands for a variety of concepts. Common uses include fractions, Rods can be used for the attributes of length, area and volume. It is important that students understand which attribute is being used in the task or activity.
Lesson Study Example  Try this out together and then take it to a class!
Task/Activity : How much can you save?
Big Ideas Explored:
Curriculum Connections:
Materials:
MindsOn:
Action:
Consolidation:
Use the following questions for discussion with the whole class:
Extension:
What's the math? Anticipating student thinking:
 Activity modified from Super Source K2 Cuisinaire Rods
Big Ideas Explored:
 Grouping the same values together make counting easier.
 Understanding the proportional value of 1, 5, and 10 cent coins
 Adding and subtracting
Curriculum Connections:
 Grouping the same values together make counting easier.
 Understanding the proportional value of 1, 5, and 10 cent coins
 Adding and subtracting
Materials:
 Relational Rods  white, yellow and orange
 Cube marked with 1,1,1,5,5,10
 White board and marker
MindsOn:
 Show students a penny, nickel and dime and ask what each is worth.
 Through exploration have students determine how much each rod would be worth if the white rod is worth 1 cent. (Yellow = nickel; orange = dime)
 Line up the rods so that the relationships can be seen.
Action:
 Working in partners, students roll the cube to see which “coin” rod they
 Students record each amount on a white board or paper. After each roll students circle the greater amount between the pair.
 Students repeat this rolling in pairs for a total of five times.
 After rolling for five times, students are to determine how much “money” they saved.
 Repeat this activity two more times.
Consolidation:
 Students can share the amounts that the spun. Have other students guess the coins that they rolled.
Use the following questions for discussion with the whole class:
 What did you notice about your list on your white board?
 What was the least amount of money that anyone saved on five rolls?
 What was the greatest amount of money that anyone saved on five rolls? Was more possible?
 Did one coin get rolled the most often? Why?
Extension:
 Students could record the ways to make make 30 cents in their math journals.
 Have students play again and find the difference between their totals.
 Ask students to make a spinner to represent the possibilities represented on the cube. Would it change if the spinner looked different?
What's the math? Anticipating student thinking:
 Real coins are not proportional to their value. This can cause some students to become confused when naming coins or counting money.
 Observing students will allow you to see if they have difficulty unitizing. If they are having difficulty naming the rods, or giving their value, you may need to guide them to go back and line the white rods (pennies) against the yellow (nickel) and orange (dime).
 Asking questions about the cube and which rods were most likely to be rolled help to develop students’ sense of probability concepts. Changing the outcomes on the cube to have equal representation (i.e. 1,1,5,5,10,10) will make the likelihood for rolling each coin equal. Likewise, changing the possible outcomes to (1, 1, 5, 10, 10, 10) will definitely result in higher totals.
 Activity modified from Super Source K2 Cuisinaire Rods
Other Sample Activities from TIPS for Manipulatives  Relational Rods
1. Build a staircase (see picture). What is the total volume? Determine the volume if there are 100 “steps”.
2. Create a structure or design. Hide it from your partner’s view then describe it so your partner can build it.
3. How many different ways can you make “trains” that have the same length as one yellow rod? (e.g. 1 purple and 1 white, or 2 reds and 1 white).
4. Describe the relationship between one purple rod and one dark green rod.
5. Jake has 1 white rod and 1 red rod. Taz has 1 orange rod and 1 yellow rod. Make a list of comparisons between their two sets.
6. Jasm has a train of 4 white rods and a train of 2 red rods. She writes the equation 4w = 2r to algebraically model what she sees. Explain the connection between the train model and the algebraic model.
7. What does one green rod represent if one red rod represents onehalf? (or viceversa).
8. Terry represents the fraction twothirds by placing a red rod on top of a light green rod. Use the relational rods and Terry’s method to build different models of twothirds.
9. Use the length of the yellow rod as a unit of measure. Measure the width of this page. Now measure the width of this page using the red rod. Can you determine the answer without actually measuring?
10. Use five different rods and 1cm grid paper. Place the rods to create a shape that can be cut from the paper. Challenge a classmate to determine how you created the shape. Can other shapes be created using the same rods so that the shapes have the same perimeter? area? Which shape has the greatest perimeter?
11. Create a pattern, Extend the pattern. Develop a rule for the pattern.
12. Create a pattern. Draw a reflection of the pattern.
1. Build a staircase (see picture). What is the total volume? Determine the volume if there are 100 “steps”.
2. Create a structure or design. Hide it from your partner’s view then describe it so your partner can build it.
3. How many different ways can you make “trains” that have the same length as one yellow rod? (e.g. 1 purple and 1 white, or 2 reds and 1 white).
4. Describe the relationship between one purple rod and one dark green rod.
5. Jake has 1 white rod and 1 red rod. Taz has 1 orange rod and 1 yellow rod. Make a list of comparisons between their two sets.
6. Jasm has a train of 4 white rods and a train of 2 red rods. She writes the equation 4w = 2r to algebraically model what she sees. Explain the connection between the train model and the algebraic model.
7. What does one green rod represent if one red rod represents onehalf? (or viceversa).
8. Terry represents the fraction twothirds by placing a red rod on top of a light green rod. Use the relational rods and Terry’s method to build different models of twothirds.
9. Use the length of the yellow rod as a unit of measure. Measure the width of this page. Now measure the width of this page using the red rod. Can you determine the answer without actually measuring?
10. Use five different rods and 1cm grid paper. Place the rods to create a shape that can be cut from the paper. Challenge a classmate to determine how you created the shape. Can other shapes be created using the same rods so that the shapes have the same perimeter? area? Which shape has the greatest perimeter?
11. Create a pattern, Extend the pattern. Develop a rule for the pattern.
12. Create a pattern. Draw a reflection of the pattern.
Recommended Websites for Relational Rods
http://nrich.maths.org/public/leg.php?code=297
http://www.arcytech.org/java/integers/integers.html  virtual relational rods http://teachertech.rice.edu/Participants/silha/Lessons/cuisen2.html  fractions with relational rods http://www.learner.org/channel/courses/learningmath/number/session8/part_b/  fractions with relational rods http://www.learner.org/channel/courses/teachingmath/grades6_8/session_02/section_02_h.html  communication http://mason.gmu.edu/~mmankus/Handson/crods.htm  template for making relational rods http://www.nzmaths.co.nz/Measurement/Length/Pythagoras.htm  pythagorean theorem with relational rods
http://www.arcytech.org/java/integers/integers.html  virtual relational rods http://teachertech.rice.edu/Participants/silha/Lessons/cuisen2.html  fractions with relational rods http://www.learner.org/channel/courses/learningmath/number/session8/part_b/  fractions with relational rods http://www.learner.org/channel/courses/teachingmath/grades6_8/session_02/section_02_h.html  communication http://mason.gmu.edu/~mmankus/Handson/crods.htm  template for making relational rods http://www.nzmaths.co.nz/Measurement/Length/Pythagoras.htm  pythagorean theorem with relational rods
Resources
NCTM. (n.d.). Research on the benefits of math manipulatives. Retrieved May 25, 2016, from https://www.hand2mind.com/pdf/learning_place/research_math_manips.pdf
OAME. (n.d.). TIPS for Manipulatives  Relational Rods. Retrieved May 24, 2016, from http://oame.on.ca/lmstips/files/Manips/RelationalRods.pdf
OAME. (n.d.). TIPS for Manipulatives  Relational Rods. Retrieved May 24, 2016, from http://oame.on.ca/lmstips/files/Manips/RelationalRods.pdf