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Topics: Addition, subtraction, measurement, skip counting
Materials: See specific lessons
Recommended Grade: K, 1, 2
Common Core: K.CC.B.4, K.CC.B.5, K.OA.A.1, K.OA.A.2, K.OA.A.3, 1.OA.A.1, 1.OA.A.2, 1.OA.D.7
This series of lessons is meant to introduce Cuisenaire rods in a creative, engaging way, and see how Cuisenaire rods can illuminate and motivate addition, subtraction, and measurement.
Cuisenaire rods are one of the great math blocks of all time. They can be used for a vast array of mathematical ideas, from counting to the four operations to fractions. This collection of lessons is designed as a first foray into Cuisenaire rods. They are designed to be engaging, and challenging; they also differentiate easily, and can be used in stations, small groups, whole classrooms, or during choice time.
Materials: Cuisenaire rods, paper bags
Part 1: Play and Discussion
To begin, show students Cuisenaire rods and tell them that they will have some time to build whatever they want. Get them playing as soon as possible, and observe what they build.After they’ve had ten or fifteen minutes to play, take a few minutes to discuss what students have noticed. How do the colors relate? Which colors are longer, and which are shorter? Can you make one color from another? (Record these and other student questions as potential ideas to explore later.) Next, challenge students to arrange the colors from shortest to longest. Each student should make their own “staircase.”
Part 2: Grab Bags
Next, students put one staircase into a paper bag and take turns playing Grab Bag. To play, a student reaches into the paper bag, and, without looking, names the color rod they believe they are holding. They remove that rod from the bag: if they had the correctcolor, they get to keep the rod. Otherwise, they put the rod back in the bag. Whoever gets the most rods wins; a collaborative game where the team just tries to empty their bag together is another option. Here’s some variations to slowly ratchet up the difficulty.
- Game 1: One of each color in the bag.
- Game 2-3: Two of each color in the bag.
- Game 4-5: Three of each color in the bag.
- Game 6: Students handpick 10 – 30 rods to put in the bag to try to make it as challenging as possible.
Materials: Cuisenaire rods, paper and pencil
Challenge students to make the staircase of every color from last time. Once they have built it, ask how many white cubes it would take to cover/build a duplicate copy of the red rod. What about the light green rod? The purple rod? No matter their answers, ask them to defend their answers. Give them time to work on their own to figure out how many white cubes it would take to build a duplicate of any rod.
Discuss with students what numbers they got for different rods, and what their strategies were to determine the number of cubes. Did they need to build every rod using all white cubes? Or did they use what they had found about smaller rods to build the larger ones? (I.e., the dark green is a yellow plus a white, and the yellow is 5 white, so the dark green is 5 + 1 = 6 whites.) Demonstrate how a way of building Cuisenaire rods corresponds to an equation, and let students try saying and writing an equation that they found.
(NOTE: Writing equations is only for students who are conceptually ready. For students who haven’t grasped one to one correspondence, just give them the building challenge without worrying about recording.) Challenge students to build yellow rod in as many different ways they can. They can record how they did it by coloring in the outlines on the worksheet and writing down equations. Students can also try to build and find equations for the larger rods.
NOTE: These equations may have more than two addends.
Students can play Grab Bags or have free play time when they’re done with building yellow rods.
Gather the students together and challenge them to fill in the Numbers Fill-ins with Cuisenaire rods. Pass out the Number Fill-ins. For the first 5-10 minutes, let students work on their own. Observe how they are filling in the outlines.
Once they have tried on their own, gather them together to show them something neat: it’s possible to fill in the “6” using exactly six rods! Which other numbers can be filled in using that number of Cuisenaire rods? Which can’t? Let them work on their own again to tackle the questions. When they find a way to build a number with that number of blocks, they can record it by coloring in outline or writing what blocks they used.
Discuss with students what they found. Could all numbers be made using that number of blocks? Which could and which couldn’t? What strategies did students use for their building? What did students notice and wonder about the whole process? What if they wanted to make two-digit numbers like 1o and 20?
Part 4. (Optional)
Students can try making two-digit numbers, or filling in other designs like the spiral.
Choose a red Cuisenaire rod, and show that the difference between a blue and black rod is exactly one red Cuisenaire rod. Ask the students to find other pairs of rods whose difference is exactly one red rod. Let the students work for a few minutes, then bring them together again to share their results. What patterns did they notice? What conjectures do they have?
Next, send students off to explore what would happen if they were looking for other differences: good ones to explore are a difference of a white, a light green, or a purple rod. Students can also experiment with building longer lines.
Discuss the patterns and ideas students have noticed from their work, and then extend to longer lines. What will the difference be between two dark greens and two purples? Between two oranges
and two browns? When will the difference be exactly two reds long? What about three reds long? If the exploration ends and you still have time, students can continue exploring the fill-ins from the last lesson.
Materials: Cuisenaire rods, paper and pencil, 10 cards for each group
Have students make the staircase of every color from last time.
Once they have built it, show the cards from the next page and pose the question of which cards describes the longest line of Cuisenaire rods.
Read all 10 cards in order (1 orange, 2 blues, etc.) so the students so they see the structure. Then pick the first two cards and pose the question of whether 1 Orange or 2 Blues will be longer.
Ask the students to guess first, then have them build and compare the line they make from each. Then repeat for 2 blues vs. 3 browns.
Once the students understand the task, distribute the cards to them and have them build all of the Cuisenaire rod lines, and determine which is the longest.
- If students don’t know how to get started on their own, encourage them to compare just two cards at a time.
- This is a great project for groups of 2 or 3 students to work on at a time.
- There’s a surprise for the kids as they build: these Cuisenaire rod lines create a symmetrical design when you put them all together (see the right drawing below). Encourage students to keep all their lines as they build. Two natural arrangements are below. When the students are done building, pose the question of why these show up in pairs that are the same length. Students won’t be equipped to answer this, but it is an excellent issue for them to wonder about.
- Look at the differences in the lengths, building on the last lesson. Is there a pattern in the differences?