Do you have your stockpile of shoestrings ready? Have you been waiting on the edge of you chair for more shoestring math ideas? Well, here are just a few more ways that shoestrings can help you address mathematical concepts.

For K-2 students

• Use shoestrings to build fluency with basic facts and to help build understanding of the various ways numbers can be decomposed. For example, have a kindergarten student string five beads onto half of a shoestring (then TIE A KNOT IN BOTH ENDS), and have the student slide one bead to the left and the rest to the right. Discuss the equation that would describe what the student sees. Or, ask a more open-ended question like, “How many different ways can you decompose five?” For first and second grade students who are responsible for decomposing 10 and 20, put 10 or 20 beads on the shoestrings, and ask them to explore the various ways the beads can be decomposed.

• Use shoestrings to build understanding of place value. Give each student at a table or group a string with ten beads, and give each table or group a small cup of nine “loose ones.” Have each group identify the largest number they could make with the tens and “loose ones” they have. Ask them to explain how they know they are correct, and allow other groups to question their thinking. Have the tables or groups build various numbers together, such as 37, 42, etc. and discuss how many tens and how many ones each number has. Ask questions like, “How many students would have to put their strings together to represent 100, 130, etc.?” This activity will be available in the kindergarten mathematical practice unit soon.

• Use shoestrings to teach the commutative property. Have two students face each other with a string of beads between them. Instruct one student to slide a bead to the left and to slide all other beads to the right. Have students record what they see as they look from left to right from their perspective. Compare the two equations. For example, one student should see 1 + 19 = 20, and the other student should see 19 + 1 = 20. Both equations have the same total, but the students are adding the numbers in a different order. This activity will be available in the 1st grade Mathematical practice unit.

For 3-6 students

• Use shoestrings to locate mixed numbers or improper fractions on a number line. Have students write the numbers one through eight evenly spaced across the shoestring. Have the students locate a fraction like 15/3. Discuss how division comes into play as they attempt to approximate where it belongs. Have students justify the location they chose.

• Have students identify where a certain fraction (e.g., 2/3 ) would be located on the shoestring, then ask them how far that fraction is from one (1/3). This will reinforce the concept of 3/3 = 1, 4/4 =1, etc. Many of your students will be using the identity property to find equivalent fractions.

• Use the shoestrings for factoring and for determining if a number is prime or composite. Place 100 beads, (or any amount you choose) on a shoestring. Ask the students if the number is divisible by three and if the students can prove it using the string of beads. Or, ask them to identify all of the prime numbers between 0 and ___. Encourage them to use their shoestring to prove they are right.

• Use shoestrings to explore the relationship between the diameter and circumference of a circle. Have students wrap the shoestring around a circle or can, then have them check to see how many diameter lengths are in that circumference. Hope fully they will see that it’s always a bit more than three. (roughly 3.14)

• Use shoestrings to find the perimeter of various objects in the classroom. By surrounding the objects, marking and comparing the lengths to a ruler, meter stick, etc., students will be cementing the idea that perimeter is about the distance around, whether they are looking at a two-dimensional shape in their textbook or a three dimensional object like a tissue box.

I am officially now out of ideas for using shoestrings to teach math concepts. I am counting on you to share your ideas. Please give a shout out in the comment section if you have tried any of my ideas or if you have any other suggestions.