Beads and Shoes, Making Twos: Extending Number Sense is one of eight units in the Contexts for Learning Mathematics’ Investigating Number Sense, Addition, and Subtraction (K–3)
This unit begins with the context of walking in line—two lines of children holding hands. The context encourages children to explore doubles while also strengthening their understanding of one-to-one correspondence. As the unit progresses, children explore containers that could hold doubles (such as egg cartons, English muffin packages, and juice boxes). Then the context shifts to an examination of pairs of shoes for varying numbers of people. As children investigate these situations, they explore both pairing and doubling—for instance, how six pairs of shoes can also be seen as six right shoes plus six left shoes (six sets of two or two sets of six). Later children work with larger numbers and the terminology of odds and evens is introduced.
In the second week, the story Grandma’s Necklaces is used to develop a context for several investigations related to patterns made with two colors. The first necklace (one blue/one green repeating) can only be made with an even number of objects, because the unit that repeats has two objects. The second necklace (five blue/five green repeating) and the third necklace (three blue/three green repeating) challenge children to see a group of objects doubled as the unit that repeats.
Minilessons in the unit are crafted to support the automatizing of doubles and their use in solving near doubles—for example, using 6 + 6 to solve 6 + 7, or 10 + 10 to solve 9 + 10. Quick images and the arithmetic rack are both used with strings of related problems. The unit also includes the Shoe Game. This game can be played throughout the year for further support in developing the use of doubles as an addition strategy.