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Cathy Fosnot Unit: Beads & Shoes, Counting by 2s

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Cathy Fosnot Unit: Beads & Shoes, Counting by 2s

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-skip counting intro
-patterns extension
-pair with six of one, half dozen of another science/engineering activity

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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.

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Special Offer: Save 30% off our list price automatically when you buy 15 or more. 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.

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Cathy Fosnot Unit: Bunk Beds & Apple Boxes

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Cathy Fosnot Unit: Bunk Beds & Apple Boxes

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-basics of number rack and ten frame
-different ways to compose numbers
-turn around facts

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Special Offer: Save 30% off our list price automatically when you buy 15 or more.

Bunk Beds and Apple Boxes: Early Number Senseis one of eight units in the Contexts for Learning Mathematics' Investigating Number Sense, Addition, and Subtraction (K-3)

This unit begins with the story of a pajama party-a sleepover during which eight children play, moving up and down bunk beds, teasing the babysitter who imagines she is losing and then gaining children!

The unit introduces the arithmetic rack as a powerful model and tool to act out the story. The arithmetic rack is a calculating frame consisting of two rows of ten beads with two sets of fives in each row. (Instructions for creating or buying your own arithmetic racks are included.) The five-structure of this apparatus supports the development of part-whole relations in early number sense. Since five is an amount that can often be perceived as a whole, it can be used to support understanding 6 as 5 + 1, or 4 as 5 - 1. It also supports the strategies of doubles and near doubles, 6 + 7 = 6 + 6 + 1, and making tens, 9 + 6 = 10 + 5. In this unit, children move the beads on the arithmetic rack to illustrate and develop an understanding that eight can be named in many ways, for example as 7 + 1, 5 + 3, or 4 + 4. The unit also includes the game Up and Down the Ladder, and employs the use of quick images (a series of related problems flashed only for seconds) to further develop early number sense.

As the unit progresses, the context shifts to an exploration of apple boxes. Children investigate the number of unique combinations for five apples of two kinds, green and red, and record the combinations for a grocer who is confused about how many arrangements there can be. In contrast to the bunk beds investigation in which children can easily imagine someone going up and down the ladder, now they must exchange. That is, instead of moving a counter to another group, the counter must be removed and replaced. This action is more difficult. The recording sheet for the grocer is designed in such a way that a staircase pattern emerges as one red apple is traded for a green apple each time. Boxes holding various numbers of apples (such as six, seven, eight, nine, and ten) are then explored to examine if the staircase pattern will always occur. Data are also collected on the number of possible arrangements for each box: a box of six apples has five possible arrangements; a box of seven has six arrangements; a box of ten has nine arrangements. This supports the development of a systematic way of producing all the possible arrangements and produces another inquiry: Can we predict the number of arrangements if we know the size of the box?

The unit ends with the Part-Whole Bingo game. This game can be played throughout the year as a way for children to extend composing and decomposing strategies as they establish equivalence, for example representing 7 as 5 + 2 or as 3 + 4, or even as 2 + 2 + 2 + 1.

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Special Offer: Save 30% off our list price automatically when you buy 15 or more. Bunk Beds and Apple Boxes: Early 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 story of a pajama party-a sleepover during which eight children play, moving up and down bunk beds, teasing the babysitter who imagines she is losing and then gaining children!