The Evolution of the Number Bond

Composing and Decomposing Numbers  “Focusing on a quantity in terms of its parts has important implications for developing number sense.” (Van de Walle, 2013, p 139)  “If basic facts are to be foundational, they must be based on an understanding of the composition and decomposition of numbers. When children know the parts of numbers through 10, they automatically know the basic facts.” (Richardson, 2012, p 43)  “Fluency is knowing how a number can be composed and decomposed and using that information to be flexible and efficient with solving problems.” (Parrish, 2010, p 38)  “Number bonds help students see that numbers can be "broken" into pieces to make computation easier. With number bonds, students recognize the relationships between numbers through a written model that shows how the numbers are related.” (Hazekamp, 2011)

The number bond is a pictorial representation of a part-part-whole relationship. They show that within a part-whole relationship smaller numbers (the parts) make up larger numbers (the whole). The number bond may be presented using circles or squares in various orientations. The number bonds of 10 have the greatest priority because students will use them for adding and subtracting across 10. Students move toward fluency in grade 1 with numbers to 10 building on the foundation laid in Kindergarten. They learn to decompose numbers to 10 with increasing fluency. (1.OA.C.6) Students learn the meaning of addition as “Putting together” to find the whole or total and subtraction as “taking away” to find a part.

Classroom Displays

Number Bonds for Ten Less Begin with Manipulatives

Number Bracelets and Rekenreks Great tool for finding the unknown in an equation. 10 = ___ = 10 - ___

Number Bonds to 10

Shake and Spill

7 + 6 = Decomposing to Make a Ten = =

Doubles Plus = = 5 1

Renaming Tens = = 7 30

Add a 1-Digit Number to a 2-Digit Number by Making a Ten = =

10 35 ? Ten More Ten Less ? ?

Subtract a 1-Digit Number from a 2-Digit Number by Making a Ten = = Hold the 30, then think 10 – 8 = 2 and = Hold the ___, then think 10 – __ = __ and ______

Recall a Fact = = Hold the ___, then think ________and _______ Hold the 30, then think 15 – 8 = 7 and =

Adding Within = = = 332

Subtracting Within = = = = 98

The Distributive Property 36 ÷ 6 30 ÷ 6 6 ÷ 6 7 x 8 5 x 8 2 x 8

The Distributive Property 48 ÷ 4 9 x 8

Number Bonds with Fractions

Number Bonds with Fractions  Draw a tape diagram that represents 1 whole.  Now shade one third.  Decompose each of the thirds in half.  How many parts are there now? Show this with a number bond.  What can we say about one third and two sixths?  Now write this as an equation using addition and multiplication.

Number Bonds with Fractions

Number Bonds with Fractions

Number Bonds with Fractions

Number Bonds with Time 40 min min. = 35 min min. = hr. 15 min.

Number Bonds with Measurement 8 in. + 7 in. = 1 ft 3 in oz + 9 oz. =1 lb 4 oz. 5 4

Number Bonds with Money