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Number Relationship 7 Materials needed: 110 popsicle sticks or straws, bundled into groups of 10 for each student or each pair of students, and one teacher set 12 x 18 foam sheet for screening (Teacher says words in italics.)

Part I: Incrementing and Decrementing Off the Decade 1. Place out 3 bundles and 2 sticks. How many sticks are there? Place out another bundle. How many sticks are there now? Continue to ten bundles and 2 sticks. Example: B B B SS B B BBBBB Remove one bundle. How many sticks are there now? Remove another ten. How many sticks are there now? Continue to zero bundles and 2 sticks. 2. Briefly display and screen two bundles and 4 sticks. How many sticks are there under the screen? Place another bundle under the screen. How many now? Continue to six bundles and 4 ones. How many sticks are there under the screen? Check to see if you are correct. Place another bundle under the screen. How many now? Continue to 10 bundles and 4 ones. How many sticks now? How many bundles? Check to see if you are correct. Remove one bundle. How many sticks are there now? Remove another bundle. How many sticks are there now? Continue to six bundles. How many now? Check to see if you are correct. Remove one bundle. How many sticks are there now? How many bundles are there now? Continue to zero bundles and 4 sticks.

****Continue this routine with various numbers, adding or removing bundles.

Š 2008. Michelle Miller & Tina Silvestri, Solon City Schools. Adapted from: Wright, R., Martland, J., Stafford, A., Stanger, G. (2006) Teaching Number.


Part II: Incrementing by Tens and Ones Unscreened 1. Direct students to build 50 with their bundles and sticks. How many bundles? How many sticks? Direct students to build 16. How many bundles? How many sticks? Direct students to find the number of sticks all together. Ask volunteers to explain how they used the bundles and sticks. Record student thinking both ways (split and jump – examples of each method are shown). Split Method 50 + 10 =60 0 + 6 =6 66

Jump Method(using the ENL) 50

60 61 62 63 64 65 66

2. Direct students to build 64 with their materials. How many bundles? How many sticks? Direct students to build 20. How many bundles? How many sticks? How many sticks all together? Ask volunteers to explain how they used the bundles and sticks. Record student thinking both ways (split and jump – examples of each are shown). Split Method

Jump Method (using the ENL)

60 + 20 = 80 4+0 = 4 84

64

74

84

****Continue this routine with various adding or subtracting using the materials.

© 2008. Michelle Miller & Tina Silvestri, Solon City Schools. Adapted from: Wright, R., Martland, J., Stafford, A., Stanger, G. (2006) Teaching Number.


Part III: Incrementing by Tens and Ones Partially Screened 1. Briefly display and then screen 4 bundles. How many sticks are there under the screen? Place 2 bundles and 7 stick beside the screen. How many next to the screen? How many sticks all together? Record student thinking both ways (split and jump – examples are shown below). Split Method 40 + 20 =60 0+7= 7 67

Jump Method (using the ENL) +10 40

+7 60

67

Ask students to write a number sentence for this problem. (40 + 27 = 67) 2. Briefly display and then screen 4 bundles and 7 sticks. How many sticks are there under the screen? Put 3 bundles next to the screen. How many next to the screen? How many sticks all together? Record student thinking both ways (split and jump – examples are shown below). Split Method

Jump Method

40 + 30 = 70 0+7= 7 77

47

57

67

77 80

84

Ask students to write a number sentence for this problem. (40 +37 = 77) 3. Briefly display and then screen 3 bundles and 5 sticks. How many sticks are there under the screen? Put 2 bundles next to the screen. How many next to the screen? How many sticks all together? Record student thinking both ways (split and jump – examples are shown below). Split Method 30 + 20 =50 5 + 0 =5 55

Jump Method

35

45

55

60

62

Ask students to write a number sentence for this problem. (35 +20 =62)

****Continue this routine with various adding or subtracting using the materials. © 2008. Michelle Miller & Tina Silvestri, Solon City Schools. Adapted from: Wright, R., Martland, J., Stafford, A., Stanger, G. (2006) Teaching Number.


Part IV: Independent Practice 1. Have students complete various problems using materials if needed. Some Everyday Math Resources that can be used from this unit are: Everyday Math 4.1 Study link is a good resource(except change number 1 to “Becky ate 10 grapes.” The start should be 10 not 11. Additional practice can be found in 4.1 Mental Math and Reflexes, 4.3 Mental Math and Reflexes, 4.4 Mental Math and Reflexes, 4.5 Mental Math and Reflexes, and 4.6 Mental Math and Reflexes.

Notes: •

Students can also use tiny ten frames or ten strips in place of bundles and sticks. Bundles and sticks provide more support, as the child is able to break apart the bundles if necessary.

Part I: Incrementing and Decrementing Off the Decade promotes the jump method of addition and subtraction. This method allows a student to solve an addition or subtraction problem without regrouping.

© 2008. Michelle Miller & Tina Silvestri, Solon City Schools. Adapted from: Wright, R., Martland, J., Stafford, A., Stanger, G. (2006) Teaching Number.


Incrementing and Decrementing Ten-Bundles and Sticks