Open Number Lines in First Grade The open number line is a number line with no markers. In first grade it is a powerful tool for: • developing a mental number line, • modeling the relationship between addition and subtraction, • seeing subtraction as the distance between two numbers • understanding patterns that occur when adding and subtracting groups of tens • developing mental math strategies Adding 2 Single-­Digit Numbers Emma has 4 more cubes than Ben. Ben has 6 cubes. How many cubes does Emma have? Student draws a line and writes the number 6 on the left because he will be adding to the 6 and numbers increase as you move from left to right on a number line. Student makes one jump, writes 7 below the number line, and 1 above to show how far he jumped. Student continue this process until he has completed 4 jumps “I started at 6. I did one jump to 7 then I jumped one more to 8. I jumped another one to 9 and jumped one more to 10. That’s 4 jumps. 6 + 4 = 10 Emma has 10 cubes.” 1 1 1 1 Modeling the Math 6 + 1 = 7 7 + 1 = 8 8 + 1 = 9 6
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9 + 1 = 10 Or, student draws 4 jumps and goes back and fills in the numbers. “I started at 6. I took four jumps and got to 10. 6 + 4 = 10. Emma has 10 cookies” Subtracting 2 Single-­Digit Numbers (2 Ways) Ben needs to take 9 steps to get to his desk. He took 4 steps. How many more steps does he need to take to get to his desk? Student puts the 9 on the right end of the number line because she will be taking numbers away from the 9 and numbers decrease as you move from right to left of a number line. Counting back starting with 9: “I started at 9. I jumped back one to get to 8. I jumped back another 1 to get to 7. Then I jumped back 1 more to get to 6 and back 1 more to get to 5. I made 4 jumps, 9 -­ 4 = 5. Ben needs to take 5 more steps to get to his desk” 1 1 1 1 Modeling the Math 9 -­‐ 1 = 8 5
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8 – 1 =7 7 -­‐ 1 = 6 Open Numberlines Grade 1 Newton Public Schools 6 -­‐ 1 = 5 1
Counting up from 4: “I started with the 4 and made jumps until I got to 9. I made 5 jumps so Ben needs to take 5 more step. , 4 + 5 = 9 “ Modeling the 1 1 1 1 1 Math 4 + 1 = 5 5 + 1 = 6 4
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6 + 1 = 7 7 + 1 = 8 8 + 1 = 9 Adding Multiples of Ten to any 2-­Digit Number does she have Dilsa has 37 crayons in her backpack. She finds 20 more. How many crayons altogether? “I started with 37. First I jumped 10 to 47, then I jumped 10 to 57. 10 + 10 = 20. 37 + 20 =57. Dilsa has 57 crayons.” 10 10 Modeling the Math 37 + 10 = 47 47 + 10 = 57 37 47 57 Subtracting Multiples of Ten from any 2-­Digit Number Adam baked 61 cookies. He gave 30 cookies to his classroom teacher. How many cookies does he have left? “30 has 3 groups of ten so I started with 61 and took one 10 away. That made 51. I took another 10 away, that made 41. I still had 10 more to take away, that made 31, so 61 -­ 30 = 31. Adam had 31 cookies left” 1
0 10 10 Modeling the Math 61 – 10 = 51 51 -­‐ 10 = 41 31 41 51 61 41 -­‐ 10 = 31 Adding a 1-­Digit Number to a 2-­Digit Number Tyler has 9 more markers than Emily. Emily has 37 markers. How many markers does Tyler have? Using landmark (friendly) numbers by moving to the nearest ten: “I started with 37. First I jumped 3 to get to 40, which is a friendly number. 9-­3 = 6 so I had 6 left. I know 40 + 6 = 46 so I jumped 6. 37 +9 = 46. Tyler has 46 markers.” 3 6 Modeling the Math 37 + 3 = 40 40 + 6 = 46 37 40 46 Another option would be to take 9 jumps of one. Open Numberlines Grade 1 Newton Public Schools 2
Second Grade Standards Subtracting a 1-­Digit Number from a 2-­Digit Number Sam has 5 fewer baseball cards than Ella. Ella has 63 cards. How many cards does Sam have Using landmark (friendly) numbers by moving to the nearest ten: I started with 63. I jumped back 3 to 60. Sam had 5 fewer so I still had 2 cards to take away. I jumped back 1 to 59 and back 1 more to 58. 63 -­5 = 58. Sam has 58 cards” Modeling the Math 1 1 3 63 -­‐ 3 = 60 60 -­‐ 1 = 59 58 59 60 63 59 – 1 = 58 Another option would be to take 5 jumps of one. Adding Two 2-­Digit Numbers (2 Ways) Pedro baked some cookies for his class. They ate 37 cookies. There were 24 cookies left. How many cookies did Pedro bake? Using landmark (friendly) numbers: “I started with 37. First I jumped 3 to 40. Then I jumped 20 to 60, 20 + 3 = 23. I needed to add one more so I jumped 1 to 61. 37 + 24 = 61. Pedro baked 61 cookies.” 3 20 1
Modeling the Math 37 + 3 = 40 40 + 20 = 60 60 + 1 = 61 37 40 60 61
Keeping one number whole, breaking apart the second number: I started with 37. I broke 24 into 20 and 4. I jumped 10 to 47 and 10 more to 57. Then I jumped 3 to 60. I had 1 more left so added 1 more to 61. 37 + 24 = 61. Pedro baked 61 cookies.” Modeling the Math 10 10 3 1 37 + 10 = 47 47 +10 = 57 57 + 3 = 60 37 47 57 60 61 60 + 1 = 61 Open Numberlines Grade 1 Newton Public Schools 3