Calculator Digit Change
Grade 3 Mathematics
Routine - Calculator Digit Change
Standards: 2.NBT.1, 2.NBT.8, 3.NBT.2, 4.OA.5, 4.NBT.1, 4.NBT.2, Mathematical Practice #5
In this routine, students enter a specific two-digit or three-digit number on the calculator. The task is to then change one of the digits in the number without simply entering the new number. For example, change 48 to 78. The classroom discussion should highlight the place value of the digit that is changing (increasing or decreasing) and the value of that digit. In this example, the ten’s digit is increasing by 3. Help students understand that 3 tens is also 30 and on the calculator, they can +30 to change the number from 48 to 78.
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When creating sets of problems for Calculator Digit Change, think about how to create problem strings - sets of problems that share a commonality and build in difficulty, allowing students to generalize about numbers and their relationships and apply strategies from one problem to solve the next. These strings might involve using the same starting point, the same ending point, or a constant difference.
Below are examples that relate to different grade level standards. In each string, the first number is the number that student type into the calculator, and the second number is the "goal number" they are trying to reach using one or more operations. For the first problem in the first string shown below, students would type the number 45 and try to reach 58, such as by +13 or + 10 and + 3 or + 20, – 5, and – 2.
As your students work through the number pairs and share their steps for reaching the target number, you might ask them:
• How does _____'s set of steps for reaching the target number compare to ______'s set of steps?
• How could you reach the target number in fewer steps? More steps? The same number of steps but with different numbers?
• How can you reach the target number using more than one operation?
• How can you reach the target number using one operation more than one time?
Grade 2 Examples
standard: Fluently add and subtract within 100 (2.NBT.5).
| Moving Forwards |
|
Moving Backwards | ||||||
|
45 to 58 45 to 78 45 to 108 |
27 to 40 27 to 100 27 to 200 |
75 to 100 48 to 100 21 to 100 |
19 to 50 29 to 60 49 to 80 |
|
80 to 50 80 to 42 80 to 17 |
100 to 75 100 to 73 100 to 53 |
40 to 32 80 to 32 100 to 32 |
93 to 53 73 to 38 69 to 34 |
Grade 3 Examples
standard: Fluently add and subtract within 1,000 (3.NBT.2).
| Moving Forwards |
|
Moving Backwards | ||||||
|
54 to 100 54 to 300 54 to 420 |
267 to 300 267 to 500 267 to 725 |
250 to 700 215 to 700 189 to 700 |
500 to 720 300 to 520 290 to 510 |
|
300 to 200 300 to 180 300 to 115 |
600 to 450 600 to 245 600 to 119 |
100 to 25 160 to 25 309 to 25 |
560 to 360 460 to 258 459 to 257 |
standard: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations (3.OA.7) and apply properties of operations as strategies to multiply or divide (3.OA.5).
| Moving Forwards |
|
Moving Backwards | ||||||
|
2 to 12 3 to 18 4 to 32 |
3 to 12 5 to 40 8 to 32 |
6 to 18 4 to 36 7 to 28 |
5 to 30 9 to 72 7 to 42 |
|
24 to 6 24 to 3 24 to 2 |
35 to 5 32 to 8 36 to 4 |
42 to 7 48 to 4 21 to 3 |
54 to 9 45 to 5 28 to 7 |
The second set of number pairs offer an opportunity to pose purposeful questions to help students explore with and discuss the use of the distributive and associative properties when multiplying or dividing. For instance, student may use one multiplicative step to go from 2 to 12 (x6) or two steps (x2 then x3 or x3 then x2).
Grade 4 Examples
standard: Multiply a whole number of up to four-digits by a one-digit whole number, and multiply two two-digit numbers (4.NBT.5) and find whole number quotients with up to four-digit dividends and one-digit divisors (4.NBT.6).
| Moving Forwards |
|
Moving Backwards | ||||||
|
30 to 180 20 to 180 60 to 180 |
40 to 240 80 to 240 20 to 240 |
40 to 360 60 to 360 90 to 360 |
25 to 100 25 to 500 25 to 450 |
|
120 to 30 120 to 60 120 to 40 |
160 to 40 160 to 20 160 to 80 |
300 to 30 300 to 60 300 to 50 |
200 to 40 200 to 20 200 to 50 |
| Moving Forwards |
|
Moving Backwards | ||||||
|
4 to 12 4 to 120 4 to 360 |
7 to 28 7 to 280 7 to 490 |
6 to 24 6 to 2400 6 to 24,000 |
9 to 36 9 to 36,000 9 to 72,000 |
|
18 to 6 180 to 6 420 to 6 |
28 to 4 280 to 4 360 to 4 |
32 to 8 3,200 to 8 6,400 to 8 |
15 to 3 15,000 to 3 27,000 to 3 |
The second set of number pairs offer an opportunity to pose purposeful questions to help students explore with and discuss the use of the distributive and associative properties when multiplying or dividing, as well as connecting back to place value standards that address how shifting digits to the right increases their value by a factor of 10. In the first string, students may solve the first pair of numbers, moving from 4 to 12 by typing "x3". Since the second pair of numbers has the same starting point, but an end point that is 10x larger, they may move from 4 to 120 by typing "x3" and then "x10" or simply typing "x30".
standard: Express a fraction with denominators 10 as an equivalent fractions with denominator 100 and use this technique to add two fractions with respective denominators of 10 and 100 (4.NF.5) and use decimal notation for fractions with denominators 10 or 100 (4.NF.6).
| Moving Forwards |
|
Moving Backwards | ||||||
|
0.2 to 0.25 0.2 to 0.26 0.4 to 0.42 |
0.5 to 0.54 0.5 to 0.59 0.7 to 0.75 |
6.3 to 6.34 6.3 to 6.38 9.8 to 9.82 |
5.6 to 5.64 5.6 to 5.67 17.9 to 17.94 |
0.23 to 0.2 0.26 to 0.2 0.35 to 0.3 |
0.54 to 0.5 0.58 to 0.5 0.69 to 0.6 |
3.42 to 3.4 3.48 to 3.4 6.82 to 6.8 |
14.36 to 14.3 14.72 to 14.7 26.95 to 26.9 |
|
Grade 5 Examples
standard: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationships between addition and subtraction (5.NBT.7).
| Moving Forwards |
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Moving Backwards | ||||||
|
0.4 to 1 0.2 to 1 0.7 to 1 |
0.1 to 1 0.5 to 1 0.8 to 1 |
0.6 to 3 0.2 to 6 0.4 to 16 |
4.3 to 5 8.2 to 9 7.6 to 8 |
|
1 to 0.3 1 to 0.9 1 to 0.4 |
1 to 0.6 1 to 0.2 1 to 0.7 |
8 to 0.6 4 to 0.2 9 to 0.7 |
7 to 4.6 3 to 1.2 8 to 3.7 |
| Moving Forwards |
|
Moving Backwards | ||||||
|
0.6 to 1.2 0.06 to 1.2 0.03 to 1.2 |
0.08 to 1.6 0.08 to 3.2 0.08 to 32 |
0.5 to 3 0.05 to 3 0.05 to 12 |
0.7 to 2.1 0.07 to 2.1 0.07 to 21 |
|
1.8 to 0.9 1.8 to 0.09 1.8 to 0.03 |
2.4 to 0.6 2.4 to 0.3 2.4 to 0.03 |
4 to 0.5 12 to 0.5 12 to 0.05 |
7.2 to 0.9 72 to to 0.9 72 to 0.09 |
The second set of number pairs offer an opportunity to pose purposeful questions to help students explore with and discuss the use of powers of ten and the distributive and associative properties when multiplying or dividing. In the first string above, for instance, the first pair of numbers (0.6 and 1.2) and the second pair of numbers (0.06 and 1.2) are similar, but the starting point for the second pair is 10 x smaller than the starting point for the second pair. Because of this, a student can use "x2" to go from 0.6 to 1.2, and then use "x20" or "x10 & x2" to go from 0.06 to 1.2.
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