Two-Digit Addition and Subtraction with Sums and Differences to 100
MATH TALK WORDS: open number line, hundreds chart, place value model, inventive strategy, add and subtract
Hundreds Chart
Place Value
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Types of Word Problems
Online word problem activities: Word Problems with Katie
Below are some examples of one and two-step word problems, as well as a link to additional examples.
One-step word problems
Two-step word problems
One-step word problems
- Some pennies were in a dish. Hank used 29 pennies and bought a piece of gum. There were 63 pennies left in the dish. How many pennies were in the dish to start?
- Lisa dyed a lot of eggs for Easter. She dipped 54 eggs in red dye and 19 eggs in blue dye. How many eggs did Lisa dye?
- Deron sold 47 pumpkins. Some of the pumpkins were sold on Thursday and 19 pumpkins were on sold on Friday. How many pumpkins were sold on Thursday?
- The girl spotted 31 red cars on the first day of her family's cross country road trip. She spotted some more red cars on the second day. The girl spotted 59 red cars on the first and second day of the trip. How many cars did she see on the second day?
- Jada has 39 marbles. Jada finds 16 more marbles in her toy box. How many marbles does Jada have now?
- The friends caught 37 fireflies one warm summer night. The next night, the friends caught 15 more fireflies. How many fireflies did the friends catch in all?
Two-step word problems
- Mrs. Longsworth asked 16 students to help her with field day. 6 of the students were fifth graders and the rest were fourth graders. The next day, she asked the same fourth grade and 4 more fourth graders to help. How many fourth graders helped on the second day?
- Mrs. Reigle buys a toy for her niece that is $45. She has $15 in her wallet. Mrs. Reigle finds $23 in her purse. How much more money does she need to buy the toy?
- Mrs. Ditmars collect 83 cans to recycle. Mrs. Ditmars collect 26 cans on Monday, 32 cans on Tuesday, and the rest of the cans on Wednesday. How many cans did Mrs. Ditmars collect on Wednesday?
- There are 76 balls on the playground. 40 were tennis balls and 29 were kick balls. The rest were softballs. How many softballs were on the playground?
- 51 children lined up to buy lunch. 12 more children joined the line, but 7 children decided not to buy lunch. How many children bought lunch?
Invented Strategy for Adding and Subtracting Two-Digit Numbers
This information below was taken from documents prepared by the CCPS Elementary Math Department.
What is an invented strategy?
An invented strategy is any method used in calculation that does not use physical materials, counting by ones, or a clearly defined set of steps or procedure. Invented strategies are flexible methods for computation that involve taking apart and combining numbers in a variety of ways. This flexibility is based on place value or numbers that work easily together. A student, a peer, or a class can invent strategies. Teachers may also suggest ideas.
Invented Strategies vs. Standard Algorithms
· Invented strategies are number-oriented rather than digit-oriented.
When using the standard algorithm for 36 + 43, children may not think of 30 and 40 but rather 3 + 4. The idea of the value of the entire number is lost.
· Invented strategies are left handed, not right handed.
Invented strategies begin with the largest parts of numbers (represented by the leftmost digits). For 75 + 26, an invented strategy might begin with 70 + 20. Starting on the left provides a sense of the size of the eventual answer in just one step. The standard algorithm, however, begins on the right with 5 + 6 is 11. Starting with the rightmost digits hides the result until the end of the computational procedure.
· Invented strategies are flexible.
Unlike standard algorithms, invented strategies use different entry points to begin solving a problem.
What are the benefits of using invented strategies in the elementary classroom?
· Students make fewer mistakes because they develop and understand their own computational strategies.
· Students develop deep understanding of place-value because invented strategies are number-oriented.
· As students develop proficiency with invented strategies, they are able to use them mentally without having to record their thinking.
· Invented strategies are often faster than the standard algorithm because they take less time than the steps to the standard algorithm.
· According to international measures of proficiency, students who use invented strategies perform as well or better than their peers who are taught only standard algorithms.
When are students taught standard algorithms?
Students first develop conceptual understanding of operations. Next, they begin to develop, discuss, and look for efficient, accurate, and generalizable computational methods (invented strategies). This stage of development is extensive, requiring months, not weeks, of work. Students do not invent flexible methods of computation spontaneously. Teachers must carefully create learning situations and environments that allow children to develop their own methods of invented computation. Finally, students are introduced to the standard algorithm. Rather than seeing it as a series of steps to follow, students better understand that the standard algorithm, like every computational method they have used, must makes sense mathematically.
Source: Van de Walle, J.A., Louvin, L.H., Karp, K.S., Bay-Williams, J.M. (2014). Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades Pre-K – 2, 2nd edition. Boston, MA: Pearson.
An invented strategy is any method used in calculation that does not use physical materials, counting by ones, or a clearly defined set of steps or procedure. Invented strategies are flexible methods for computation that involve taking apart and combining numbers in a variety of ways. This flexibility is based on place value or numbers that work easily together. A student, a peer, or a class can invent strategies. Teachers may also suggest ideas.
Invented Strategies vs. Standard Algorithms
· Invented strategies are number-oriented rather than digit-oriented.
When using the standard algorithm for 36 + 43, children may not think of 30 and 40 but rather 3 + 4. The idea of the value of the entire number is lost.
· Invented strategies are left handed, not right handed.
Invented strategies begin with the largest parts of numbers (represented by the leftmost digits). For 75 + 26, an invented strategy might begin with 70 + 20. Starting on the left provides a sense of the size of the eventual answer in just one step. The standard algorithm, however, begins on the right with 5 + 6 is 11. Starting with the rightmost digits hides the result until the end of the computational procedure.
· Invented strategies are flexible.
Unlike standard algorithms, invented strategies use different entry points to begin solving a problem.
What are the benefits of using invented strategies in the elementary classroom?
· Students make fewer mistakes because they develop and understand their own computational strategies.
· Students develop deep understanding of place-value because invented strategies are number-oriented.
· As students develop proficiency with invented strategies, they are able to use them mentally without having to record their thinking.
· Invented strategies are often faster than the standard algorithm because they take less time than the steps to the standard algorithm.
· According to international measures of proficiency, students who use invented strategies perform as well or better than their peers who are taught only standard algorithms.
When are students taught standard algorithms?
Students first develop conceptual understanding of operations. Next, they begin to develop, discuss, and look for efficient, accurate, and generalizable computational methods (invented strategies). This stage of development is extensive, requiring months, not weeks, of work. Students do not invent flexible methods of computation spontaneously. Teachers must carefully create learning situations and environments that allow children to develop their own methods of invented computation. Finally, students are introduced to the standard algorithm. Rather than seeing it as a series of steps to follow, students better understand that the standard algorithm, like every computational method they have used, must makes sense mathematically.
Source: Van de Walle, J.A., Louvin, L.H., Karp, K.S., Bay-Williams, J.M. (2014). Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades Pre-K – 2, 2nd edition. Boston, MA: Pearson.