K-4 MATHEMATICS STANDARDS

    WHOLE NUMBER COMPUTATION
    ACTIVITY II

    Standard's bullets addressed by activity

    • model, explain, and develop reasonable proficiency with basic facts and algorithms
    • use a variety of mental computation and estimation techniques
    • select and use computation techniques appropriate to specific problems and determine whether the results are reasonable

    Technology

    • Calculators can later be used to verify answers after problems are mentally computed.

    Description of Activity

  • Group or classroom management practices

      • Students work individually. Students can also work in pairs or in small groups to share and discuss their strategies before sharing with the whole class.

    Given situational contexts for basic facts, students use the facts that they already know to arrive at sums of unknown facts. For example:

    • Alicia has seven baseball cards. Her best friend gave her nine more. How many baseball cards does she have now?

    The students should be able to use derived strategies such as the following:

    • I know that 7 + 7 = 14. Because 9 is 2 more than 7, then 7 + 9 has to be 16.
    • I know that 8 + 8 = 16. I took one off the 9 to make the 7 an eight. I've changed the problem to 8 + 8.
    • I can make the 9 a ten by taking one from the 7. My new problem is 10 + 6 = 16.

    Another example:

    • Rosa bought 6 packs of pencils. Each pack had 5 pencils. How many pencils did Rosa buy altogether?

    Possible strategies:

    • I can count by fives for each pack of pencils­5, 10, 15, 20, 25, 30. There are 30 pencils.
    • I know that 5 x 5 = 25; one more group of 5 makes 30.

    Another example:

    • Passing by the candy shelves, Juanita wanted two different kinds of candy. One cost 48¢ and the other cost 23¢ (no sales tax). She has 75¢ with her. Does she have enough money to buy the two kinds of candy?

    Possible strategies:

    • 48¢ is about 50¢ and 23¢ is about 25¢. Yes, she has enough money. She'll even get change back. Her change will be 4¢.
    • I know that 40 + 20 = 60 and 8 + 3 = 11, so 60 + 11 = 71. Both candies will cost 71¢. Yes, she has enough money.

    Suggested questions:

    • Does anyone else have a different way of solving the problem?
    • Was there a strategy different from yours that you thought was easier? Why do you think it was easier? Will you use that strategy with other problems?
  • Extensions

    • Give situational problems where the solutions are given. Ask the students if the answers are reasonable. The following is an example:

      Three fourth-grade teachers at Talofofo Elementary School decided to take all their students on a picnic. Mrs. Tenorio spent $26.84 for refreshments. Since the three teachers wanted to share the cost of the picnic, Mrs. Tenorio used her calculator to determine that each teacher should pay her $13.47. Is her answer reasonable? Explain.

    After the students figure out that the answer is not reasonable, another extension to this problem would be to ask the students how Mrs. Tenorio got her answer.

    Reference

    National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM. pp. 44-45.