Math Journal #6

  1. How can you create more culturally sustaining addition and subtraction problems for elementary students?
    1. Provide 3 examples. Include the problem and reasoning for its cultural sustainability.
  2. A carpenter has a board 200 inches long and 12 inches wide. They make 4 identical shelves and still have a piece of board 36 inches long left over. How long is each shelf?
    1. Solve the problem, and write down each step of your process. Why did you do each step?
  3. Albert ate 2 ¾ veggie dogs and Reba ate 1 ½ veggie dogs. What part of all of the hot dogs they consumed did Albert eat?
    1. Solve the problem, and write down each step of your process. Why did you do each step?
  4. Write a real-world math problem that fits naturally with the equation
    1. What method  of solving this would a student use?
  5. Write equations that correspond to the make-a-ten method for adding  depicted below. Your equations should make careful and appropriate use of parentheses.
    1. Which property of arithmetic do your equations illustrate?
  6. Zachary added 3.4 + 2.7 and got the answer 5.11.
    1. How might Zachary have gotten this incorrect answer? Explain to Zachary why this answer is not correct and why a correct method for adding 3.4+2.7 makes sense.
  7. The standard subtraction algorithm described in the text is not the only correct subtraction algorithm. The next subtraction algorithm is called adding the complement. For a 3-digit whole number, N, the complement of N is 999-N. For example, the complement of 486 is . Notice that regrouping is never needed to calculate the complement of a number. To use the adding-the-complement algorithm to subtract a 3-digit whole number, N, from another 3-digit whole number, start by adding the complement of N rather than subtracting N. For example, to solve , first add the complement of 486. . Then cross out the 1 in the thousands column, and add 1 to the resulting number: 1236 → 236 + 1 = 237. Therefore, according to the adding the complement algorithm, 723 – 486 = 237.
    1. Use the adding the complement algorithm to calculate 301-189 and 295-178. Verify that you get the correct answer.
    2. Explain why the adding the complement algorithm gives you the correct answer to any 3-digit subtraction problem. Focus on the relationship between the original problem and the addition problem in adding the complement. For example, how are the problems 723 – 486 and 723 + 513 related? Work with the complement relationship 513 = 999 – 486, and notice that 999 = 1000 – 1.
    3. What are some advantages and disadvantages of the adding the complement subtraction algorithm compared with the common subtraction algorithm described in Beckmann’s text?
    1. Show how to calculate the sum and show how to write the answer as a fraction and as a decimal.
    2. Show how to calculate the sum and show how to write the answer as a fraction and as a decimal.
    3. Discuss briefly what kinds of errors you think students who are just learning about fraction and decimal addition might make with the problems in parts a and b.
  9. Can the following problems about Sarah’s bead collection be solved by adding ¼ + ⅕? If so, explain why. If not, explain why not. Solve the problems if they can be solved. Write a different story problem about Sarah’s bead collection that can be solved by adding ¼ + ⅕.
    1. One-fourth of the beads in Sarah’s collection are pink. One-fifth of the beads in Sarah’s collection are long. What fraction of the beads in Sarah’s collection are either pink or long?
    2. One-fourth of the beads in Sarah’s collection are pink. One-fifth of the beads in Sarah’s collection that are not pink are long. What fraction of the beads in Sarah’s collection are either pink or long?

10.As we read about addition and subtraction, and you used mathematical reasoning to process through your thoughts, what things came up in your mind as you were solving problems? What was maybe difficult to comprehend at first, but became easier? How did you get to that point?  How did doing math with this level of attention feel in contrast to how you’ve done mathematics before?