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Mathematical Task 3.1A

Explore various mathematical tasks involving addition, subtraction, and set models with examples of binary operations, properties, and strategies for solving equations. Understand the concepts through set models, measurement models, and take-away or missing-addend approaches.

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Mathematical Task 3.1A

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  1. Mathematical Task 3.1A

  2. Warm-Up What is the largest 2-digit number in Base-10? What is the largest 3-Digit number in Base-10? What is the largest 3-digit number in Base-5? What is the largest 4-Digit number in Base-5? HOW DO WE KNOW?

  3. Number Talk

  4. Number Talk

  5. Mathematical Task 3.1B

  6. Addition and It’s Properties Set Model To find “3+2” using a set model, one must represent two disjoint sets: one set ,A , with three objects and another set, B, with 2 objects. Recall that n(A) denotes the number of elements in set A. The number a+b , read “ a plus b,” is called the sum of a and b, and a and b are called addends or summands of a+b.

  7. Addition is called a binary operation because two (“bi”) numbers are combined to produce a unique (one and only one) number. Multiplication is another example of a binary operation with numbers. Intersection, union, and set difference are binary operations using sets.

  8. Measurement Model 3+4=? Addition can also be represented on the whole-number line. Even though we have drawn a solid arrow starting at zero and pointing to the right to indicate that the collection of whole numbers is unending, the whole numbers are represented by the equally spaced points labeled 0,1,2,3 , and so on. The magnitude of each number is represented by its distance from 0 .

  9. Properties

  10. Properties

  11. Thinking Strategies (Addition Facts) • Commutativity • Adding Zero • Counting on by 1 and 2 • Combinations to 10 • Doubles • Adding 10 • Associativity • Doubles / Associativity

  12. Figure 3.12

  13. Subtraction The Take-Away Approach There are two distinct approaches to subtraction. The take-away approach is often used to introduce children to the concept of subtraction. The problem “If you have 5 coins and spend 2 , how many do you have left?” can be solved with a set model using the take-away approach. Also, the problem “If you walk 5 miles from home and turn back to walk 2 miles toward home, how many miles are you from home?” can be solved with a measurement model using the take-away approach (Figure 3.14).

  14. The number “a-b” is called the difference and is read “a minus b,” where a is called the minuend and b the subtrahend.

  15. The Missing-Addend Approach The second method of subtraction, which is called the missing-addend approach, is often used when making change. For example, if an item costs 76 cents and 1 dollar is tendered, a clerk will often hand back the change by adding up and saying “76 plus four is 80 , and twenty is a dollar” as four pennies and two dimes are returned.

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