Chapter 3: Estimation and Computation

3.3 Algorithms for Addition and Subtraction

3.3.1. Developing Algorithms for Addition

3.3.1.1. Using Models as a Foundation for Addition Algorithms

3.3.1.1.1. Base-Ten Blocks – see ex. 3.14 p. 144-147

3.3.1.1.2. Your turn p. 149: Do the practice and the reflect

3.3.1.2. Developing and Using Paper-and-Pencil Algorithms for Addition

3.3.1.2.1. Expanded Algorithm for Addition –

3.3.1.2.1.1. sometimes called left to right addition

3.3.1.2.1.2. emphasis on place value

3.3.1.2.1.3. see purple box bottom of p. 147

3.3.1.2.2. Standard Algorithm

3.3.1.2.2.1. right to left method

3.3.1.2.2.2. no emphasis on place value

3.3.1.2.2.3. rather abstract

3.3.1.2.2.4. see purple box top p. 148

3.3.1.2.3. See example 3.15 p. 148-149

3.3.1.2.4. Your turn p. 149: Do the practice and the reflect

3.3.1.2.5. Using properties of whole numbers to verify addition algorithms

3.3.1.2.5.1. t-proof format – statements and reasons

3.3.1.2.5.2. see p. 149

3.3.2. Developing Algorithms for Subtraction

3.3.2.1. Using Models as a Foundation for Subtraction Algorithms

3.3.2.1.1. Base-Ten Blocks – see ex. 3.16 p. 150-151

3.3.2.1.2. Your turn p. 151: Do the practice and the reflect

3.3.2.2. Developing and Using Paper-and-Pencil Algorithms for Subtraction

3.3.2.2.1. Expanded Algorithm for Subtraction –

3.3.2.2.1.1. sometimes called left to right subtraction

3.3.2.2.1.2. emphasis on place value

3.3.2.2.1.3. see purple box top of p. 152 – NOT a good way to do this

3.3.2.2.1.4. See example in class for a better model – more analogous to the addition model shown previously

3.3.2.2.2. Standard Algorithm

3.3.2.2.2.1. right to left method

3.3.2.2.2.2. no emphasis on place value

3.3.2.2.2.3. rather abstract

3.3.2.2.2.4. see purple box bottom p. 152

3.3.2.2.3. See example 3.17 p. 152-153

3.3.2.2.4. Your turn p. 153: Do the practice and the reflect

3.3.2.2.5. Using properties of whole numbers to verify addition algorithms

3.3.2.2.5.1. t-proof format – statements and reasons

3.3.2.2.5.2. see example 3.18 p. 154

3.3.2.3. Your turn p. 154: Do the practice and the reflect

3.3.3. Calculator Techniques for Addition and Subtraction

3.3.3.1. Example 3.19 p. 155-156

3.3.3.2. Your turn p. 156: Do the practice and the reflect

3.3.3.3. Example 3.20 p. 156-157

3.3.3.4. Your turn p. 157: Do the practice and the reflect

3.3.3.5. Solving a multiple-step problem

3.3.3.6. Example 3.21 p. 158-159

3.3.3.7. Your turn p. 159: Do the practice and the reflect