# Adding and Subtracting Number to 100

**Strand:** Number

**Outcomes:** 8, 9

## Step 3: Plan for Instruction

### Guiding Questions

- What learning opportunities and experiences should I provide to promote learning of the outcomes and permit students to demonstrate their learning?
- What teaching strategies and resources should I use?
- How will I meet the diverse learning needs of my students?

### A. Assessing Prior Knowledge and Skills

Before introducing new material, consider ways to assess and build on students' knowledge and skills related to counting. For example:

- Can the student read number sentences such as 4 + 5 = , 7 – 5 = or variations such as 4 + = 9, + 5 = 9, – 5 = 2, 7 – = 2? (Does the student use the terms: "plus," "minus," "add," "subtract", "equal" and, when appropriate, a term for the variable, such as "something", "blank," "box," or "what/some number"?)
- Can the student demonstrate the meaning of such number sentences to sums of 20 or with minuends no larger than 20, by dramatizing a problem with manipulatives, with pictures or with diagrams? If not, can the student do so to answers of 10? Clarify whether the problem is with the size of the numbers, the concepts of addition and subtraction or the vocabulary. If the student is not yet able to demonstrate competence with addition and subtraction facts to ten, check for rote counting and one-to-one correspondence to 10 and then 20.
- Model the addition of 12 and 4 using concrete or visual representations and record the process symbolically. Can the student create addition models (to sums of 20) and write the corresponding symbolic representations?
- Model the subtraction of 8 from 13 using concrete or visual representations and record the process symbolically. Can the student create subtraction models and record the process symbolically (using numbers no larger than 20 for the minuend)?
- Can the student create an addition or subtraction story problem for various number sentences such as: 13 – 8 = or 8 + = 13?
- How accurately and how rapidly does the student solve these problems?
- Can the student verbalize the strategy used?

If a student appears to have difficulty with these tasks, consider further individual assessment, such as a structured interview (see sample), to determine the student's level of skill and understanding. The Kathy Richardson books listed in the bibliography contain excellent structured interviews for investigating concept development. They also indicate how a teacher can address the development of missing concepts.

Sample Structured Interview: Assessing Prior Knowledge and Skills

If the student is very proficient in producing correct answers quickly and can verbalize the strategies being employed, you may need to consider additional challenges for this student while others are developing their skills to this level. Challenges could range from developing recognition of alternate personal strategies and flexibly using them, to employing the skills in more complex story problems. Students can be challenged to improve their explanations of personal strategies used. Searching for relationships amongst problems is another way to challenge students who are proficient with these operations and the related concepts. For example, students could be asked to solve a series of problems and examine their solutions to find a relationship or pattern and explain why it exists. One such series of problems is: 25 – 13, 26 – 14 and 27 – 15. There are many opportunities to challenge students in this area of the curriculum.

### B. Choosing Instructional Strategies

Consider the following guidelines for teaching addition and subtraction:

- Use "subtract" or "minus," but not "take away," so as not to reinforce a narrow, incomplete definition of subtraction.
- Interchange "is the same as" with "equal" frequently to reinforce the meaning of "equal."
- Teach frequently in a problem-solving context. Research shows that by solving problems using addition and subtraction, students create personal strategies for computing and develop understanding about the relationship between the operations and their properties (NCTM 2000, p. 153). Overly simple problems make it easy for some students to develop strategies such as identifying two large numbers in a problem means that you add, whereas a large and a small number in a problem indicate subtraction.
- Provide time for students to create personal strategies to solve the problem and share these strategies with members of their groups or with the entire class.
- Choose problems that relate to the student's own lives. Contextual problems might derive from recent classroom experiences, including literature sharing, a field trip, or learning in other subject areas such as art or social studies.
- Provide a variety of problems representing the different addition and subtraction situations with varying degrees of difficulty to differentiate instruction.
- Work with the whole group initially and have the students paraphrase the problem to enhance understanding and to recognize which numbers in a problem refer to a part or to a whole.
- Provide a variety of manipulatives, including base ten blocks and others that can be grouped in tens and ones, such as tiles, pennies, stir sticks, straws, ice cream sticks, Unifix cubes, multilinking cubes or beans for students to use as needed.
- Guide the discussion about the operations of addition and subtraction by asking questions to encourage thinking about number relationships, the connections between addition and subtraction and their personal strategies. Such questions could include:
- When we add two numbers, is the sum usually bigger or smaller than either of the numbers? We have to be careful not to say "always bigger," since when students add negative numbers eventually, this is not so. Also, when we add zero, the number stays the same.
- When we subtract two numbers, is the difference usually less than or more than the number we subtracted from?
- Does the difference change if we subtract a subtrahend one larger than the last from a minuend that is one larger than the last? What about if we decrease both numbers in the subtraction problem by one? What if we were to increase or decrease both numbers in the problem by 2? What if we increase the minuend by 1 and the subtrahend is decreased by 1?
- Can we break numbers up in ways that make it easier for us to add or subtract the parts in order to arrive at the answer mentally and efficiently?

- Challenge the students to solve the problem another way, do a similar problem without models or clarify the explanation of their personal strategies.
- Have the students evaluate their personal strategies as well as those of their classmates to decide which strategy works best for them and why.
- Limit the number of story problems that students are solving a day to one or two and leave half a page where each solution can be shown and explained.

### C. Choosing Learning Activities

Learning Activities are examples of activities that could be used to develop student understanding of the concepts identified in Step 1.