Adding and Subtracting Number to 100

Strand: Number
Outcomes: 8, 9

Step 5: Follow-up on Assessment

Guiding Questions

What conclusions can be made from assessment information?
How effective have instructional approaches been?
What are the next steps in instruction?

A. Addressing Gaps in Learning

Students who have difficulty solving addition or subtraction problems by using personal strategies will enjoy more success if one-on-one time is provided. This time will allow for open communication to diagnose where the learning difficulties lie. Observing a student solving problems will provide valuable data to guide further instruction. Success in problem solving depends on a positive climate in which the students are comfortable taking risks. Find out which concepts and skills each student already has and build upon them.

If the difficulty lies in understanding the problem, use the following strategies:

Provide problems that relate to the student's interests and personalize the problem by using the student's name in the problem and/or the names of his or her friends or family members.
Initially use smaller numbers in the problem.
Ask the student the following questions about the problem:
- What are you asked to find out?
- What do you know?
- What information do you need?
- Is some of this information unnecessary?
Have the student paraphrase the problem.
Guide the student to determine if the numbers refer to a part or the whole.
Ask the student if the unknown in the problem refers to a part or a whole.
Provide manipulatives for the students to represent the problem as needed.
Have the student act out the problem, using other students and manipulatives as needed.
Have the student decide which operation should be used and why.
Ask guiding questions to show the connections between addition and subtraction and the possible option of thinking addition for subtraction.

If the difficulty lies in using personal strategies to solve addition and subtraction problems, use the following strategies:

Initially use smaller numbers in the problems.
Review place value, counting by tens beginning with any number (the hundred chart or base ten blocks are useful for this) and number facts.
Provide counters that can be grouped in tens or base-ten materials as needed.
Think aloud a personal strategy that you would use to solve the problem and explain why this strategy is more efficient than another one that you describe.
Emphasize flexibility in choosing a personal strategy; a strategy that is efficient for one student may not be efficient for another student.
Build on the student's understanding of place value and number facts to guide him or her in finding a strategy that works.
Provide ample time for students to think and ask questions to clarify their thinking.
Have students work in groups so that they learn strategies from one another.
Guide students to critique various personal strategies to find one that can be used on a variety of problems efficiently.
Have students explain their personal strategies to the class so others can hear how they work in kid-friendly language.
Post various personal strategies in the classroom for students to share and critique.

B. Reinforcing and Extending Learning

Students who have achieved or exceeded the outcomes will benefit from ongoing opportunities to apply and extend their learning. These activities should support students in developing a deeper understanding of the concept and should not progress to the outcomes in subsequent grades.

Consider strategies, such as the following.

Provide parents information about the importance of students learning to make sense of addition and subtraction situations and developing their own strategies for solving these problems prior to learning the traditional algorithm. If you need detailed information on the rationale to support invented strategies over traditional algorithms, Van de Walle and Lovin (2006) compare the two and lay out the benefits of invented strategies (pp. 160, 161). The benefits include the enhancement of base ten concepts, fewer errors, a foundation for estimation and mental mathematics, and less time consuming, as previously mentioned. Other benefits include less reteaching required and student proficiency on standard tests is at least equal. Show parents the variations in the structure of story problems that exist. Explain that students need practice with all these types of problems and their variations. Let parents know that using key words is not a successful strategy. Give them some samples of the kinds of strategies that students might invent or adopt as personal strategies, so they understand what to look for and encourage.
Provide suggestions for parents about opportunities to involve their students in authentic adding and subtracting situations at home or in the community. For example, at home adding might include how many:
- loads of wash are done in a week, month or year in your household
- pieces of silverware are on the table if each person has a knife, spoon and fork for various numbers of settings
- cans of food are left in the cupboard if you use 6 to make chili
- doors and windows there are in your home
- more or less doors and windows are there in another home than yours.
In a restaurant, help students use amounts rounded to the closest dollar or up to the next dollar to determine how much various options will be or if they have enough money for a particular order.

Take the students shopping and figure out sums of various purchases and differences between purchase options (costs may have to be rounded to the next dollar due to the limitations of the calculation skills of Grade 2 students).

Have the students create problems showing the various types of addition and subtraction problems (change, both joining and separating; part–part–whole; comparison and equalizing) and write appropriate number sentences for each one. These problems can be displayed in a chart or on a bulletin board.
Have the students make their problems more interesting by adding story details or including extraneous information and numbers. Have them write their solutions on the backs of these problems and share their problems with the class.
Have the students create problems with different contexts but using the same numbers, such as 29 and 21. They could follow this up by having the class decide which of the problems could be solved using a given number sentence, such as 29 + 21 = ?
Have the students critique other students' personal strategies and explain why they work or not. Which strategy would be the most efficient and why?
Have the students write explanations of a personal strategy so that everyone in the class can understand it. Challenge the students to solve a problem in a second way.