## Using Strategies to Solve Math Problems

A child’s concept of number relationships through engaging, meaningful and connected exposure to real math gives them the secure knowledge to carry out calculations mentally. This “mental math” can then be easily applied to problem-solving situations.

Below, you will find an easy to use elementary math assessment. It includes a list of facts which children typically memorize – not because of drill and kill skill work, but instead simply through repetitive use. This list may be used as an assessment tool when conferencing with students about their math work. Solution strategies demonstrated may be circled. If the same form will be used more than once, the person doing the assessment may wish to include a small notation of the date each strategy is first noticed.

Beneath the list of “Known Facts,” you will find a list of alternative strategies typically used by children in grades K-6. This same elementary math assessment can be used as a tool or anecdotal record for inclusion in student portfolios, or for conferencing with parents.

## Known Facts

**Double Facts**

- 0+0
- 1+1
- 2+2
- 3+3
- 4+4
- 5+5
- 6+6
- 7+7
- 8+8
- 9+9
- 10+10
- 20+20
- 25+25
- 100+100
- 0thers:

**Combinations to 10**

- 0+10
- 1+9
- 2+8
- 3+7
- 4+6

**Combinations to 20**

- 0+20
- 1+19
- 2+18
- 3+17
- 4+16
- 5+15
- 6+14
- 7+13
- 8+12
- 9+11

**Combinations to 100**

- 0+100
- 1+99
- 10+90
- 75+25
- 20+80
- 30+70
- 40+60
- 50+50

## Other Strategies Demonstrated

- using doubles facts
- counting on from first
- direct place value
- joining to
- compensating
- skip counting
- double +1
- counting on from larger
- separating to
- joining all
- invented algorithm
- trial/error
- making 10
- counting back
- separating from
- incrementing
- derived facts
- combining 10's and 1's
- estimating
- matching
- dealing
- grouping

## Conferencing with Parents

Having this elementary math assessment on hand when conferencing with parents gives both you and them a clearer picture of what the student is capable of doing. It also gives parents a better understanding of what available strategies the student still has yet to master. When used over time (say, once per quarter) this assessment is a strong tool for demonstrating growth…or lack of growth.

## Videotaping a Problem-Solving Session

I have found that the most valuable tool for conferencing with parents is a video of their child during a problem-solving session. At the beginning of the year, I ask parents to sign a release form allowing me to video tape their child engaging in a variety of activities – reading books out loud, giving presentations and even solving math problems. Just before conferences, I send the video home and ask parents to watch these videotaped sessions. I then refer back to the problem-solving sessions when discussing the math strategies currently used by their child. Parents can clearly understand what I am referring to, and get a glimpse of what their child can do…which is sometimes different than the level they are performing at when working at home! These video taped sessions also serve as a wonderful demonstration of growth over the year. Best of all…they are a terrific keepsake from their time spent in my classroom!

## This post is part of the series: CGI Math In Your Classroom

- CGI – An Approach to Teaching Mathematics
- Teaching Different Types of Math Story Problems
- Using Cognitively Guided Instruction for Teaching and Assessment
- Math Skills Assessment for Division Problems Using Cognitively Guided Instruction
- Elementary Math – Assessment of Strategies for Solving Math Problems