Math Problem Solving Strategies: Keywords, Relevant Information, Creating Visuals

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Many times children have trouble solving word problems because they do not know which operation (+, -,  X, ÷) to use to solve the problem.  When trying to figure out which operation to use, it is important to pay attention to keywords (clues to what the problem is asking you to do) and necessary information. Word problems often contain extra information that is not relevant to the problem.

Below is a chart of key words students can use to help them figure out what the problem is asking.

Addition Keywords + Subtraction Keywords – Multiplication Keywords X Division Key Words ÷
add(ed) to
all together
both
combined
in all
increase by
more than
perimeter
plus
sum
total
decreased by
difference
fewer than
how many more
left
less
less than
minus
remaining
take away
area
multiplied by
of
by
per
product of
rate
times
triple
twice
each person, each group, etc.
every
total
quotient
divide
into
amount of each
divided by
equal parts
split up
break up
per
out of
each get(s)
each have/has
every

You can print out this chart for your child or students and have them refer to it when trying to solve a word problem.

Keep in mind that the chart above is just a guide and not a hard and fast rule for every single word  problem. You will also sometimes find overlap with different operations such as “total” in addition and multiplication or “per” in multiplication and division. If your child is struggling to figure out what the question is asking after looking for key words and relevant information, encourage him to draw a picture of the problem as shown in the examples below. If the numbers are very high (above 15 or 20) it will be too cumbersome to draw the problem. In this case, the child can recreate the same problem with lower numbers and then draw the picture to figure out the operation needed to solve the problem. Once the child knows the correct operation, he can plug in the larger numbers.

Drawing a picture of the problem, gives children a way to see what the problem is actually asking. When they read the problem, the question may seem abstract or confusing to them because they can’t visualize the components of the question. Drawing a picture helps them clearly see what is going on in the problem and for many children makes it easier to solve.

When working with your children or students, show them an example (such as one of the ones below) of how to underline key words and relevant information, and how to draw their math problems. After you have shown the child an example, let them try to apply this strategy on their own to different problems. If they have difficulty finding the keywords, relevant information, or drawing the pictures, guide them through the process, giving them as much assistance as necessary. As their ability to use this strategy  improves, gradually fade out your guidance.

The word problems below have the keywords and relevant information underlined. There is a corresponding drawing to go with each problem.

Example 1:

Addition
Tanya likes to go to the park and look at the clouds in the sky. This week she saw 3 clouds on Monday, 1 cloud on Tuesday, and 4 clouds on Wednesday. Home many clouds did she see in all?

3 + 1 + 4 = 8

Addition picture

Example 2:

Subtraction
Jimmy picked 10 apples from a tree and put them in his basket. He didn’t know his basket had a hole in the bottom. 3 apples fell out on his way home. How many apples were left in Jimmy’s basket when he got home?

10 – 3 = 7

subtraction picture

Example 3:

Multiplication
David’s mom bought too much bottled water from the supermarket. David decided to give 2 bottles of water to each boy in his swim class. There were six boys in his swim class. What was the total number of bottles that David gave away?

6 x 2 = 12

multiplication picture

Example 4:

Division
3 very hungry girls wanted sandwiches at a picnic. There were 12 sandwiches at the picnic. The girls needed to split up the sandwiches, so that each girl got the same number of sandwiches. How many sandwiches did each girl get?

12 ÷ 3 = 4

division picture

If you want to make things even more concrete for the child you can try using real objects such as pieces or fruit, coins, or Math Manipulatives to represent the objects in the pictures. Some children do better when they can touch, move, and set up the objects that represent the problem.

Keep in mind that every child is different. Some respond to several strategies, others respond to a few, while others may not respond to any strategies you try. If your child is significantly struggling with math or acquiring other academic skills, despite consistent practice and guidance, talk to your child’s school and/or doctor. They should be able to refer you to the appropriate professionals to determine what might be interfering with your child’s progress and what additional strategies might help.

Remember to always stay calm when working with a child or student, even if you think they should be getting something that they are not getting.  If you get frustrated with them, they may start to feel anxious, angry, inferior, stupid, etc. which will lead to a less productive learning session. Keep sessions short (5 to 10 minutes for younger children or children who get easily frustrated and 10 to 15 minutes for older children or children who can work for longer periods without frustration), unless the child is eager to keep going. I also recommend reading Getting Kids Motivated With Timers and Compliance for suggestions on how to encourage homework completion, especially when homework is taking a long time and the child is giving up, frustrated, rushing through the work, distracted, or refusing to complete the work.

Additional Information
For a highly rated computer based learning program to improve reading and/or math skills for your child or students, try K5 Stars. K5 Stars includes over 300 educational computer games for ages 5 to 10. K5 Stars lets you track your child’s or students’ progress and create playlists for their specific needs. Click here to read our full review on K5 Stars.

You also might find interest in our article 78 Free IPAD Apps to Help With Learning, Behavior, and Language Development.

Wise Education and Behavior writes weekly articles to support children with reading, writing, spelling, math, and behavior. See all of our articles here.

We also invite you to visit our  Wise Market  and E-Learning Center, two stores completely devoted to childhood development, learning, and behavior. All of the programs in our E-Learning Center can be downloaded immediately to your computer for use. Our Wise Market products are available for shipping.

For links to free worksheets and activities check out our resources page.

We also recommend reading A Great Place to Purchase Supplies to Support Kids’ Development!, which talks about the benefits of shopping at Discount School Supply®, an online store with over 6,000 products from over 25 different categories including Dramatic Play; Active Play; Infant & Toddlers; Furniture, Storage & Equipment; Math; Science; Language; and Special Needs.

Thank you for reading and thank you for supporting kids!

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