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Maths Problem SolvingHow kids solve problems and where they go wrong…
Maths question vs Maths Problem
A maths problem is
• A task that there is not a readily accessible procedure that guarantees or completely determines the solution Charles & Lester jr 1985 p232
Problem solving involves
• detecting steps or processes “between the posing of the task and the answer” Goldin 1982 p97
35+28+27=
There are 35 students on the first bus, 28 students on the second bus and 27 students on the third bus. How many students are there in total?
When mathematicians have a problem they:
•Read and understand the problem
•Plan a strategy to start solving the problem
•Carry out their plan
•Check their result
Polya calls this: See Plan Do Check
A Mathematician’s Strategy Toolbox includes:
• Act it out
• Use objects
• Draw a picture
• Draw a diagram
• Guess, check & improve
• Simplify the problem
• Write a number sentence
• Make an organised list
• Make a table
• Make a model
• Look for a pattern
• Find a formula
• Work backwards
5 prompts to solving a problem
1. Please read the question to me. If you don’t know a word, leave it out
2. Tell me what the question is asking you to do
3. Tell me how you are going to find the answer
4. Show me what to do to get the answer
– think aloud as you do it so I can understand how you are thinking
5. Now write down your answer to the question
Where Students Make Mistakes
1. Reading the problem
2. Comprehending what is read
3. Turning the words into maths
4. Applying the process of the strategy
5. Expressing the answer
For most students the greatest difficulty in solving problems is:
understanding the question.
>50% of errors occur before
students get to use their process skills
Reading the Problem
• What is the probability of…?
• What is the fourth consecutive number…?
• Which block is adjacent to the blue block…?
Comprehending what is read
• A bell chimes every hour…
• A rectangular garden bed…
• A water tank measures….
• times, volume, space, take away
Turning the words into maths
• Total
• Sum
• Add
• Less
• Minus
• Take away
• Change
• Multiply
• Lots of
• Times
• Share
• Divide
• Amongst
• Between
• Groups
Key word strategy
Read the problem several times – discuss or rewrite in own words
Ask internal questions eg what do I have to find? What information is important?
Underline the important words
• Jill gave away 6 cookies in the morning. She gave away 2 cookies in the afternoon. How many cookies did she give away that day?
The Strategies
• Pepi has built a tower of four blocks. The red block is between the blue block and the yellow block. The green block sits on top of the blue block. What colour block is on the bottom of the tower?
Act it out Use objects Draw a picture Draw a diagram Guess, check & improve Simplify the problem Write a number sentence Make an organised list Make a table Make a model Look for a pattern Find a formula Work backwards
The Strategies
• Four people can sit one behind the other in the log ride. In how many different ways can four friends sit?
Act it out Use objects Draw a picture Draw a diagram Guess, check & improve Simplify the problem Write a number sentence Make an organised list Make a table Make a model Look for a pattern Find a formula Work backwards
The Strategies
• At the first stop three passengers get on the bus. At the second stop, one gets off and four get on. How many are there on the bus now? Act it out
Use objects Draw a picture Draw a diagram Guess, check & improve Simplify the problem Write a number sentence Make an organised list Make a table Make a model Look for a pattern Find a formula Work backwards
The Strategies
• There are six people in a room. If everyone in the room shakes hands once with everyone else, how many handshakes will there be?
Act it out Use objects Draw a picture Draw a diagram Guess, check & improve Simplify the problem Write a number sentence Make an organised list Make a table Make a model Look for a pattern Find a formula Work backwards
The Strategies
• There is a one metre wide path around a 4m x 4m garden bed. What is the area of the path? Act it out
Use objects Draw a picture Draw a diagram Guess, check & improve Simplify the problem Write a number sentence Make an organised list Make a table Make a model Look for a pattern Find a formula Work backwards
The Strategies
• A snail climbs up from the bottom of a 10 metre deep slippery well. Each day it climbs up three metres but slips back one metre each night. How long will it take to reach the top?
Act it out Use objects Draw a picture Draw a diagram Guess, check & improve Simplify the problem Write a number sentence Make an organised list Make a table Make a model Look for a pattern Find a formula Work backwards
The Strategies
• There are chickens and cows in a pen. If there are 12 heads and 32 legs, how many cows are there? Act it out
Use objects Draw a picture Draw a diagram Guess, check & improve Simplify the problem Write a number sentence Make an organised list Make a table Make a model Look for a pattern Find a formula Work backwards
The Strategies
• There are one hundred people in a room. If everyone in the room shakes hands once with everyone else, how many handshakes will there be?
Act it out Use objects Draw a picture Draw a diagram Guess, check & improve Simplify the problem Write a number sentence Make an organised list Make a table Make a model Look for a pattern Find a formula Work backwards
How you can help
Involve your child in everyday problem solving • Set the table• Estimate/calculate the cost of the drive through takeaways, the fuel• Pack their own lunchbox• Play with water and sand at the beach• Plan the trip/holiday• Measure their height• Calculate when dinner will be ready if it will take 35 minutes to cook• Cook a recipe• Set an alarm or timer• Thread bead patterns
Example problems
Peruse the example maths exercises.
• Which questions are problems?
• What makes a question a problem?
• What strategies would you choose?
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