This document discusses and provides examples of routine and non-routine problem solving. Routine problems involve using arithmetic operations to solve practical problems and have clear, straightforward procedures. Non-routine problems require more creativity, originality, and higher-order thinking skills as they may have multiple solutions or approaches that are not immediately obvious. Ten examples are given that illustrate the differences between routine and non-routine problems of increasing complexity.

1. Routine and
Non-routine Problem

2. Routine and non-routine problem solving
We can categorize problem solving into two basic types: routine and
non-routine. The purposes and the strategies used for solving
problems are different for each type.

3. Routine problem solving
From the curriculum point of view, routine problem solving involves
using at least one of the four arithmetic operations and/or ratio to
solve problems that are practical in nature.
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Routine and non-routine problem solving

4. Example:
Sofia had _____ dimes. She game some to her friend. Now she has
______ dimes. How many did she give to her friend?
whatihavelearnedteaching.com
Routine problem solving

5. Non-routine problem solving
A non-routine problem is any complex problem that requires some
degree of creativity or originality to solve. Non-routine problems
typically do not have an immediately apparent strategy for solving
them. Often times, these problems can be solved in multiple ways.
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6. Example:
There are 45 questions in an exam. For every correct answer 5 marks
awarded and for every wrong answer 3 marks are deducted. Melissa
scored 185 marks. How many correct answers did she give?
youtube.com/inspired Learning
Non-routine problem solving

7. Differences between routine and non-
routine problems
ROUTINE QUESTIONS
 Do not require students to use HOTS.
 Use clear procedures.
NON-ROUTINE QUESTIONS
 Require HOTS.
Increase the reasoning ability.
Use answers and procedures that are not immediately
clear.
Encourage more than one solution and strategy.
Expect more than one answer.
Challenge thinking skills.
Produce creative and innovative students.

8. Differences between routine and non-
routine problems
ROUTINE QUESTIONS
 Do not require students to use HOTS.
 Use clear procedures.
NON-ROUTINE QUESTIONS
 Require solutions that are more than simply making
decisions and choosing mathematical operations.
Require a suitable amount of time to solve.
Encourage group discussion in finding the right
solution.
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9. Illustrative examples:
1. Sofia had 42 dimes. She game some to her friend. Now she has
17 dimes. How many did she give to her friend?
2. Ali eat 2 piece of cakes. 5 minutes later, he eat 1 more piece of
cakes. How many piece of cakes that Ali eat?
3. There are 45 questions in an exam. For every correct answer 5
marks awarded and for every wrong answer 3 marks are deducted.
Melissa scored 185 marks. How many correct answers did she give?
4. A watch cost $25 more than a calculator. 3 such watches cost as
much as 8 such calculators. What is the cost of each calculator?

10. 5. At a stadium, there were 243 women and 4 times as many men as
women. There were 302 more children than adults. How many children
were at the stadium?
6. Peter had $1800. After he gave $400 to John, he had twice as much
money as John. How much money did John have at first?
7. Abbey and Ben had some money each. The amount of money that
Abbey had was a whole number. Abbey wanted to buy a watch using all
her money but she was short of $90.50. Ben wanted to buy the same
watch using all his money but he was short of $1.80. The total amount of
money that both of them had was still not enough to buy the watch. How
much was the watch?
Illustrative examples:
youtube.com/Mr. Matthew John ; youtube.com/Danny Lim

11. 8. In a farm there are twice as many chickens as cows. If there are
980 legs altogether. Find the number of chickens in the farm.
Illustrative examples:
youtube.com/inspired Learning

12. 9. Let f be a function, with the domain the set of real numbers except
0 and 1, that satisfies the equation
2𝑥𝑓 𝑥 − 𝑓
𝑥 − 1
𝑥
= 20𝑥.
Find 𝑓
5
4
.
Illustrative examples:
PEAC-InSet 2018

13. 10. If (a, b, c, 2c) are real numbers such that (a)(b)(c)≠ 0 and given
condition
𝑏𝑥+ 1−𝑥 𝑐
𝑎
=
𝑐𝑥+ 1−𝑥 𝑎
𝑏
=
𝑎𝑥+ 1−𝑥 𝑏
𝑐
then,
prove that a = b = c.
Illustrative examples:
youtube.com/Raveena Chimnani

14. THANK YOU
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