If two people can work the same problem and get different answers, something is missing. This is the thing that was missing.
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Teach students why the order of operations exists before asking them to use it. The main idea is simple: if two people can look at the same math problem and get different answers because they worked in a different order, we have a problem. Mathematics needs an agreed order so the same problem has the same answer.
By the end of the lesson, students should understand this hierarchy: parentheses first, then multiplication and division from left to right, then addition and subtraction from left to right.
The goal is not simply to memorize those three lines. Students should understand why the hierarchy is needed and how to work through it.
Before explaining the order, show the student why we need one. Write 8 + 4 x 2, and tell the student that two students tried to solve the same problem.
The first simply started on the left: 8 + 4 is 12, then 12 x 2 is 24. The second did the multiplication first: 4 x 2 is 8, then 8 + 8 is 16.
Ask your student: how can the same math problem give us two different answers? That question gives you the reason for the entire lesson. Mathematicians use an agreed order so everyone knows what should happen first, and using that order the correct answer is 16, because multiplication comes before addition.
🚨 Students may assume that every problem should simply be worked from left to right. The opening example shows why that does not work.
They may also think multiplication always comes before division, or addition always comes before subtraction. Keep returning to the hierarchy: parentheses first; multiplication and division are together, left to right; addition and subtraction are together, left to right.
Before the student calculates anything, ask what has to happen first. Have the student identify the first operation before solving it.
On 6 + 3 x (8 - 4), ask what has to happen first. There are parentheses, so begin there: 8 - 4 is 4. Now the problem is 6 + 3 x 4. Ask again. Multiplication comes before addition, so 3 x 4 is 12, and 6 + 12 is 18.
As you teach, keep asking the student why each step comes next. That turns the order of operations into a thinking process instead of a rule the student repeats from memory.
The Bible repeatedly shows us that God values order rather than confusion. 1 Corinthians 14:33 says that God is not the author of confusion but of peace, and 1 Corinthians 14:40 says to let all things be done decently and in order.
These verses are speaking about order within the church, not giving us a rule for mathematics. But they remind us of something we can see throughout creation: we serve a God of order, not disorder. Mathematics helps us recognize and describe some of that order.
Numbers also appear repeatedly throughout Scripture. Numbers such as 3, 7, 12 and 40 occur again and again in biblical events and patterns. We do not need to invent hidden meanings for every number to recognize that Scripture regularly uses numbers, measurements, quantities, days, years, generations, distances and groups of people.
Math is not separate from God's creation. It is one of the tools we use to understand and describe the orderly world He made.
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Before You Start
The words this lesson uses. Tap a card to see what it means, then come back to them whenever a question uses one.
Part One
Questions about the story you just read. Pick your answer straight off, or press Find it in the story if you would rather hunt for the sentence first.
Part Two
The word cards are at the top of this page. Look back at them as often as you need, then answer.