Teaching order of math operations without parentheses

Teaching Order of Math Operations Without Parentheses

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When learning about the order of math operations without parentheses, students become fluent in evaluating numerical expressions (without parentheses) following the order of operations, as well as in using the order of operations in solving problems involving numerical expressions.

To make these lessons more inviting for 5th graders, math teachers and homeschooling parents can enrich their classroom with interactive teaching methods and activities. We bring you a few such methods and activities in this article. Read on to learn more.

Methods to Teach the Order of Math Operations Without Parentheses

What Is an Order of Operations?

For starters, explain both the word order and the word operations to students. Point out that the word ‘arrangement’ is a synonym for the word ‘order’. Then, explain that when we say ‘operations’ in math, we are referring to addition, subtraction, division, and multiplication.

With this in mind, point out that the ‘order of operations’ refers to the correct arrangement of the operations involved in a numerical expression, which as students know, is a mathematical phrase that represents a single value, and consists of one or more numbers and operations.

In other words, the order of operations is a set of math rules that tell us which operation (ex: multiplication, addition, etc.) to do first. In math, we can’t just do anything whichever we’d like and however we’d like to, we need to follow rules to get accurate and valid answers!

For instance, James and Sally were asked to give the value of 5 + 2 × 10 – 3. James and Sally came up with different answers. Provide their separate calculations and ask students who they think got it right.

Explain that while both calculations might look okay, only one of them is correct. Point out that in this given case, it was Sally that got the right answer. Why? Because she followed the order of math operations while doing her calculations.

Multiplication – Division – Addition – Subtraction (MDAS)

Explain to students that the order of operations we need to follow while evaluating numerical expressions (without parentheses) or solving problems involving numerical expressions is as follows: multiplication – division – addition – subtraction (or simply MDAS).

Point out that we can use the following steps to follow the MDAS rule:

  • Step 1 – we always work from left to right
  • Step 2 – we perform multiplication or division, whichever comes first, from left to right
  • Step 3 – we perform addition or subtraction, whichever comes first, from left to right

Now that students are familiar with the rule that we apply evaluating numerical expressions (without parentheses), you can go through Sally and James’s answers and illustrate to students which one followed the MDAS rule.

Explain that in James’s case, he performed addition first, by adding 5 + 2 = 7. After that, he performed multiplication, by multiplying 7 and 10. Finally, he performed subtraction and subtracted 3 from 70 to get 67.

Point out that it’s clear that James didn’t stick to the MDAS rule, because we can’t perform addition before we have done the multiplication in a mathematical phrase with operations without parentheses. So James’s answer is incorrect.

Ask students to inspect Sally’s calculations. From what we can observe, Sally did multiplication first, by multiplying 2 and 10. Then she did addition, by adding 5 and 20. Finally, she did subtraction, by subtracting 3 from 25 to get 22.

So Sally clearly followed the MDAS rule, because she first performed multiplication and only then did she do addition and subtraction. This means that Sally’s answer (22) is the correct answer to 5 + 2 × 10 – 3.

Order of Operations in the Real World

Point out that the MDAS rule is also used to solve real-life problems. These problems happen on a daily basis, without us realizing that we are using such a rule. By connecting the MDAS rule to real-life situations, you’ll be able to make this math lesson less abstract as well.

Example:

Martha bought 5 pairs of pants for $30 each. She paid the cashier $200. If we’d like to write a numerical expression that represents the problem, we’ll start with the money she gave in total, (200) and then subtract the total price for all jeans (5 × 30). In other words: 200 – 5 × 30.

So the first step was writing a numerical expression to represent the problem. Now that we’re done with that, point out that we can proceed with evaluating this expression, which will give us the answer to how much money Martha has left.

Add that when evaluating the expression 200 – 5 × 30, according to the MDAS rule, we’ll first perform the multiplication, that is: 200 – 150. Then, we’ll deal with the subtraction 200 – 150 = 50. So Martha has $50 left.

A student standing in front of a white board

Additional Resources:

If you have the technical possibilities in your classroom, you can also use multimedia materials in your lesson on the order of math operations without parentheses. For instance, you could incorporate diverse free videos on this topic.

This video is a great resource on teaching the order of math operations without parentheses, as it provides a simple introduction, followed by a fun example where two different people try to solve the same problem while (not) following the order of operations.

Activities to Practice the Order of Math Operations Without Parentheses

Order of Operations Matching Game

This game will help students reinforce their skills in evaluating numerical expressions by using the order of math operations (without parentheses). To implement this game in your classroom, you’ll need orange and blue construction paper, some scissors and some markers.

Create two sets of task cards, one set of orange task cards and another blue set. The orange cards contain numerical expressions without parentheses (one expression per card). The blue cards contain the corresponding answers to the numerical expressions (one answer per card).

For example, let’s say you write the following expression on an orange card: 45153 + 2 – 4 + 3. There must be a corresponding blue card that would contain the answer to this expression, that is, 10. Create as many sets as you have groups in your class.

Divide students into groups of 3, 4 and hand out one orange set and one blue set of cards per group. Provide instructions for the game. The cards remain face down until you give students the signal to start the game.

Students in each group work together to first evaluate the numerical expressions on the orange cards they received and then match them with the blue card that contains this answer. This is a fast-paced game, so each group should try to match the cards as quickly as they can.

Provide a few minutes for students to complete the card-matching. You can also use a timer for this. Once the time is up, check the final number of correctly matched cards per group. The group with the biggest number of such matches wins the game.

Order of Operations Interactive Game

This is an online game where students will get the opportunity to hone their ability to use the correct order of math operations and the MDAS rule when evaluating numerical expressions without parentheses.

To use this game in your class, make sure there is an adequate device for each student. Students play the game individually, which also makes it suitable for parents who are homeschooling their children.

Explain to students that they will be presented with several exercises containing different numerical expressions in the game, where they would have to apply their knowledge of the MDAS rule to evaluate the expressions correctly.

Provide a few minutes for students to complete the exercises. Once they’re done, create space for discussion and reflection. Which operation did students perform first when evaluating the expressions? Which operations did they perform second?

Before You Leave…

We hope you’ve enjoyed our methods and activities on teaching the order of math operations without parentheses! Make sure to check out our worksheets and resources on how to teach this topic to 5th graders. These are all pdf files, so you’ll be able to print them out easily:

To get the Editable versions of these files, join us inside the Math Teacher Coach Community:

These activities are from:

Unit 1 – Numerical Expressions

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