Order of Operations & Decimals

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SWBAT apply the order of operations to simplify expressions involving whole numbers and decimals.

Big Idea

Students will use EVERYTHING they have already learned to simplify some tricky expressions (exponents, decimals, and order of operations are all combined).

Warm Up

15 minutes

The following message is posted on the board. 

Fold a sheet of paper into fourths.  Write and solve a equation for each of the four operations. Please include at least one decimal in each problem.

This warm- up is designed to  students remember what they have earned about working with decimals in each of the operations.  It is a tool for refreshing their memory and it will provide a model as they solve more problems during class. 

In the interest of time, I ask students to check their work with a calculator*

Before moving on, students share what they know about adding, subtracting, multiplying, and dividing with decimals by sharing examples on the board and explaining their thinking.

*Note about calculator use:

I my class, calculators are used to check understanding rather than merely provide answers.  Part of the classroom culture that I have worked to establish is for students to value effort, process, and mistakes because math is also about the journey, not just the destination. Calculators allow students to get immediate feedback about their work so they can check for any errors on the spot. Another added bonus is that students learn how to use this tool correctly. They will use these real world tools throughout their lives.

Guided Practice

10 minutes

I connect the students back to the vobackulary game at beginning of this unit by asking them find someone in the class who shared the same vobackulary word that they had. Together, they talk about their word, and why they think it belongs on the list.  

Some students' don't know why their word was on the list, or what it means yet because we haven't completed the topic, there are still words that haven't been used in class.  Other students' words have been used regularly but they are not confident in the meaning, or sure why it fits on this list.  The benefit of having more than one student with the same word is that collaboration is built in.  

I write this expression on the board.  

[(32 + .03)/3] + 30f        f = 7

I ask the students to look at this algebraic expression and compare it with the others we have been solving this week.  Students notice that is has brackets and decimals.  

We solve this expression together.  I emphasize that this problem appears to be a bit more challenging at first because it includes decimals.  But as we solve it together, the students can see that the same order of operations applies.

Now You Try It

25 minutes

Students work in pairs to simplify more expressions.  

After they "prove they can do it their own" by simplifying three expressions, students are given the choice to use a calculator.  

This allows the students to continue to practice PE MD AS* without becoming bogged down by the computations. Is is an example of when I really ask myself what my objective is.  I want the students to simplify expressions, they have sufficient time to practice multiplying and dividing with decimals - therefore, I allow them to use a calculator to do the computations so they can focus on the order of operations.  

*When I write the order of operations, I usually write it 





This helps the students visually see that multiplication and division fall on the same step in this order of operations, so they must be solved left to right.  

The same goes for addition and subtraction.

I like to write it vertically so that students can begin to break the mold of solving equations from left  to right. 

Ticket Out

5 minutes

This is the last day that I plan to focus on order of operations so as a ticket out, I ask students to write a reflection (3 faces) about evaluating expressions.  I can use these reflections to help create warm-ups and small groups to differentiate instruction and help all students master this standard as the year moves on.


Some students are over confident in their ability to solve problems with more than one operation.  I am careful to check their work for common errors.  These errors include:

• always multiplying before dividing: if an equation has multiplication and division operations, these must be solved from left to right.  

• always adding before subtracting

• When there are multiple operations within a set of parenthesis the order of operations must be applied here too.  Many times students will work left to right within a set of parenthesis.