Multi-Step Expressions and the Real World

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SWBAT write expressions that represent real-world problems

Big Idea

Expressions can be used to represent a mathematical or real-world problem in an abstract way using numbers and symbols to make meaning of and understand problems.

Think About It

7 minutes

Students work independently on the Think About It problem.  My goal with this problem is to have students struggle a bit translating a multi-step expression into words.  It may be a little tricky for kids to articulate that the expression inside of the parentheses need to be evaluated first.

I'll tell the class that I'm really excited about the verbal expression that I've created.  I share out 'Fifteen minus five plus three,' intentionally making a mistake.  I ask students what they think of the expression.  Some students will let me know that they think I've done a good job.  

Ideally, students will flag for me that the words I've used don't let my reader know that there are parentheses in the numeric expression.  However, if the majority of the class seems to think I've correctly translated the numeric expression, I'll ask kids to translate my words back into numbers.  The big idea I want kids to pull out of the discussion is that they'll need to be sure to use words to group terms in math, as needed.  

Intro to New Material

20 minutes

In this lesson, students will write multi-step expressions for real-world scenarios.  Students will need to access what they learned about the order of operations as they are translating the scenarios into expressions.  

To start the Intro to New Material section, I ask students to articulate the relationship between Lucas and Javier.  I'll cold call a student to let the class know which operations we'll need to represent the relationship.  I'll then ask for volunteer to name and define a variable for this scenario.  It's important that the variable makes sense for this scenario - I don't want students using l for Lucas.  It's the cookies Lucas has that is unknown, so students will most likely pick c for the variable (although any variable would be fine, so long as it is defined as the number of cookies Lucas has). 

Once we've defined the variables and identified the operations, I'll ask students what we need to have happen first - twice the number of cookies or 5 less than twice?  Twice has to come first because it says 5 less than twice, that amount of twice Lucas must be performed.  Then we are taking 5 cookies away from that so we would have 2c – 5.     

Example 1 also gives me the opportunity to review key vocabulary from this unit.  I ask students to identify the constant and the coefficient in our expression.

I'll go through the same process for Example 2.  With this example, I highlight the need for grouping symbols, because we need the total quantity that Janice's brother ate.

Example 3 gives students a chance to write their own expressions.  I'll model one for the class first, by writing 'The math test today has six fewer than three times as many questions as the test yesterday.'  Students then get 2-3 minutes of writing time, and I'll have 2-3 kids share out their expressions.

Partner Practice

15 minutes

Students work in pairs on the Partner Practice.  As they work, I circulate around the classroom and check in with each pair.  I am looking for: 

  • Are students correctly identifying the variable?
  • Are students correctly identifying the constant?
  • Are students correctly identifying the coefficient?
  • Are students correctly translating the verbal expression into numerical form?

I am asking:

  • How did you know what the variable was? What does the variable represent?
  • How did you know what the constant was? What does the constant represent?
  •  What does this quantity represent (referring to items like 2n or (8 + c))?Will the expression have the same answer if you changed the order of the terms?
  • What amount are you starting with?
  • What does the expression mean?
  • Are there any values that must be grouped?
  • Is there any multiplication/division?
  • Is there any addition/subtraction?
  • How did you know which operation to use?
  • Why did you write this expression to represent this problem?
  • What does the entire expression represent? 

After 10 minutes of work time, the class comes back together.  I share the correct expressions for problems 1-3, and answer any clarifying questions from the class.  I then ask for 3 volunteers to share out their responses for question 4.  

Students complete the Check_for_Understanding question independently. 

Independent Practice

15 minutes

Students work on the Independent Practice.  As students work, I am circulating and making sure they're following the steps we've worked on in this unit.  I expect to see students:

1)      Read and annotate.

2)      Use a variable to represent unknowns and digits/operations for different values.

3)      Define the variable.

4)      Identify what amount you are starting with.

5)      Determine if any terms or operations are grouped (parentheses).

6)      Determine if there is any multiplication or division performed on the starting amount.  Translate.

7)      Determine if there is any addition or subtraction.  Translate.

8)      Check by restating and comparing to the written expression.  

Students may have difficulty interpreting all of the operations involved in a problem and order them correctly.  You could address this by replacing the variable with a value and asking students to solve the problem arithmetically first. Then, students can use those steps to create an expression.

Closing and Exit Ticket

8 minutes

After independent work time, I have students turn to their partners to compare and discuss their responses for Question 12.  This problem requires the use of grouping symbols.  Students must also correctly translate '5 less than.'  It is a common mistake for students to write 5 - (2x + 3) rather than (2x - 3) - 5.

Students work independently on the Exit Ticket to end the lesson.