Terry's Taco Shack: What Does "How Many More" Mean?

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Objective

SWBAT solve comparison problems using addition or subtraction strategies.

Big Idea

Students oftentimes struggle with comparison problems since there is no "action" in the problem (i.e: nothing is getting taken away or added). In this lesson, students practice strategies for solving comparison problems.

Problem of the Day

15 minutes

We are going to work on a problem of the day: 

The table below shows the tacos that were sold at Terry's Taco Shack. 

Day

Tacos Sold

Monday

22

Tuesday

72

Wednesday

35

Thursday

17

 How many more tacos did Terry sell on Tuesday than on Thursday? 

I hand out white boards to students and have them work to solve the problem independently for 3-5 minutes.  As students work, I circulate and ask students guiding questions:

--Can you explain your strategy to me?

--Why did you choose to subtract?

--Why did you choose to add?

--What clues does the question "How many more" tell us? 

In this video, a student responds to guiding questions: 


When students have finished, I ask one student  to share his or her strategy.  Some students may say " I knew to subtract because it says 'how many more''.  Make sure to push students to explain WHY they are subtracting.  

In these videos, two students share their strategies for solving comparison problems. 

If students are struggling to come up with an appropriate number sentence, pull out cubes--have students help you to line up 72 cubes to represent the 72 tacos sold on Tuesday.   Then, put aside 17 cubes to represent the number of tacos sold on Thursday. Then ask " Do I add to these cubes to determine how many more were sold on Tuesday? "  Introduce the word "difference"--we want to know the difference between 72 and 17.  Thus,  we should not add 72 and 17 together to find the answer. Most students will recognize that adding will give a larger number and that adding the two together does not compare the two amounts.  

Ask students, "What should I do instead of adding the two together?"  Some students might suggest writing 17 + _______= 72.  Others might suggest putting the two lines of cubes together and comparing them, which will likely lead to the number sentence 72-17=_____. Both of these strategies are correct.  

NOTE: Mathematical Practice Standard 5 (MP5) asks students to use appropriate tools strategically--this lesson pushes students to use the tools of addition and subtraction strategically to create number sentences that appropriately compare numbers.  If students are struggling, push them to use what they already know about addition and subtraction to help them! 

Guided Practice

10 minutes

In order to give students more practice on these problems, I give every student a guided practice problem.  I encourage students to use cubes just as we modeled during the problem of the day.  Students should have about 5-6 minutes to complete the problem. 

As students work, I circulate to check for understanding and support any students who are struggling with the problem of the day. 

When finished, I bring students back together and have them share their answers or strategies.  If a student used cubes to solve the problem, have them model using cubes and then explain what number sentence describes their model.  If a student used a number sentence, ask them to show how they know that number sentence is correct using a drawing or cubes.  At this point, I am checking to see which students are still struggling on this skill so that I can check in with them during the independent practice. 

Independent Practice

15 minutes

Independent Practice is differentiated (I use yesterday's lesson as well as today's guided practice to inform groupings).  

During the independent practice, I spend most of my time working with Groups A and B to support and ask guiding questions:  (1) what strategy are you using?  (2) Explain what number sentence matches your strategy.  (3) What are you doing to make sure your work is accurate? 

Group A: In need of intervention

Students in this group will use cubes to model comparison problems with numbers 10-30.  (This group will need the most teacher support during independent practice).

Group B:  Right on track!

Students in this group will use their strategies to model and solve comparison problems with numbers 10-60.  

 Group C: Extension

Students in this group will use their strategies to model and solve comparison problems with numbers 10-100. 

Exit Ticket

10 minutes

As students finish their independent practice, I invite them back to the rug and hand out an exit ticket.  I allow students to work silently on their exit ticket for 5 minutes.  When finished, invite a student from each group (A,B, C) to share his/her answers and strategies.  As students share ask the following guiding questions:

--Why did you use this strategy?

--How did you choose your strategy?

--What did you do to make sure your work was accurate?  How did you check your work?

--Why did you add/subtract?