Lesson 9

How Addition and Subtraction are Related (Part 3 of 3)

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SWBAT use a number line to write equivalent addition and subtraction expressions

Big Idea

Students use a number line to explore the relationship between addition and subtraction.


10 minutes

In the introduction, I will introduce the essential questions and the vocabulary.  The vocabulary of sums and differences will help present clarity when discussing various problem (MP6).  Instead of students saying "that number" or "the number in back of the addition sign" they can say the subtrahend or the second addend.  


We will review how to add and subtract on the number lines.  I will pass out the pointers that we use for number lines.  Then, students will solve the 8 problems.  Again, this part of the lesson should go quickly as students already have worked with adding and subtracting  on number lines in previous lessons.  Despite this, there will be students who have difficulty so I will suggest they have a partner read through the steps for solving the problem.  The partners will verify the correctness of each step before moving on. 

Problem Solving

15 minutes

Students will work in their duos and trios to first re-write sums as differences.  I anticipate students having some difficulty getting started with A1.  They may be able to solve 5 + -2 but not know what to do next.  I will ask them what is the sum of 5 and -2.  They answer -3.  Then, I will ask them to use their subtraction model and ask, "how can we get from 5 to -3 using subtraction?".  I will look for them to move left 2 steps.  This will represent a subtraction of positive two.


Question B then asks students to call upon MP7 and MP8  to come up with a way to rewrite addition problems as subtraction problems.  


Problems for C and D are the same, but now students are asked to go from subtraction to addition. 

It may be helpful to stop the groups after problem D and review answers.  As groups share, we can use a sample problem to see if their method makes sense (MP3) and uses precise language (MP6).  All methods can be verified using the number line model.

Problems E and F can be a final check for understanding to make sure individuals are ready for the independent practice.  If I see any mistakes here, I will ask students to model the sum and difference on a number line.  If they are able to model correctly, then they should be able to see their own errors quickly.



Independent Practice & Extension

20 minutes

Problems 1-8 ask students to apply the conclusions from the previous section to re-write sums as differences and differences as sums.  In effect, they are applying "add the opposite" or "subtract the opposite" to the expressions.

Problems 13-18 present 2 sums and 2 differences.  Students are asked to find the one expression that is not equivalent to the other three without evaluating.  This requires students to reason abstractly and quantitatively (MP2) and understand the structure of equivalent addition and subtraction problems (MP7).


The extension question 19-21 could be solved in a number of ways.  Students may choose to explain their reasoning by explaining what happens when you add or subtract a positive or negative value.  Other students may choose to first apply what was learned from the lesson today.  Either way is fine.  When we discuss these answers, I will try to find students who answered in a variety of ways or else I may present an alternative explanation.  


Question 22 is especially difficult.  Students may need the following question to guide them: 1) What is the opposite of a positive number?  2) What is the opposite of a negative number?  3) What are possible values for J and S.

Exit Ticket

5 minutes

The exit ticket has two questions.  Students are asked to write an addition problem as a subtraction problem and then vice versa.  By the end of the problem solving section, students should be able to answer this question.  They should be even more prepared at this point after having worked through the independent practice.