MARS task lesson, 6th grade
Alison, Kerry, Tracy
Topic: Adding and Subtracting Integers
Where does this lesson fit?
This lesson fits in with a unit on integers. It would come after an understanding of
negative integers. Students need an understanding of the word “difference.” They
should be able to add and subtract positive numbers fluently. These ideas will be
essential for algebra and geometry (solving equations, graphing functions, etc.) plus
the multiple real-life applications (money, temperature, etc.)
The new knowledge students will gain will be an understanding of how to add and
subtract integers. This addresses standards 6.NS.5 and 6.NS.7. b and c. It also
addresses mathematical practices 2 and 7.
6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite
directions or values; use positive and negative numbers to represent quantities in real-world contexts,
explaining the meaning of 0 in each situation.
MP2 Reason abstractly and quantitatively.
MP7 Look for and make use of structure.
Goals of the lesson
Our goal is for students to proficiently add and subtract integers using visual
models. Students should also be able to write an expression to represent the model.
We anticipate students will have difficulty subtracting negative integers.
It will develop Mathematical Practice 2. Starting with concrete models will develop
the schema in students’ minds and then they will be able to move to an abstract
understanding. It will also develop Mathematical Practice 7 through an
understanding of the general structure of the number system.
ELL students will be able to use models to show their thinking. There are few
vocabulary words – subtraction, integer, difference, addition.
Lesson Steps (this lesson is planned to occur over several days)
Freezing in Fargo (2012 MARS task, 6th grade)
NCTM elevator activity (http://illuminations.nctm.org/Lesson.aspx?id=4075)
Hot Air Balloon (http://www.supermathunits.com/files/hot_air_ballon_unit.pdf)
Hot Air Balloon Homework
Spin to Win Game
Hotel Elevator (2014 MARS task, 6th grade)
Possible Difficulties
What does the sand do, what does the air do?
Act out different scenarios using the model.
Students confused which way to move on the number line?
Act out problems as a group, with students explaining their thinking.
Students confuse the sign of numbers with the operation.
What is the answer to 8+(-3)? Do you think you would get the same answer for 8-3?
Solve problem both ways and see if the answer is different.
Students subtract the wrong way in order to obtain a positive answer.
What is the difference between 8-3 and 3-8? Do you think you should get the same
answer?
Thinking that subtracting a negative is the same as subtracting a positive.
If you are taking away sand, is the balloon going to go down or up?
Extension Problems for Students Who Need More Challenge
5+(-7)+(-2)+4=
8-(4+5)
-2+(-3-(-6))=
-7-(-3)+5-2=
Evaluation
We will use observations and the elevator MARS task as the post assessment. We
will compare this with Freezing in Fargo, which is our pre-assessment, to determine
growth. The pre-assessment will help us determine needs and misconceptions.
We will collect the worksheet and listen to the class discussion to determine
understandings/misunderstandings. For homework students will compare and
constrast 3-(-5) and 3+5. Then they will come up with multiple ways to get from -2 to
5. We will then consider the posttest to determine next steps for instruction.
Name ________________________________
Date____________________________
Spin To Win
3
7
-8
+
-6
-5
8
Spinner 1
Spinner 1
-
-
-7
Spinner 2
6
-9
Operation Spinner
Operation
-4
Spinner 2
Expression
Total:
Score