Integer Addition & Subtraction Assessment

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Objective

SWBAT add and subtract integers mentally and/or using a number line.

Big Idea

Students demonstrate their understanding that subtracting is equivalent to adding the additive inverse.

Intro & Rationale

The warm up for this assessment has students focus on the patterns of subtraction and engages them in some critical thinking about the relationships in the subtraction problems. I don't want to just practice the rules of calculation, because students so often make mistakes when they try to blindly follow rules and shortcuts without thinking about them. Students are prone to rushing through especially during an assessment and I want to slow them down and make them think about what is going on with the math.

Warm up

15 minutes

The Warm up subtraction pattern today reads:

"Erika says you get a positive answer when you subtract a negative number from a negative number. Edith says you get zero and Ramiro says you get a negative answer. Show that they can all be right."

I expect some students to struggle with how to show this, but I really want ideas to come from them. I circulate to see what students are coming up with. I may get through half the class or more before someone has started something, but I want them to try to figure out how best to show this rather than give them hints from the teacher's brain. If a student has an example of a subtraction problem or has a number line I share those ideas with the class.

  • "Brandon has come up with an example that has a positive answer."
  • "Samantha is trying out a number line."
  • "Maddy has an example with a negative and a zero answer, she must be working at finding one with a positive answer."

As some students finish sooner than others I encourage the class to come up with more than one example of each or share their examples with their math family group and look for patterns. I tell them if they have multple examples of each type they might be able to find a way to tell if any subtraction will be positive, negative, or zero.

When we go over this problem I ask students to share some examples to support the statements in the warm up (3 to 4 examples for each statement). For each one I ask the class to call out (on the count of three) the equivalent addition problem that will give up the same answer and I model the changes to the subtraction problems.

Then I ask students to look at each section and decide how they can tell whether the answer will be positive, zero, or negative. Answers should be something to the effect of:

  • "it will be positive if the number being subtracted is more negative than the number it is subtracted from"
  • "when you are subtracting more negatives than you have"
  • "when the number being subtracted is farther from zero" and vice versa for a negative answer.
  • For an answer of zero we are "subtracting the same number from itself".

White boards

10 minutes

This should be very quick review just before the test. I want them to get the feel for deciding whether or not they are going to change the problem. They have already taken a quiz addition only and the assessment mixes in some addition with the subtraction. One thing I expect is for students to try to change the addition problems as well. Sometimes they will change it correctly and sometimes they won't. Either way they usually get it wrong because subtraction is harder to do in your head and most of them are trying not to use the number lines or symbols any more. If this happens on the second problem below I remind them that it is their choice to do either the addition or the subtraction and ask which is usually easier. (addition)

-5 - 3

7 + (-10)

4 - (-6)

-2 - (-5)

-2 + (-7)

Assessment & homework

29 minutes