Quiz 2: Assessing Decomposition & Mixed Number Problems

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SWBAT show more than one way to decompose a fraction in order to add and subtract mixed numbers.

Big Idea

This assessment discerns how well students can add and subtract mixed numbers and solve word problems using decomposition skills.

Warm Up: The Whole Buzz!

10 minutes

I often play guessing games with students about numbers to get them to think about operations. What's my number can be played several ways, but I wanted to quickly see if they could add & subtract some fractions in their heads quickly enough to tell me if the number produced a whole number or not. This game is called "The Whole Buzz"

I led this game because it was a little tricky to lead for most students. My above grade level performing students probably will be able to lead this the next time we play. It requires some extra thinking that they weren't ready for just yet...at least to lead. I like to have them lead when they can.

I told my students that they needed to decide if my fraction equation would produce a number that was  one whole or larger. I would subtract or add.I told them they needed to jump up from their desk and shout "Buzz!" if it did.

So I started with 1  1/4 - 3/4. 4 students jumped up and yelled "Buzz". Two students were totally confused, so I told them to ask one of the students who had not jumped up. He explained that if we had a whole and just a little over a whole, that taking away anything larger than 1/4 would make less than a whole, therefore, he didn't jump.

I tried again. 6/8 + 7/8 All jumped up and yelled "Buzz" this time. I yelled "Yay!".

We played like this for 10 minutes. The toughest ones were the subtraction ones. They just really were slow at figuring out if they were less than one whole or not.

Quiz 2: Administering the quiz

40 minutes

Quiz 2 Decomposing Mixed Numbers

 This quiz builds conceptually upon Quiz 1 as a way for students to prove the scaffolded process of how the standards link to one another. I used this quiz the day after Quiz 1. It could be given later if student's need more remediation on the standard. This is one of the greatest things about Common Core! 

In the first quiz, students showed mastery in simple addition and subtraction algorithms and word problems. Then, students learned to decompose fractions to create improper fractions as they learned the meaning of the whole number mixed with a fractional part of another whole. They need to show me that they can decompose the fractions to show how many wholes are in an improper fraction to create a mixed number, or decompose a whole number using fractions to create an improper fraction.

The word problems are addition and subtraction. Only one requires decomposition. I want to know if they can distinguish when decomposition is necessary or not within a word problem.

Like all of the tests and quizzes I write, I make sure standards are written at the top in student friendly language so that they understand what they are being assessed.