Adding and Subtracting Decimals with Card Sort Activity

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Objective

Big Idea

What do fractions have to do with decimals?!

Do Now

10 minutes

During their 5th grade math curriculum, my students have been introduced to decimals.  Today's Do Now assesses their prior knowledge of decimals and place value.

Do Now:

For each pair of numbers, determine <, >, or =

1) 2.914  ____ 2.91

2) 47  ____  47.00000

3) 8.3214 ____ 8.3241

My students will have 3 - 5 minutes to complete the problems. After this time, I will randomly call students to the board to show their answers and explain their reasoning.  As students share their reasoning, I will be listening for their understanding of place value. I will also help them to use appropriate mathematical vocabulary in their explanations (MP6).

Card Sort Group Activity

25 minutes

This activity has been revised from the CMP3 Curriculum.

The Adding & Subtracting Card Sort Activity is designed to help students further understand place value. During the activity students make connections between the decimal and fraction representations of a number. They use their understanding of place value to add and subtract fractions. I highlight the connection for my students by saying that, "You will use your understanding of fractions to better understand decimals." I find that my students gain confidence working with decimals as they increase their understanding of the equivalence of fractional and decimal representations of numbers.

Teacher's Note: This activity is from the CMP3 Curriculum which we use in my school.

To get the Activity started I give each group of students a set of Adding & Subtracting Cards. I try to pre-cut the cards for my students to save time for mathematical reasoning, but this is not always possible. Then, I give my students the following directions:

1. Spread the cards out on your table so everyone in the group can see them.
2. Sort the cards into groups with equivalent expressions.  For example, 7 4/10 and 7.4 are equivalent, so they can be grouped together.  As you do, ask yourself questions like, "Are there any other cards in this group?"
3. Communicating with your group is very important for this activity, so be sure to work together. Discuss questions like, "Are there other groups that we can form?"

I give my students about 20 minutes to work through the activity.  As students work, I circulate throughout the classroom to assess their understanding. It is typical for groups to struggle with some of the cards, but it's important to let them work together to complete the activity (See Card Sort Activity video).

Activity Review

10 minutes

We will review the Card Sort Activity using a class discussion.  I will ask some leading questions to motivate groups to share their thoughts and strategies.

• How many different groupings did your table sort the cards into?

Students may respond with different answers.  Some groups may realize through the class discussion that some of their card groups can be combined.

• Describe the cards on one of your groups. Why did you group them together?

It's best to start with one group of students and have them share a set of cards that they matched, while other students see if they've matched the same cards. Students should explain their thought process and strategies.  I will call on several groups to answer this question, because it is helpful for students to hear different strategies.

• Does anyone disagree with this grouping? Are their any cards that you think do not fit in the group?

If there are students who disagree that a card fits in a group, it is important to discuss the different interpretations of the card. It is possible that the students have made a mathematical error. I prefer to discuss the groupings, rather than to provide an answer key. I like to let my class discuss the cards until they've agreed upon the answers. When we do, it is usually because we have found the correct groupings.

Towards the end of the discussion I will select various students to show the groupings on the board and we will agree on the final groupings (See Card Sort Student Work). By the end of the discussion, it should be revealed that students can use the denominator of the fractions to determine the place value of the decimal. To bring the discussion to closure I like to ask the following question:

• Based on the card sort activity, what is one strategy for adding or subtracting decimals?

Students should realize that they can convert the decimals to fractions and use their prior knowledge of adding/subtracting fractions.

Exit Ticket

5 minutes

As an assessment of my students' understanding of the content in today's lesson, I will give them a problem to complete. After 5 minutes, I will collect their work and use my assessment of it to prepare for future lessons.

Exit Ticket

Using a fraction strategy to find the following sum:

8.9 + 2.43 =

If students complete the task quickly, I will encourage them to try to check their answer by adding the numbers as decimals.