Battle of the Tenths
Students will be able to write decimals in expanded form.
Introduction (15 minutes)
- Write "219.536" on the board.
- Have students read the decimal out loud in proper form (two hundred nineteen and five hundred thirty-six).
- Give students tips on saying it properly and correct any misconceptions about pronunciation.
- Repeat if needed with a different decimal.
- Pose this question: What is the place value of the digit 9?
- Have students pair up and discuss it with their partners. Encourage them to think deeply about the question.
- Have a few students share their ideas, and discuss it as a whole group.
- Explain that the value is one and the digit tells us there are nine of them.
- Ask students to think about the fractional equivalents of 0.1, 0.01, and 0.001. (1/10, 1/100, 1/1000).
- Explain that today, they will write in expanded form using fractions.
Explicit Instruction/Teacher Modeling (20 minutes)
- Write "872.461" on the board.
- Have students copy it down on their whiteboards and read the decimal to their partner.
- Encourage students to coach each other.
- Pose this question: What is the place value of the digit 2?
- Have students discuss with one another.
- Encourage students to explain their reasoning.
- Explain that the place value of the 2 is ones, so we have 2 ones.
- Ask students to write an equation to explain this.
- Scaffold their understanding to get to the point where they understand that the expression of the value of the 2 in the ones place is (2 x 1) because we have 2 ones.
- Pose this question: What is the place value of the 4 and how would we express that in an equation?
- Have students discuss with their partners.
- Write the equation on the board (4 x 1/10) and ask if this works.
- Lead the students in a discussion about the ways we can write in expanded form, with fractions and decimals. Explain that today, they will be writing only with fractions.
- Repeat with the the other digits until you have (8 x 100) (7 x 10) (2 x 1) (4 x 1/10) (6 x 1/100) (1 x 1/1000) on the board.
- Ask students how all of these equations equate to the original number of 872.461.
- Discuss as a whole group.
- Lead students to the understanding that each equation equals a digit and place value of the original number. Help them understand that we need to add additional signs in between each equation so they show how we are adding each term together to get the original number. (8 x 100) + (7 x 10) + (2 x 1) + (4 x 1/10) + (6 x 1/100) + (1 x 1/1000)
- Explain that they will use this information to play a game.
Guided Practice/Interactive Modeling (30 minutes)
- Hand out the decimal cards and have students cut them out.
- Have students mix up the cards and put them face down in a pile.
- Each student will pick a card without letting the other see it.
- They will both write the decimal in expanded fraction form and underline the tenths place. If there is no tenths place, have them place a decimal and a 0.
- When both students have completed their expanded fraction forms. Have them flip up their cards. The player who has the largest tenths place is the winner and keeps the cards. If they have the same size tenths place, then they should compare the hundredths place, etc.
Independent Working Time (10 minutes)
- Distribute the Decimals in Expanded Fraction Form worksheet and have students complete it independently.
- Enrichment Advanced students can round their decimals to the nearest tenths place, then compare. If they have the same tenth as their partner, it would be a draw.
- Support Students who need support can use a place value chart to help them remember the place values.
Assessment (10 minutes)
- Collect the worksheets and create groups for students depending on their misconceptions.
- Students who are having trouble using the fractions instead of decimals can be put into one group.
- Students who are struggling to determine proper place values can be put in another group.
- Pull groups aside during the next day's activities to clear up any misconceptions.
Review and Closing (5 minutes)
- Discuss as a group any struggles or successes students saw while they were playing the game.