Guided Lessons

# Whose is Longer?: Decimals in Expanded Form

Teach your students how to write decimals in expanded decimal form with this fun game. Students will be writing and comparing decimals while not even realizing they are learning one of the most complicated year 6 maths standards.

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Students will be able to write decimals in expanded form.

(15 minutes)
• Write "523.912" on the board.
• Have students read the decimal out loud in proper form (five hundred twenty-three and nine hundred twelve thousandths).
• Give students tips on saying it properly and correct any misconceptions about pronunciation.
• Repeat if needed.
• Pose this question: What is the place value of the digit 3?
• Have students discuss in their pairs or groups. Encourage them to think deeply about the question.
• Have a few students share their ideas, and discuss the question as a whole group.
• Explain that the value is one and the digit tells us there are three of them.
(20 minutes)
• Write "489.215" on the board.
• Have students copy it down on their whiteboards and read the number to their partner.
• Encourage students to coach each other.
• Pose this question: What is the place value of the digit 9?
• Have students discuss with their groups.
• Encourage students to explain their reasoning.
• Explain how the place value of the 9 is ones so we have 9 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 9 in the ones place is (9 x 1).
• Pose this question: What is the place value of the 8 and how would we express that in an equation?
• Have students discuss with their partners.
• Discuss as a whole group and write the equation on the board (8 x 10).
• Repeat with the the other digits until you have (4 x 100) (8 x 10) (9 x 1) (2 x 0.1) (1 x 0.01) (5 x 0.001) on the board.
• Ask students how all of these equations equate to the original number of 489.215.
• Discuss as a whole group.
• Lead students to the understanding that each equation represents a digit and the place value of the original number.
• Explain that students will use this information to play a game.
(30 minutes)
• Have students get into pairs and cut out the decimal cards.
• Have them mix the cards up and place them in a pile.
• Instruct the students to each take a card and not let the other person see it.
• Have them write their numbers in expanded decimal form following the example that is still on the board.
• When both partners are done, have them count to three and flip their boards over, showing their decimal in expanded decimal form to their partner.
• The partner who has the most expressions (most digits) wins that card.
• The player with the most cards when the game is over is the winner.
(10 minutes)
• Distribute the Decimals in Expanded Form worksheet and have students complete it independently.
• EnrichmentHave advanced students also compare the decimals to see which one has the largest decimal.
• SupportHave students who need support play the game using a place value chart so they can recall the value of each place.
(10 minutes)
• Collect the worksheets and separate students into groups who need further assistance.
• Look for students who are not putting the addition sign in between terms and put them into a group.
• Look for students who are not multiplying the digits by the appropriate place values and put them into a group.
• Pull these groups aside during the next day's activities to clear up any misconceptions.
(5 minutes)
• Have students each write on a sticky note one thing they felt successful with and one thing they struggled with today.

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