The Decimal Point Slide

This resource was created by Big Ideas in Beta, a Big Ideas Fest project, with acknowledgement to Amelia Terrapin

LEARNING OUTCOMES:

• Students will understand that a digit in one place represents 10 times the place to its right and 1/10 of the place to its left. 
• Students will be able to multiply by powers of 10. 
• Students will be able to express multi-digit numbers and decimals to thousandths in expanded form.

COMMON CORE STANDARDS ADDRESSED:

Understand the place system

5.NBT.1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

5.NBT.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

5.NBT.3. Read, write, and compare decimals to thousandths.

• Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
• Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons

5.NBT.4. Use place value understanding to round decimals to any place.

TIME REQUIRED FOR LESSON:

45 minutes

TIME REQUIRED FOR TEACHER PREPARATION:

Ten minutes

MATERIALS FOR LESSON:

• Blackboard/whiteboard 
• Pencils and paper 
• On the floor make boxes for 1000, 100, 10, 1, 1/10, 1/100, 1/1000 places using tape or string with a spot or cone for a decimal point; label each box either on the floor or on the wall above with the appropriate place 
• Open space; push desks aside, going to the gym or outside is ideal

OVERVIEW OF LESSON:

1.) Begin by writing a two-digit whole number on the board, for example, 40.  As a pre-assessment, ask the students “If we multiply by 10 what do we get?  How many zeros do we add?  If we take the same number and multiply by 1/10 what do we get? How many zeros do we take away?” Allow time for discussion and record the students’ ideas on a chart paper or the board.

2.) Now tell the students that we will demonstrate this with our bodies.  Ask the students, “How many tens are there in the number 40?”  Ask for volunteers to come up to each represent a ten, allowing them to decide how many people they need (4).  Ask them “How many ones are in the number 40?”  Ask for a volunteer to represent a zero with a big round shape.

3.) Now tell the students that we will multiply this number by 10.  Ask them “Do we add or take away zeros?”  Tell the students to notice that you add the same number of zeros as there are in the multiplier.  Ask for another volunteer to represent another zero.  Ask “How many hundreds are in this number? How many tens? How many ones?” (4, 0, 0)

4.) Now tell the students that we are going to multiply this number by 1/100.  Ask them “Do we add or take away zeros?”  Again, ask them to notice that you take away the same number of zeros as there are in the denominator.

5.) Split the class in half and move to your prepared tape or string boxes.  One group will be writing with pencil and paper and the other half will move.  Put the writers into smaller groups so they can work cooperatively.  Write a multi-digit number plus decimals on the board (be sure to choose a number that uses all students, for example, 211.05 for 9 students). Ask the writers to write the number down. Ask the movers to represent the number using the prepared boxes for each place value.  (2 people in the hundreds place, one person in the tens place, one person in the ones place, zero people in the 1/10 place, 5 people in the 1/100 place.)

6.) First ask the writers to multiply the number by 10.  Ask the student “Which direction do we move the decimal point?”  Now ask the movers to multiply by 10.  Ask them “Do we need more bodies? Less bodies? Or do we just move to a different box?”  Discuss that we can move the decimal point OR move the bodies to different boxes.  Try both ways.

7.) Change groups so that the writers now become movers and vice versa.  Again, put the writers into smaller cooperative groups. Choose another number, for example, 301.6 for ten students.

8.) Ask the writers to write the number down and the movers to demonstrate the number with their bodies.  Say to the students, “Now let’s multiply by 100.”  Ask the students, “Which direction does the decimal point move?”  Ask them first to move the decimal point.  Then go back to the original number and ask them to move their bodies to different boxes so that they represent the same number with the decimal point in the correct place.

9.) Now ask the movers to create their own number by choosing any box they like.  They can use any place box they want, so the number can be in the thousandths digit all the way down to the 1/1000 digit.  The writers’ job is to correctly write this number down on paper in expanded form.  For example, the number 2011.302 would be (2 x 1000 + 0 x 100 + 1 x 10 + 1 x 1 + 3 x 1/10 + 0 x 1/100 + 2 x 1/1000.)

10.) Switch groups and repeat the process.  Ask the movers to represent a number by choosing a place box.  The writers will write the number down in expanded form.

11.) As a post-assessment, ask each student to write down their name and birthday month and day, for example, 6/26 on an index card.  Tell the students, “Now write this number with a decimal point:  6.26.  Multiply your decimal number by 100 and record your answer (626).  Then multiply your original decimal number by 1/10  and record your answer(.626).”  If time allows ask each person to use the prepared boxes and place their classmates in the proper boxes to represent their birthday numbers.  As the students work, make sure to reinforce the core standards introduced in this lesson.