Extending Decimal Place Value Understanding Through Problem Solving - Math Coach's Corner

I was planning with my 5th grade team today, and they’re getting ready to move into decimal place value. The 5th grade standard is to extend decimal place value from the hundredths place to the thousandths place. We decided to start with a very quick Ticket In the week before the unit actually starts to get a feel for what the kiddos retained from 4th grade.

On Day 1, we’re going to focus on reading decimal numbers, starting out with decimals to the hundredths (4th grade skill) and extending to the thousandths (5th grade skill).

Write the following on the board/document camera:  (2 x 100) + (3 x 10) + (6 x 1) + (1 x 0.1) + (5 x 0.01).  Talk with your partner about how you would write this number in standard form. Accept responses and have a class discussion about which the class feels is the correct way to write the number. Be sure that they come to the conclusion that it should be written 236.15. Who thinks they can read the number?  Accept responses.  You may have students that try to read it two hundred thirty-six point fifteen, because they often hear adults use that short cut.  Tell kiddos that mathematicians are more precise and would read it two hundred thirty-six and fifteen hundredths.  We say the word and when we reach the decimal point, and we always include the decimal place value name.

Write the decimal place value names above the number and ask if students notice anything about the place value names.  If they don’t notice the symmetry between the whole and decimal place value names, draw the arrows as shown below to illustrate the relationship.

Change the number to 1,236.158 by adding a 1 in the thousands place and an 8 in the thousandths place.  Turn and talk to your partner.  How should we label the place value position names of the new digits?  You’re hoping that they will conclude that since the 1 is in the thousands place, then the 8 must be the thousandths place.  Remember, you’re wanting them to see the relationship between the place value positions.

Continue practicing reading decimal numbers to the thousandths.  Be sure to write the numbers with the place value names labeled to support the learning.  Try letting the student who reads the number correctly be the one to write the next number.

Give a quick Ticket Out to determine how well students understood the concept.

Day 2 moves us into comparing decimals.  Again, we’ll frame it in a problem solving context.

Give each pair of students the two place value mats shown below, manipulative money (3 dollar bills, 10 dimes, and 10 pennies), and base-10 blocks (3 flats, 10 rods, and 10 units).

Huh.  I wonder which is bigger, 0.9 or 0.09?  Let’s read these decimals to make sure we’re clear on them.  Nine tenths and nine hundredths. Great! I’ve given you some materials.  You may use these materials to prove your answer.  You also need to be able to explain in words and pictures how you decided which is the bigger decimal.

Give students some time to work in pairs on the problem, and then come back together to discuss.  See if students can make any generalizations.

Give students additional numbers to build and compare.  Here are some good ones to try:  0.17 and 0.4; 1.08 and 1.18; 2.2 and 2.24; 1.5 and 1.67

Be sure to bring the class back together to discuss their results and strategies for comparing. If you feel they have really grasped this lesson, you might try…

Huh.  I wonder which is bigger, 0.102 or 0.14?  🙂

Click here to grab your mats!  Looking for additional decimal resources?  Check out my Common Core: Decimals & Fractions Using Models and Manipulatives unit.  It’s a best-seller!


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