Understand the place value system (Decimals)

Decimal Place Value Visualization Activity

Students can use this activity to produce models and build concrete knowledge in decimal concepts.

Prior to Lesson: Collect place value block manipulatives (examples below). The place value solid becomes your "whole." The flat become .1. The rod becomes .01, and the unit becomes .001. Pre-package manipulatives with flats, rods, and units. The solid is useful for students, but having one as an example is all that is needed. If the basic concepts of fractions have been taught prior to this lesson, students are able to make great connections.

Place Value Solid (1000) Place Value Flat (100)

Place Value Rod (10) Place Value Unit Cube (1)

1. Begin by telling students that these blocks are different than the ones they have seen in the past. Students need to erase the idea of 1000 block, 100 block, 10 block, and 1 block from their heads and look at the manipulatives in a different way.

2. Explain to the students that the solid now represents a whole. "How do we represent a whole in math?" (students should come to the conclusion of 1)

3. "If the solid is one, what might the flat represent?" "How many flats do I need to make a whole?" (10) Follow the same steps with the rods (100) and cubes (1000).

4. Create a table with a diagram, word form, fraction form, and decimal form of each place value.

5. Create models of decimals. For example,

Students can model the decimals and get a feel for what they actually represent.

Extension: Starting with this lesson lends itself perfectly to comparing, ordering, and rounding. If students can visualize the decimal, they can tell which is larger. They can also decide which hundredth, tenth, or even whole, it is closest to.

Focus Content Area Standards

CCSS.MATH.CONTENT.5.NBT.A.3

Read, write, and compare decimals to thousandths.

CCSS.MATH.CONTENT.5.NBT.A.3.A

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).

CCSS.MATH.CONTENT.5.NBT.A.3.B

Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

CCSS.MATH.CONTENT.5.NBT.A.4

Use place value understanding to round decimals to any place.

Standards for Mathematical Practice

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6 Attend to precision.

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.