Primary Standards:

MAFS.5.NBT.1.3: Read, write, and compare decimals to thousandths.

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).

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

MAFS.5.NBT.1.4: Use place value understanding to round decimals to any place.

Connecting Standards:

MAFS.5.NBT.1.1: 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.

Content Knowledge:

In the first Unit, students explored the place value relationships in the base-ten number system, including with decimals.  In this Unit, students will extend their understanding of decimals to model, read, and write decimals to the thousandths.  Through explorations with base-ten models, students visualize thousandths and make connections to base-ten understandings to make sense of this extended decimal place.  Students should understand that a modification of materials must be made to be able to model the thousandths place.  For example, by making the large base-ten block cube a whole, students must make sense of what each successive piece now models.  5th grade students continue to explore ways to say and write numbers, including decimals, using standard, expanded, and word forms.

In this Unit, students will also apply their place value understanding to compare decimals.  Through investigations, modeling, and discussions, students will extend their understanding of comparing tenths and hundredths to the thousandths place.  Rather than simply telling students to “add a 0” to a decimal value, students should use models and place value charts to justify comparisons using place value language.

In rounding decimals, students can revisit and revise techniques used with whole numbers, testing to see if their discoveries apply to decimals as well.  Decimal number lines allow students to visualize the nearest tenth, hundredth, or whole number.

GCG 1 – Learning Goal: As a mathematician, I will be able to read, write, and represent decimals to the thousandths place

• Step 1: Read and write names of decimals to the thousandths place in word form
• Step 2: Write and represent decimals in standard and expanded form

GCG 2 – Learning Goal: As a mathematician, I will be able to compare decimals to the thousandths place

• Step 1: Use models and place value understanding to demonstrate and justify comparison of decimals to the thousandths place
• Step 2: Use place value understanding and inequality symbols (<, >, =) to compare decimals to the thousandths place
• Step 3: Compare two decimals that are written in different formats

GCG 3 – Learning Goal: As a mathematician, I will be able to round decimals using place value understanding

• Step 1:Connect work with base-ten models, place value charts, and number lines to round numbers
• Step 2: Round a given decimal to any place value; explain and justify using place value strategies