Unit 1

Place Value and Decimal Fractions

 

Grade 5
Math

 

Unit Length and Description:

 

20 days

 

Students extend their understanding of patterns in the base ten system as they work with multi-digit whole numbers and decimals to the thousandths place.

 

Students use whole number exponents to denote powers of 10. They will begin to understand why multiplying by a power of 10 shifts the digits of a whole number or decimal that many places to the left. Students explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of ten.

 

Students build on the understanding they developed in fourth grade to read, write, and compare decimals to thousandths using base-ten numerals, number names and expanded form. Students use decimal notation for fractions with denominators of 10 and 100 to decimals to the thousandths. Students compare two decimals to the thousandths place using >, =, and < symbols to record the results of the comparisons. Students use place value understanding to round decimals.

Students apply their place value understandings to problem solving with metric conversions.

 

Standards:

 

NBT - Number and Operation in Base Ten

Understand the place value system.

5.NBT.A.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.A.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 power of 10.

5.NBT.A.3

Read, write, and compare decimals to thousandths.

a. Read and write decimals to thousandths using baseten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (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.

5.NBT.A.4

Use place value understanding to round decimals to any place.

MD Measurement and Data

Convert like measurement units within a given measurement system.

5.MD.A.1

Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

(Note: Unit 1 addresses the metric system component of this standard.)

Standards for Mathematical Practices

1.   Make sense of problems and persevere in solving them.

2.   Reason abstractly and quantitatively.

3.   Construct viable arguments and critique the reasoning of others.

4.   Model with mathematics.

5.   Use appropriate tools strategically.

6.   Attend to precision.

7.   Look for and make use of structure.

8.   Look for and express regularity in repeated reasoning.

 

Instructional Outcomes:

 

         5.NBT.A.1:

o   I can understand and explain the value of digits.

o   I can recognize that in a multi-digit number, a digit in one place represents 1/10 of the place value to its left.

         5.NBT.A.2:

o   I can represent powers of 10 using whole number exponents (103 = 10 x 10 x 10 = 1000)

o   I can explain patterns when multiplying a number by powers of 10.

o   I can explain the relationship in the placement of the decimal point when a decimal is multiplied or divided by powers of 10.

         5.NBT.A.3

o   I can read and write decimals to thousandths using base ten numerals.

o   I can read and write decimals to thousandths using number names.

o   I can read and write decimals to thousandths using expanded form.

o   I can compare decimals using >, =, <.

o   I can compare two decimals to the thousandths based on the place value of each digit.

         5.NBT.A.4

o   I can round decimals to any place.

         5.MD.A.1

o   I can divide and multiply to convert metric measurements.

o   I can convert units of measurement within the metric system.

o   I can solve multi-step, real world problems that involve converting metric measurement units.

 

 

 

Enduring Understandings:

 

         Understanding the multiplicative patterns of the base ten system helps me compose and decompose numbers.

         It is important to understand that a digit represents 10 times the value of what it represents in the place to its right, and 1/10 of what it represents in the place to its left.

         Using exponents involving powers of 10, helps me solve problems with metric conversion.

         Understanding place value helps me read, write, compare and round decimals and perform mathematical operations.

 

Essential Questions:

 

         What is the relationship between the number of factors of 10 and the shift of the position of the digits on a place value chart?

         How can I use place value to solve problems involving metric conversion?

         How can I use exponents or unit fractions to represent numbers in expanded form?