Unit 1

Place Value and Decimal Fractions and Metric Measurement Conversions

 

Grade 5
Math

Description:

Students understand patterns in the base ten system as they work with multi-digit whole numbers and decimals to the thousandths place. They will understand that in multi-digit numbers, a digit in one place represents 10 times what it represents in the place to its right and of what it represents in the place to its left. Students will use whole number exponents to denote powers of 10. Students will also explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of ten.

 

Students read, write, and compare decimals to thousandths. Students will extend their understanding with using decimal notation for fractions with denominators of 10 and 100 to 1000. They read decimals using fractional language and write decimals in fractional form, as well as in expanded notation. Students compare two decimals to the thousandths place using >, =, and <. Students will use place value understanding to round decimals to any place. Students will apply their place value understandings to problem solving with metric conversions.

Louisiana Student Standards for Mathematics (LSSM)

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 and apply patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain and apply patterns in the values of the digits in the product or quotient, when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. For example, 100 = 1, 101 = 10 and 2.1 x 102 = 210.

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.

5.NBT.B7

 

 

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; justify the reasoning used with a written explanation.

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, and use these conversions in solving multi-step, real world problems. (e.g., convert 5 cm to 0.05 m; 9 ft. to 108 in).

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

 

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?