Primary 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.

MAFS.5.NBT.1.2: 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 powers of 10.

Connecting Standards:

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

1. 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).

Content Knowledge:

In 4th grade, students discovered the relationship between consecutive places in whole numbers; specifically, that each place value position is 10 times greater than the value of the place value position to its right.  In 5th grade, students will extend this relationship between values of digits directly to the left and right, (each place value position is 1/10 of the value of the place value position to its left) and to all place values from the thousandths to the millions.  They will also extend this understanding as they recognize that the relationship between values in the digits of decimals is the same as for whole numbers.

Also, in 5th grade, students are introduced to exponents to show powers of ten.  They discover that the exponent is the number of times 10 is a factor, so 103 is 10 × 10 × 10 (1,000).  As they model expressions, students see patterns appear in powers of ten as they observe the number of zeros in the product.  They will also explore patterns related to the placement of decimal points when numbers are multiplied or divided by a power of ten.

GCG 1 – Learning Goal: As a mathematician, I will be able to relate whole number place values

• Step 1: Compare and explain the relationship between values of whole number digits in any place value
• Step 2: Relate multiplying by 10, dividing by 10 (or multiplying by 1/10) to explain the relationship between adjacent whole number place values

GCG 2 – Learning Goal: As a mathematician, I will be able to relate whole number and decimal values

• Step 1: Compare and explain the relationship between values of digits directly to the left or right in decimals
• Step 2: Relate multiplying by 10, dividing by 10 (or multiplying by 1/10) to explain the relationship of adjacent whole number and decimal place values

GCG 3 – Learning Goal: As a mathematician, I will be able to apply and explain patterns when multiplying and dividing by powers of ten

• Step 1: Use models and place value understanding to multiply decimals by powers of ten
• Step 2: Use models and place value understanding to divide decimals by powers of ten
• Step 3: Explain and apply patterns when multiplying and dividing by powers of ten

GCG 4 – Learning Goal: As a mathematician, I will be able to relate patterns with powers of ten to exponents

• Step 1: Understand what an exponent is and express powers of ten using exponents (i.e. 10 × 10 × 10 = 1000 = 103)
• Step 2: Connect multiplying and dividing by powers of ten to multiplying and dividing by exponents with a base of ten