Primary Standards:

MAFS.5.NBT.2.7: 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; relate the strategy to a written method and explain the reasoning used.

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).

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.

MAFS.5.NF.2.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Content Knowledge:

In this unit, students multiply and divide to the hundredths.  Students’ understanding of place value helps them to use what they know about whole number computations and adapt that understanding to make sense of the decimal process.  Students multiply tenths by tenths or hundredths, but not hundredths by hundredths because the products exceed their understanding of decimal place value.

Using base-ten models initially helps the students visualize the factors and make sense of the products.  After exploring problems with decimal and whole number factors, problems are posed in which both factors are decimals.  Using 10 x 10 grids to represent decimal multiplication in the same way they used them to represent fraction multiplication.  As students explore, they should also look for patterns related to whole number multiplication and use estimation to accurately determine where to place the decimal point.

As with multiplication, it is important for students to build understanding of division with decimals through problem solving and place value models.  It is not the goal of the standard for students to use a standard algorithm, instead they are simply using models or a partial quotient approach.  Their understanding of decimal multiplication (and repeated decimal addition/subtraction) support them in this process.  Initial investigations with manipulatives and drawings help students visualize the division process when decimals are involved.

GCG 1 – Learning Goal:  As a mathematician, I will be able to model multiplication of whole numbers and decimals

• Step 1: Use models and place value understanding to multiply a whole number by a decimal
• Step 2: Use models and place value understanding to multiply a decimal by a whole number

GCG 2 – Learning Goal:  As a mathematician, I will be able to model multiplication of decimals by decimals

Step 1: Model multiplication of two decimal or mixed numbers using base-ten blocks, grid or area models, then pictures

Step 2: Make connections to whole number multiplication to justify and describe a written method for recording multiplication of decimals

GCG 3 – Learning Goal:  As a mathematician, I will be able to model division of decimals by whole numbers

Step 1: Divide decimals by whole numbers using place value understanding and base ten models

Step 2:  Divide decimals by whole numbers using place value and relate to a written method

GCG 3 – Learning Goal:  As a mathematician, I will be able to model division by tenths and hundredths

• Step 1: Divide decimals by decimals (tenths) using place value understanding and base ten models
• Step 2:  Divide decimals by decimals (hundredths) using place value understanding and base ten models