Maryland Math 6.NOS.B.3

6.NOS.B.3 is a cluster heading. These are the individual standards under it.

• 6.NOS.B.3.a

  Extend estimation strategies to estimate and assess the reasonableness of products and quotients.

• 6.NOS.B.3.b

  Generalize whole number strategies to multiply and divide decimals.

• 6.NOS.B.3.c

  Use a standard algorithm to multiply and divide decimals.

• 6.NOS.B.3.d

  Determine and explain when a strategy or algorithm is most efficient.

01

What Students Need to Do

Students multiply and divide multi-digit decimals, including numbers with three decimal places, in word problems. They estimate to check their answers and use standard algorithms for exact answers. They explain when mental math would be faster.

02

What Mastery Looks Like

A student estimates that 12.4 gallons at $3.275 per gallon will cost about $40, then calculates $40.61. They can show why 7.5 ÷ 0.125 becomes 7500 ÷ 125 and explain why counting eighths may be faster than long division.

03

Common Misconceptions

Some students line up decimal points when multiplying instead of using place value to place the point in the product. Others move only the divisor's decimal point when dividing, or accept an answer ten times too large without checking an estimate.

04

How to Assess It

Exit ticket: Gas costs $3.275 per gallon. Find the cost of 12.4 gallons and the number of 0.125-liter cups in 7.5 liters. Estimate both, show both standard algorithms, and explain which answer is easier to find mentally.

1. 01

   Give pairs eight paper 1-liter strips marked in eighths; have them model 7.5 ÷ 0.125 and check with long division.

2. 02

   Ask, “For 7.5 ÷ 0.125, would you count eighths or use long division? Which is faster, and why?”

3. 03

   Post 4.016 × 2.5 and 18.75 ÷ 0.375; pairs estimate, use standard algorithms, and check each other's decimal placement.

4. 04

   Use a gas receipt showing 12.4 gallons at $3.275 per gallon; students estimate the total, calculate it, and check the charge.

• 5.NOS.B.7

  Apply and extend previous understanding of multiplication and division of whole numbers to multiply and divide decimals to hundredths in context.

• 4.NOS.B.3

  Fluently add and subtract multi-digit whole numbers within 1,000,000.

• 5.NOS.B.4

  Fluently multiply multi-digit whole numbers.

• 6.NOS.B.2

  Fluently divide multi-digit numbers.