Standard #: MA.3.NSO.2.3

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.3.NSO.2.2 
• MA.3.NSO.2.4 
• MA.3.AR.1.1 
• MA.3.AR.1.2 
• MA.3.GR.2.2 
• MA.3.GR.2.4

Terms from the K-12 Glossary

• Expression 
• Equation 
• Factor 
• Whole Number

Vertical Alignment

Previous Benchmarks

• MA.2.NSO.2.2

Next Benchmarks

• MA.4.NSO.2.2 
• MA.4.NSO.2.3

Purpose and Instructional Strategies

The purpose of this benchmark is for students to use place value reasoning to multiply single- digit factors (0-9) by multiples of 10 up to 90 (10, 20, 30, 40, 50, 60, 70, 80, 90) and multiples of 100 up to 900 (100, 200, 300, 400, 500, 600, 700, 800, 900). Because the expectation of this benchmark is at the procedural reliability level, students should develop accurate, reliable methods for multiplication that align with their understanding and learning style. 

• Instruction should connect known facts of one-digit factors (e.g., 6 × 7), to then apply to products of one-digit numbers and multiples of 10 or 100 (e.g., 6 × 70, 60 × 7, 6 × 700, 600 × 7) (MTR.5.1). 
• Teachers should use place value representations (e.g., pictures, diagrams, base ten blocks, place value chips) to show relationships between known facts and multiplying one-digit factors by multiples of 10 or 100. For example, 3 × 4 can be interpreted as 3 groups of 4 ones, or 12 ones. 3 × 40 can be represented as 3 groups of 4 tens, or 12 tens. 12 tens is equal to 120 ones. 3 × 400 can be represented as 3 groups of 4 hundreds, or 12 hundreds. 12 hundreds is equal to 120 tens or 1,200 ones (MTR.5.1). 
• This standard lays the foundation for multi-digit multiplication. For benchmark 3.AR.1.1, students use the distributive property to multiply 34 × 8 as (30 × 8) + (4 × 8). This benchmark (MA.3.NSO.2.3) helps students reason that 30 $x$ 8 is the same as 3 tens × 8, or 24 tens (240). 
• Instruction should not focus on “adding zeroes to the end” when multiplying one-digit factors by multiples of 10 and 100. For example, 7 $x$ 50 should not be reduced to “7 × 5 with one zero at the end.” This trick does not focus on place value methods, as Clarification #1 of the benchmark requires.

Common Misconceptions or Errors

• Students can quickly jump to the conclusion that they can “count zeroes” to determine the number of zeroes in the product (e.g., the product of 7 $x$ 500 will have two zeroes because 500 has two zeroes). This can confuse students when the products of the known facts already end in zero (e.g., using 5 × 8 = 40 to multiply 5 × 80). Students who rely on this trick will often indicate that 5 × 80 = 40 because they see only one zero in the factors.

Strategies to Support Tiered Instruction

• Instruction includes opportunities to connect grouping numbers by multiples in different ways. 
  • For example, students may place the following facts on the hundreds chart: 1 × 10, 2 × 10, 3 × 10, 4 × 10, 5 × 10, 6 × 10, 7 × 10, 8 × 10 and 9 × 10. The teacher asks students what patterns they notice.

• Instruction includes opportunities to use a number line. Students skip count by multiples on the number line. This will support a conceptual understanding of what is happening with the numbers, instead of focusing on the “zero trick.” 2×200 = 400 

• Instruction includes opportunities to connect grouping numbers by multiples. 
  • For example, students use manipulatives to show that 5 groups of 20 is 100 and 5 groups of 200 is 1,000. Teacher should be explicit about the multiples and not point out the zeros trick.

Instructional Tasks

Instructional Task 1 

• The table below shows the costs for entry at the Sunnyland Amusement Park. 

• a. How much does entry cost for nine adults? Write an equation to show the total cost? 
• b. Write an expression that shows the total cost for one senior and one 2-year-old child to attend Sunnyland Amusement Park. 
• c. The Suarez Family purchases 2 adult tickets, 1 senior ticket, and 1 ticket for their 6- year-old daughter. Write an equation to show the total cost of entry for the family. 
• d. Which cost of entry is less expensive, 2 seniors or 3 children? Explain how you know using words, a picture, or equations.

Instructional Items

Instructional Item 1 

• Write two different equations using a one-digit whole number and a multiple of 10 that show a product of 120. 

Instructional Item 2 

• Write two different equations using a one-digit whole number and a multiple of 100 that show a product of 2,400.

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.