Connecting Benchmarks/Horizontal Alignment

• MA.4.AR.1.1
• MA.4.M.1.2 
• MA.4.M.2.1 
• MA.4.GR.2.1
• MA.4.GR.2.2

Terms from the K-12 Glossary

• Expression 
• Equation 
• Factor

Vertical Alignment

Previous Benchmarks

• MA.3.NSO.2.2
• MA.3.NSO.2.3
• MA.3.NSO.2.4

 

Next Benchmarks

• MA.5.NSO.2.1

Purpose and Instructional Strategies

The purpose of this benchmark is for students to become procedurally fluent in using a standard algorithm. Work with standard algorithms began in the procedural reliability stage when students explored a variety of methods and learned to use at least one of those methods accurately and reliably. To demonstrate procedural fluency, students may choose a standard algorithm that works best for them. A standard algorithm is a method that is efficient and accurate (MTR.3.1). A standard algorithm is also generalizable, meaning that it works no matter how many digits are involved.

• It is important to challenge students to explain the steps they follow when using a standard algorithm (i.e. regrouping, proper recording and placement of digits by place value). For example, when students use a standard algorithm, they should be able to justify why it works conceptually. Teachers can expect students to demonstrate how their algorithm works, for example, by comparing it to another method for multiplication (MTR.6.1).
• Along with using a standard algorithm, students should estimate reasonable solutions before solving. Estimation helps students anticipate possible answers and evaluate whether their solutions make sense after solving.
• This benchmark supports students as they solve multi-step real-world problems involving combinations of operations with whole numbers (MA.4.AR.1.1).

Common Misconceptions or Errors

• Students that are taught a standard algorithm without any conceptual understanding will often make mistakes. For students to understand a standard algorithm or any other method, they need to be able to explain the process of the method they chose and why it works. This explanation may include pictures, properties of multiplication, decomposition, etc. Students may make computational errors while using standard algorithms when they are unable to reason why their algorithms work.
• Some students may struggle with this benchmark if they do not have a strong command of basic addition and multiplication facts.

Strategies to Support Tiered Instruction

• Instruction includes explaining mathematical reasoning while using a multiplication algorithm. Instruction also includes determining if an algorithm was used correctly by reviewing the reasonableness of solutions. 
  • For example, students use an algorithm to determine 41 × 23 and explain their thinking using place value understanding. Explicit instruction includes: “Begin by multiplying 3 ones times 1 one. This equals 3 ones. We will write the 3 ones under the line, in the ones place. Next, we will multiply 3 ones times 4 tens. This equals 12 tens. We will write the 12 tens under the line in the hundreds and tens place because 12 tens is the same as 1 hundred and 2 tens. This gives us our first partial product of 123. Now we will multiply the 1 one by the 2 tens from 23. This equals 2 tens or 20. We will record 20 below our first partial product of 123. Next, we, we will multiply 2 tens times 4 tens, which equals 8 hundreds. We will write the 8 in the hundreds place of our second partial product. Our second partial product is 820. Finally, we add our partial products to find the product of 943.” 

• For example, students determine 41 × 23 using an area model and place value understanding. 

• For example, students use an algorithm to determine 4 × 36 and explain their thinking using place value understanding. Instruction includes stating, “Begin by multiplying 4 ones times 6 ones. This equals 24 ones or 2 tens and 4 ones. We will write the 4 ones from 24 under the line, in the one's place. We will write the 2 tens from 24 as a 2 above the 3, as a regrouped digit in the tens place. Next, we will multiply 4 ones times 3 tens. This equals 12 tens. We will add the 2 tens to the 12 tens for a total of 14 tens. We will write the 14 tens under the line in the hundreds and tens place because 14 tens is the same as 1 hundred and 4 tens. Our product is 144.” 

• For example, students determine 4 × 36 using an area model and place value understanding. 

• Instruction includes the use of known facts to find unknown multiplication facts. 
  • For example, if the student does not know the product for 4 × 6 from the previous 120 +24 144 example, have students use a known fact such as 4 × 5. The known fact of 4 × 5 = 20 can be used to find the product of 4 × 6 by adding one more group of 4 to the product of 20 to find the product of 24.

Instructional Tasks

Instructional Task 1 (MTR.4.1, MTR.5.1) 

Using the digits 1, 2, 3 and 4, arrange them to create two 2-digit numbers that when multiplied, will yield the greatest product.

Instructional Task 2

Part A. Solve  using an area model or the distributive property.

Part B. Solve  using a standard algorithm.

Part C. Explain the relationship between your partial products from Part A and your partial products from Part B.

Instructional Items

Instructional Item 1 

Select the expressions that have a product of 480.

• a. 10×48
• b. 16×30 
• c. 24×24 
• d. 32×15 
• e. 40×80 

Instructional Item 2

A multiplication problem is shown.

Part A. What is the missing value in the box in the problem shown?

Part B. What is product of 38 X 62?

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