Grade 5 Lesson Title: Multi-Digit Multiplication

Grade 5 Lesson Title: Multi-Digit Multiplication

Unit 1: Whole Number Computation Time Frame: 6 – 7 days

Essential Question: How do you choose different multiplication strategies to multiply multi-digit numbers?

Targeted Content Standard(s): / Student Friendly Learning Targets
5.NBT.5Fluently multiply multi-digit whole numbers using the standard algorithm. / I can…

Multiply multi-digit whole numbers.
Explain how various models can be used to represent and solve problems involving multiplication.

Targeted Mathematical Practice(s):
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure.
Look for an express regularity in repeated reasoning
Supporting Content Standard(s):(optional)
5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. (EOY)
Purpose of Lesson
Students will learn to fluently multiply multi-digit numbers using place value understanding. This lesson is not just rote procedure; and students are expected to reason about their calculations and the calculations of others.
Explanation of Rigor:(Fill in those that are appropriate.)
Conceptual: Students will modelmultiplication with multi-digit numbers using the base-ten number system through the use of the area model and partial products. (5.NBT.5) / Procedural: Students will use place value strategies and properties of operations to multiply multi-digit whole numbers (5.NBT.5) / Application: Students will use multiplication to solve real-world situations.
Students should also be able to use estimation to check the reasonableness of the their answers.
(5.NBT.5)
Vocabulary:
Multiply Digit Equations
Tens Parentheses Expanded Form
Hundreds Partial Products
Thousands Regrouping
Evidence of Learning (Assessment):
Pre-Assessment: Assess students’ place value understanding of base-ten system (Segment #1), Using Area Models for Multi-Digit Multiplication
Formative Assessment(s): Area Model Pairs Check Worksheet
Partial Product Method Worksheet
Summative Assessment: Review Cards
Multi-Digit Multiplication Summative Assessment
Self-Assessment:
Lesson Segments:

Assessing Place Value Understanding
Multiply Multi-digit Numbers with Area Models
Multiply 2-digit numbers by 2-digit numbers using strategies
Multiply 3-digit numbers by 2-digit numbers using strategies
Multiply multi-digit numbers using column method
Multiplication practice
Assessment

Procedures:
Segment 1
Approximate Time Frame:
20 - 25 minutes / Lesson Format:
Whole Group
Small Group
Independent
Modeled
Guided
Collaborative
Assessment / Resources: Place value activity envelopes with index cards with digits 0-9 (one envelope per group of four students).
Place Value Understanding Observation Checklist
Using Area Models for Multi-Digit Multiplication
Focus:
Assess students’ place value understanding of the base-ten system. / Modalities Represented:
Concrete/Manipulative
Picture/Graph
Table/Chart
Symbolic
Oral/Written Language
Real-Life Situation
Math Practice Look For(s):

MP2:Reason abstractly and quantitatively. Students will show their understanding of place-value concepts.
MP3: Construct viable arguments and critique the reasoning of others.

/ Differentiation for Remediation: Have students who are having difficulty use base-ten manipulatives as concrete representations of the numbers.
Differentiation for English Language Learners:
Clarify ones, tens, hundreds, and thousands place value.
Differentiation for Enrichment: Have students use additional digit cards and form larger numbers and then tell the value of individual digits within the numbers formed.
Potential Pitfall(s):
Many students continue to have difficulty with place value understanding so it is important that the students use place value language in explaining the value of their digits so that you can be aware of any misconceptions the students may have. / Independent Practice (Homework):
Steps:

Each group of four students receives an envelope which contains index cards with one of each digit 0-9.
Without looking, each student takes out one card and then in cooperation with their partners, forms the greatest number they can make using their chosen cards.
Each group lines up with their cards in front of them displaying their ‘greatest’ number.
Ask several Individual students to tell the value of their individual digit in their group’s number (e.g. student with the 8 in the number 3681 needs to state “The value of my digit is 80.) Have them write out the number in expanded form.
All groups then line up in order based on the value of their four-digit numbers. Have students explain why their number is smaller or larger than another group’s number.
If some students have the same digit but in different places in their group’s number, have them explain the difference between the value of each persons’ digit. Whose digit has a greater value? Why?
Repeat activities having groups form the four-digit number with the least value. Continue with variations of this activity, to assess place value understanding of individual students and groups.
Give students the Using Area Models for Multi-Digit Multiplication Pre-assessment to determine how much time should be spent on segment 2.

/ Teacher Notes/Reflection:
Segment 2
Approximate Time Frame:
2 – 3 days (based on 50-60 minute class periods) / Lesson Format:
Whole Group
Small Group
Independent
Modeled
Guided
Collaborative
Assessment / Resources:
Centimeter grid paper (optional)
Base Ten Blocks (optional)
Area Model Note Taking Sheet
Area Model Pairs Check Worksheet
Area Model Summative Assessment
Focus:
Students will be able to multiply multi-digit numbers using the area model. / Modalities Represented:
Concrete/Manipulative
Picture/Graph
Table/Chart
Symbolic
Oral/Written Language
Real-Life Situation
Math Practice Look For(s):

MP2:Reason abstractly and quantitatively. Students make sense of the place value of the numbers being multiplied.
MP4:Model with mathematics. Students use area models to multiply multi-digit numbers.
MP7: Look for and make use of structure. Through the use of place value concepts and partial products, students can understand the structure behind multiplying multi-digit whole numbers.

/ Differentiation for Remediation:
Allow students to first solve two-digit by one-digit problems using centimeter grid paper. It offers a more concrete model vs. the more abstract area model. This helps struggling students better connect the area of the rectangle to the product. Students could also build the area model with base ten blocks to make it more concrete.
An example of the area model using centimeter grid paper:
Differentiation for English Language Learners:

Differentiation for Enrichment: Students can create their own real-life multiplication problems.
Potential Pitfall(s):
Review the rules of multiplying by multiples of ten. / Independent Practice (Homework):
Use the area model to explore this problem.
Thirteen people ordered a dozen cookies from the bakery. How many cookies were sold?
If twenty-three people would order a dozen cookies, how many cookies were sold?
Describe how the products would change from the first question to the second question.
Answer:
The product would increase by 240 from the first to second questions. If you notice in the area model, only two of the partial products would change since the amount of people increased by 10.
10+ / 3
10
+ / 10 x 10 = 100 / 10 x 3 =30
2 / 2 x 10 = 20 / 2 x 3 =6
20+ / 3
10
+ / 20 x 10 = 200 / 10 x 3 =30
2 / 2 x 20 = 40 / 2 x 3 =6
Steps:
Introduce the area model by using a real-world example such as: 23 students in a class are each mailing 34 postcards to armed service members for Veteran’s Day.
Feel free to use the Area Model Note Taking sheet or have the students to write their work in their notebooks.
Step 1: Write the problem in expanded form.
34 / / +
X 23 / +
Step 2: Place the numbers written in expanded form in the correct location on the area model.
Step 3: Calculate the area of each rectangle.
Have the students work in pairs to try and sketch orbuild this model with base ten blocks before you continue with the solution.
Step 4: The sum of the areas equals the product.

Thus,
Another example to use with the class:
A theater has 78 rows of seats and there are 45 seats in each row. How many total seats are in the theater?
45 x 78

Thus,
While the students are working on the sample problems have them answer the following questions:
1)Estimate your answer.
2)How do you re-write the problem in expanded form?
3)Where do you place the expanded form of the numbers on the area model? Would it make a difference if they were placed in a different location? Why?
4)Why does the sum of the products in the separate rectangles equal the product of the original problem?
Step 5: Continue to do a variety of sample problems: 2 by 2 digits, 3 by 2 digits, 4 by 2 digit problems (class, pairs, and independently) until the students feel comfortable with the procedure. Instead of telling students directly how to solve a 3 by 2 digit or a 4 by 2 digit problem, have them discuss and apply what they know about the area model to it.
Step 6: Once the students have had ample time to solve problems using the Area Model, you can assess them using the Area Model Pairs Check Worksheet.
Step 7: To wrap up this segment, either have the students work in pairs or independently to complete the Area Model Summative Assessment. / Teacher Notes/Reflection:
Segment 3
Approximate Time Frame:
1 - 2 days
(based on 50-60 minute class periods) / Lesson Format:
Whole Group
Small Group
Independent
Modeled
Guided
Collaborative
Assessment / Resources:
Transparency of Partial Product Multiplication Worksheet
Partial Product Multiplication Worksheet (1 per student)
Focus:
Students will be able to multiply two 2 digit-numbers using the base-ten number system. / Modalities Represented:
Concrete/Manipulative
Picture/Graph
Table/Chart
Symbolic
Oral/Written Language
Real-Life Situation
Math Practice Look For(s):
MP2: Reason abstractly and quantitatively. Students will see use place value concepts when solving multiplication problems with partial products.
MP7: Look for and make use of structure. Through the use of place value concepts and partial products, students can understand the structure behind multiplying multi-digit whole numbers.
MP8: Look for an express regularity in repeated reasoning. After students have fully developed conceptual understanding of multi-digit multiplication, they can fluently use a standard algorithm to solve a problem. / Differentiation for Remediation:
Have base-ten manipulatives available as concrete representations for students who are having difficulty with place value concepts or use the area model. If students are having problems keeping their numbers in-line while writing, have students solve their problems on cm grid paper or turn their paper sideways.
Differentiation for English Language Learners:
Differentiation for Enrichment:
Potential Pitfall(s): Regrouping will not make sense to the students if they do not understand the place value involved in multiplication. / Independent Practice (Homework):
Ask the students to explain how partial products and area models are related.
Procedure:

The 5.NBT.5 Segment 3 Partial Product Multiplication worksheet provided will be the lesson plan.
Hand out the worksheet and go over the instructions. Go over the sample problem with the students. 56 x 32.

While you are solving the sample problem, connect the area model from the previous lesson to show how each partial product is represented on the area model. It is recommended that you draw the area model to represent 56 x 32 and complete each step as you solve the partial products method so students can see the connection.

Ask the students the value of each digit in the problem.
What is the value of the 5 in 56? Ans. 50 or 5 tens. What is the value of the 6 in 56? Ans. 6 or 6 ones. What is the value of the 3 in 32? Ans. 30 or 3 tens. What is the value of the 2 in 32? Ans. 2 or 2 ones.
Can students explain why these problems are in parentheses? (2 X 6) (2 X 50) (30 X 6) (30 X 50) Students may need guidance to answer this question. Lead them to seeing that they are using the place value associated with each of the digits being multiplied. Once again, discuss how the partial products relate to the area model. Those partial products can then be added to get the product of the original two numbers, 56 and 32.
Continue working through problems 1-3 with the students. After those examples, the teacher may decide how to proceed. Either, have students work independently, with a partner of similar skill or continue working whole group and continue asking questions similar to the example question so that the students are hearing the place value associated with this method of multiplication.
When multiplying 6 x 2 be sure to say 6 ones x 2 ones = 12 ones. Students will better understand why the 1 (1 ten) is regrouped in the tens place. Continue using the place value form of the number as you work through sample problems.

/ Teacher Notes/Reflection:
Segment 4
Approximate Time Frame:
1 - 2 days
(based on 50-60 minute class periods) / Lesson Format:
Whole Group
Small Group
Independent
Modeled
Guided
Collaborative
Assessment / Resources:
Dry Erase Boards or Paper (1 per student)
Dry Erase markers or Pencils (1 per student)
Calculators
Review Cards
Focus:
Students will be able to multiply numbers up to 3-digit by 2-digit by using a variety of strategies. / Modalities Represented:
Concrete/Manipulative
Picture/Graph
Table/Chart
Symbolic
Oral/Written Language
Real-Life Situation
Math Practice Look For(s):
MP5: Use appropriate tools strategically. Students can decide what is the best method for them to solve the multi-digit multiplication problem.
MP7: Look for and make use of structure. Through the use of place value concepts and partial products, students can understand the structure behind multiplying multi-digit whole numbers.
MP8: Look for an express regularity in repeated reasoning. After students have fully developed conceptual understanding of multi-digit multiplication, they can fluently use a standard algorithm to solve a problem. / Differentiation for Remediation: Review the area model and/or the partial products method. Help students understand the connection between both methods.
Differentiation for English Language Learners:
Differentiation for Enrichment:
Potential Pitfall(s): If studentsdo not understand the place value associated with the multiplication, they will not fully understand the process of the algorithm. They will merely be solving the algorithm based on rote procedures without connecting meaning to it. / Independent Practice (Homework):
Procedure: This lesson extends and reviews thearea model andpartial product multiplication strategy and should lead into a standard algorithm for multiplication in the next segment.
Note: There are many ways that Review cards can be used. Listed are a few resources/strategies:
*Partner work -
*Math Scavenger Hunt -
*Group Work – Assign a problem for each group to work on. Each group member completes a step to solve the problem and then passes the work to the next member, repeat until the problem is complete.
*Summative Assessment-Assign one problem from the Review Cards for students to complete independently. Evaluate their ability to solve the problem. / Teacher Notes/Reflection:
Segment 5
Approximate Time Frame:
1-2 days
(based on 50-60 minute class periods) / Lesson Format:
Whole Group
Small Group
Independent
Modeled
Guided
Collaborative
Assessment / Resources:
Multiplication Template(s)
Plastic Sleeve/Sheet protectors (optional)-1 per pair
Dry Erase Markers (optional)-1 per pair
Focus:
Students will solve multi-digit multiplication problems using the column method. / Modalities Represented:
Concrete/Manipulative
Picture/Graph
Table/Chart
Symbolic
Oral/Written Language
Real-Life Situation
Math Practice Look For(s):
MP6: Attend to precision. Students need to be accurate with regrouping using the column method of multiplication to ensure accuracy with their calculations.
MP7: Look for and make use of structure. Through the use of place value concepts and partial products, students can understand the structure behind multiplying multi-digit whole numbers.
MP8: Look for an express regularity in repeated reasoning. After students have fully developed conceptual understanding of multi-digit multiplication, they can fluently use a standard algorithm to solve a problem. / Differentiation for Remediation: Students will need to refer to the partial products method while solving to connect place value meaning to the column method.
Differentiation for English Language Learners:
Differentiation for Enrichment:
Potential Pitfall(s):
Students will not understand the concept of regrouping and misplace the number in the incorrect column or they follow rote procedures without place value understanding. / Independent Practice (Homework):
Steps:
Students should have a good foundation of breaking apart numbers at this point in 5th grade. This lesson extends the partial products strategy and should lead into the standard algorithm of multiplication. Whenever students understand the place value associated with multiplication, they are ready for the standard algorithm. Regrouping will make sense when students are ready.

Put the following multiplication equation on the board: 33 x 24
Have a discussion with students stating that the school bought a class of 24 students (or use the number of students in your class) new math textbooks. Each textbook costs $33. How much did all the textbooks cost?

Ask them if it would be possible to solve the problem this way: 33 x 4 + 33 x 20. Allow time for discussion.

To solve this problem, students should understand that 24 = 2 tens and 4 ones, so they can simply multiply 33 x 4 = 132, then multiply 33 x 20= 660, and then add those partial products together. 132 + 660 = 792

Explain they have been working with the area model and the partial products strategy for the past few days. The column method is a similar to the partial products, but it uses fewer steps to solve it. Reviewing the break-apart strategies should help them when they are regrouping.

Show the multiplication template (either draw it on the board or use it as a transparency.)