Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 49728
Multiply by Multiples of 10 with Number Cubes
In this lesson students will use various strategies to multiply one-digit numbers by multiples of 10 within the range of 10-90. The strategies will
encompass the Distributive, Commutative, and Associative properties, place value, number lines, base-ten blocks, diagrams, hundreds chart.
Students will play a game with number cubes to practice this multiplication.
Subject(s): Mathematics
Grade Level(s): 3
Intended Audience: Educators
Suggested Technology: Document Camera, Microsoft
Office
Instructional Time: 1 Hour(s)
Freely Available: Yes
Keywords: multiples of 10, multiply one-digit whole numbers, operations, Commutative property, Distributive
property, Associative property
Instructional Design Framework(s): Structured Inquiry (Level 2)
Resource Collection: CPALMS Lesson Plan Development Initiative
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will understand and know how to multiply one-digit whole numbers by multiples of 10 in the range 10-90.
Students will be able to apply properties of operations and place value understanding to solve multiplication problems.
Students will be able to explain their reasoning.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should know how to interpret products of whole numbers, e.g., interpret 5 X 7 as the total number of objects in 5 groups of 7 objects each.
Students should understand the array as a representation of a multiplication problem.
Students should have a flexible understanding of place value so that they understand 20 = 2 tens or 6 tens = 60
Students should be able to apply properties of operations as strategies to multiply and divide single-digit combinations. Specifically, students should understand that in
the multiplication problem 7 x 8 we can decompose (or break apart) the 7 groups into 5 groups of 8 and 2 groups of 8. They should know that they would then need to
take these two partial products (40 and 16) and add them together to get the final product 40 + 16 = 56. While the students may not know the name distributive
property, they should understand why the steps work.
Guiding Questions: What are the guiding questions for this lesson?
How can you use prior knowledge of multiplication facts to solve multiplication equations with multiples of 10?
Where have you seen something like this before?
page 1 of 4 How could thinking about place value help you?
Will this always work? Why?
Students should be able to apply known multiplication facts to solve unknown multiplication facts problems. For example, the student should understand the following
steps to find the product of 5 X 60.
If a student knows that 5 X 5 = 25, then the student will also know that 5 X 50 is the same as 5 groups of 5 tens which is 25 tens. 25 tens = 250.
Then, the student will need to know that 5 X 10= 5 x 1 ten = 5 tens which = 50
Finally, the student should add both products (250 +50) to equal 300.
Also, 5 X 60 can be represented as 5 groups of 6 tens, which is 30 tens, 30 tens = 300.
Using the Associative property 5 X 60 = 5 X (6 X 10) = (5 X 6) X 10 = 30 X 10 = 300.
Do you know another way to solve?
Could you show me with the base-ten blocks? Could you show me in an array? Could you show me on the number line? Could you draw a picture? Would the hundreds
chart help?
Could you use repeated addition?
Is there a more efficient way to solve the problem? How? Why does this work? If I need to multiply 7 X 10, would I get the same answer, if I multiplied 10 X 7? Why?
Teaching Phase: How will the teacher present the concept or skill to students?
The teacher will administer the formative assessment piece. The students should complete the formative assessment in 3-5 minutes. After the teacher collects the
assessment, the teacher can evaluate the students' needs in regard to multiplying one-digit whole numbers by multiples of 10 and applying properties of operations.
1. The teacher will present a blank formative assessment on the document camera for the whole class to view. The teacher may choose to read the question out loud.
2. Then the teacher should ask the students: What are strategies that you used to solve this problem? The teacher will be looking for students to describe the
Commutative property and the Distributive property. They do not need to know the names but should be able to correctly talk about the steps. Students may have
other strategies for solving, however, students should be familiar with the different properties and be able to use them when necessary.
3. The teacher will ask students to come to the board to work the problem while explaining their solution, or the teacher may ask students to bring their work to the
document camera to show their work as well as explain how they solved their work.
4. The problem 5X70 can be solved multiple ways. This is one example the teacher will want to show using the Distributive property.
5. 5X70= (5X30) + (5X40)
6. 5X30 is related to 5X3=15 because 5 x 3 tens = 15 tens which equals 150 (30+30+30+30+30=150) Just as 5X3 is 3+3+3+3+3=15. The students may want to use
the Commutative Property to think of 3x5=5+5+5 or 3 groups of 5 tens = 15 tens or 150.
7. 5X40 is related to 5X4=20 because 5 x 4 tens = 20 tens or 200, so 5X40=200 (40+40+40+40=200) Just as 5X4 is 4+4+4+4+4=20
8. 150+200=350
Please note: These strategies may be shown using place value blocks and the array. Show 5 rows of 7 tens. Group the 5 groups of 3 tens and the 5 groups of 4 tens.
Formative assessment multiplying by multiples of 10
Guided Practice: What activities or exercises will the students complete with teacher guidance?
To continue practicing multiplying one-digit whole numbers by multiples of 10 the teacher will present two problems.
1. Joel and his cousin are collecting canned food donations for charity. So far they have 7 boxes with 80 cans in each box. How many cans of food do they have for
their charity?
2. Ask students to think of what they know that could help them solve this challenge. Ask students to show their work with base-ten blocks, a number line, diagrams,
hundreds chart, or some other way.
3. As the students are working, make a note of which students you want to share their strategies with the class. Start with a student who has used place value blocks
and the array then move to more abstract solutions. Ask the student to to explain his/her reasoning. Ask for other methods used to solve the problem, until various
strategies are shown. If there are other ways to solve the problem, ask questions, so that another solution could be displayed. Always move the presentations to
the class from the most concrete to the most abstract.
4. Students may suggest that they know a double...7X7=49. So then 7X70= 7 groups of 7 tens or 49 tens which is equal to 490. Since 7X80 was distributed into
(7X70) + (7X10), then we need to add 70 from the (7X10) to 490, which is 560. In this example the Distributive property was used to break apart the original
multiplication sentence.
In the above example, students may not understand how 7X7 and 7X70 are related. Show the students the 7 groups of 7 ten rods. Students may be able to make
another connection by expanding 7X70 using repeated addition to visually see 7 groups of 70. (70+70+70+70+70+70+70)
1. Display the next example, George is making cookies for his bakery. He has 9 orders of 30 chocolate chip cookies and 9 orders of 30 peanut butter cookies. How
many cookies will George be baking in all?
2. Once again ask students to think of what they know that could help them solve. Ask students to share different strategies to answer the question, showing and
explaining their work.
3. One solution - Students may know 9X3=27 and therefore, 9X3 tens =27 tens or 270. (Once again students may need to see the repeated addition or the array to
see the relationship between 9X3 and 9X30.)
4. We can then set up the expression as: 9 X (30 + 30). Next we can expand the expression to look like (9X30) + (9X30). Ask students to solve for the first expression
(9X30, 9 groups of 30) which is 270. Then ask students to solve for the second expression (9X30, 9 groups of 30), which is 270. Now, students should be able to
add the products to get 540.
Students should be encouraged to use various strategies, so they can reason when a particular strategy is most efficient.
Also, as students are using the different properties of operations it is important to allow students to guide the teacher through their ideas of how they can use what they
know to solve. As students are guiding the teacher, the teacher can then point out and name the different properties which are being used.
page 2 of 4 Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Students will continue practicing multiplying one-digit whole numbers by multiples of 10 while playing the number cube game. Students will work in small groups or
pairs of students. Students will be using number cubes to roll one and two digit numbers. The students will then use these numbers to multiply using properties of
operations.
1. Students will decide who rolls the number cubes first.
2. Then, player 1 will roll both of the number cubes for the first time. Player 1 will take both numbers which were rolled and find their sum. The sum will be the onedigit whole number for their multiplication problem. This number will be how many groups they have.. For example; if player one rolls a 6 and a 2, then his
equation will look like 8 X ___ (8 groups of ?) (Students should note that if they roll two numbers with sums greater than 9, they need to roll both number cubes
again.)
3. Then, player 1 will record the first digit (how many groups) on his/her paper.
4. Player 1 will now roll the number cubes again to create the multiple of 10. For example; if player 1 rolls a 5 and a 4, then player 1 will first find the sum of both
numbers and then add a zero to make a multiple of 10. The equation would now look like 6 X 90. (Students should note that if they roll two numbers with sums
greater than 9, they need to roll both number cubes again.)
5. Next, player 1 will solve using an operation, diagrams, base ten blocks, or a number line.
6. Player one should explain to the other players how he/she solved.
7. Next is player 2's turn. Player 2 will follow steps 2-6.
The teacher may want to practice the game with the whole group first. I usually select a volunteer student to practice two or three times so that I can answer any
questions the students think of regarding rules, how to play, etc. Keep the place value blocks, particularly plenty of ten rods, nearby.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will assist students in organizing the knowledge they have gained by asking them,
What properties of operations did you use to solve these problems?
How might you use base ten blocks, an array, a number line, a diagram, or hundreds chart to solve the problem?
How did you use what you knew to solve?
The teacher should also circulate and review student work during the number cube game. The teacher should continue to ask the guiding questions during the game.
Finally, the teacher will give the summative assessment. The students will solve two multiplication sentences by multiplying one-digit whole numbers by multiples of 10.
The teacher will be evaluating the students' strategies as well as how efficient they were in solving. A rubric will also be used to help guide teachers in assessing
student progress.
Rubric For Multiplying by Multiples of 10
Summative assessment Multiplying by multiples of 10
Summative Assessment
The teacher will determine if the students have reached the learning targets for this resource when the students successfully complete the summative assessment:
multiplying by multiples of 10. The summative assessment can be measured using the rubric.
Formative Assessment
The teacher will present a formative assessment: multiplying by multiples of 10. The teacher will evaluate the students' knowledge on their use of the different
properties of operations and place value. The teacher can use this information to determine the level of knowledge that students have in regard to understanding place
value and utilizing the different operations to solve multiplication equations with multiples of 10 and adapt instruction accordingly.
During the lesson the teacher will monitor the students' work and ask guiding questions to lead students to develop various strategies to solve multiplication by 10
problems.
Feedback to Students
The students will initially receive feedback from the formative assessment during the teaching phase of the lesson. The students will be able to listen to peers describe
the different solution methods.
At this point, the teacher will give the names to these strategies that the students "discover," though students need not use formal terms for these properties. After
becoming familiar with these strategies, the students will be able to practice using these methods. The teacher will circulate the classroom and take notes on student
performances and provided feedback so that students can more effectively understand and utilize the different properties of operations.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Students may choose to roll the number cube only using numbers 1-3 during the game (for students who do not have fluency multiplying).
Students may need extra practice writing out the repeated addition to see the relationship between place values or build the arrays with the place value blocks.
English Language Learners may need support with unfamiliar vocabulary.
Extensions:
Students who have shown mastery of multiplying by multiples of 10 may want to try adding a third digit to multiply by. For example, 2X30X4.
Students who have mastery of multiplying by multiples of 10 may want to estimate the product first, and then solve.
Suggested Technology: Document Camera, Microsoft Office
Special Materials Needed:
Number cubes (Two per team)
Paper to show solutions
Base ten blocks
page 3 of 4 Hundreds charts
Blank number lines
Worksheets for assessments
Further Recommendations:
Students may want to take the game rules and number cubes home for extended practice or for homework.
Students may want to have the rubric for the summative assessment to preview before they complete the assessment.
Additional Information/Instructions
By Author/Submitter
This lesson plan utilizes the Mathematical Practice Standard: MAFS.K12.MP.7.1: Look for an make use of structure and MAFS.K12.MP.5.1 Use appropriate tools strategically.
SOURCE AND ACCESS INFORMATION
Contributed by: Lindsey Johannessen
Name of Author/Source: Lindsey Johannessen
District/Organization of Contributor(s): Brevard
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.3.NBT.1.3:
Description
Multiply one­digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based
on place value and properties of operations.
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