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Arithmetic (all content)

Course: Arithmetic (all content) > Unit 3

Lesson 1: Multiplication intro
Math
Arithmetic (all content)
Multiplication and division
Multiplication intro
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Intro to multiplication

Google Classroom
Use arrays and repeated addition to visualize multiplication.

Getting started with multiplication

Multiplication helps us find the total number of items quickly.
For multiplication we will think about the number of equal sized groups and the number of items in each group.
Let's take a look at an example:
Each time you visit your neighbor's dog Tuffy, you give him two dog treats.
Each equal sized group has 2 treats.
You visited Tuffy 5 times last week. So there are 5 equal sized groups.
We can use multiplication to find out how many total treats you gave Tuffy.
The symbol for multiplication is start color #11accd, times, end color #11accd. If we translate this symbol into words it means "start text, start color #11accd, g, r, o, u, p, s, space, o, f, end color #11accd, end text."
For this problem, we have 5 start text, start color #11accd, g, r, o, u, p, s, space, o, f, end color #11accd, end text 2 dog treats. We can use the start color #11accd, times, end color #11accd symbol to write the problem:
5, start text, start color #11accd, space, g, r, o, u, p, s, space, o, f, space, end color #11accd, end text, 2, equals, 5, start color #11accd, times, end color #11accd, 2

Let's try another one

This week you visited Tuffy 4 times. You thought he looked too skinny so you gave him 3 dog treats each time you visited.
Problem 1, Part A
How many dog treats are in each equal sized group?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Problem 1, Part B
How many groups of dog treats are there?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Problem 1, Part C
Which expression can we use to show that you visited Tuffy 4 times and gave him 3 dog treats each time?
Choose 1 answer:

Picturing multiplication

Equal sized groups

Picturing equal sized groups is a great way to make sense of multiplication. In this example, let's think about the total number of petals on these flowers.
We can think of this as start color #e07d10, 3, end color #e07d10 flowers with start color #ca337c, 5, end color #ca337c petals on each flower.
The expression start color #e07d10, 3, end color #e07d10, times, start color #ca337c, 5, end color #ca337c means start color #e07d10, 3, end color #e07d10 groups with start color #ca337c, 5, end color #ca337c items in each group.
Problem 2, Part A
Each ladybug represents one group of spots.
There are
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
groups of spots with
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
spots in each group.

Problem 2, Part B
Which expression could we use to calculate the total number of spots?
Choose 1 answer:

Practice Problem 3
  • Current
Which expression could we use to calculate the total number of fish in the aquarium?
Choose 1 answer:

Arrays

We can also use arrays to show multiplication. An array is an arrangement of objects in equal sized rows.
An array with 3 rows with 8 dots in each row shows the expression 3, times, 8:
Problem 5, Part A
Use the array to answer the next question.
There are
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
rows with
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
dots in each row.

Problem 5, Part B
Which expression could we use to calculate the total number of dots in the array?
Choose 1 answer:

Finding the total

Repeated addition

Let's go back to the problem about Tuffy and the dog treats from earlier. You fed Tuffy treats on 4 days and gave him 3 treats each day.
We learned that 4 groups with 3 treats in each group is the same as 4, times, 3.
If we count the treats one by one we get a total of 12.
We can also use repeated addition to find the total number of treats. There are 4 groups of 3, so we can add 3, plus, 3, plus, 3, plus, 3.
Whether we multiply or use repeated addition, we are finding the total of 4 groups of 3 treats.
4, times, 3, equals, 12
3, plus, 3, plus, 3, plus, 3, equals, 12
There are 12 total treats.
Practice Problem 6
  • Current
Which expression is equal to 2, times, 7?
Choose 1 answer:

Skip counting

Skip counting is another method that we can use to find the answer to a multiplication problem.
Let's use an array to show how this works.
The array shows 4 rows with 5 dots in each row. This is the same as 4, times, 5 or 5, plus, 5, plus, 5, plus, 5.
To find the total number of dots we could count each dot, use repeated addition, or we could use skip counting to count up by five one time for each row:
5 ... 10 ... 15 ... 20
Skip counting is the same as repeated addition.
5, plus start color #01a995, 5, end color #01a995, equals, 10
10, plus start color #01a995, 5, end color #01a995, equals, 15
15, plus start color #01a995, 5, end color #01a995, equals, 20
Whether we skip count 5 ... 10 ... 15 ... 20
use repeated addition 5, plus, 5, plus, 5, plus, 5, equals, 20
or multiply 4, times, 5, equals, 20
we get the same answer!

Let's try a problem

Practice Problem 9
Which methods can we use to find the total number of dots in the array?
Choose all answers that apply:

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