Transcript Module 3 Lesson 25 - Peoria Public Schools

Math Module 3
Multi-Digit Multiplication and Division
Topic F: Reasoning with Divisibility
Lesson 25: Explore properties of prime and composite numbers to 100 by using
multiples.
4.OA.4
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Lesson 25
Target
You will explore
properties of prime
and composite
numbers to 100 by
using multiples.
Fluency
Test for Factors
40 64 54 42
• Write down the
numbers that have
10 as a factor.
Lesson 25
÷ 4 = 10
Fluency
Test for Factors
Lesson 25
• Use division to prove
both 4 and 2 are
factors of 40.
Fluency
Test for Factors
54 = 27 x 2
= (9 x 3) x 2
= 9 x (3 x 2)
Lesson 25
• Prove that both 3
and 2 are factors of
54 using the
associative property.
Fluency
Test for Factors
42 = 21 x 2
= (7 x 3) x 2
= 7 x (3 x 2)
Lesson 25
• Prove that both 3
and 2 are factors of
42 using the
associative property.
Fluency
Test for Factors
40 54 64 42
• Write down the
numbers that have 8
as a factor.
Lesson 25
Fluency
Test for Factors
40 = 10 x 4
= (5 x 2) x 4
= 5 x (2 x 4)
Lesson 25
• Prove that both 4
and 2 are factors of
40 using the
associative property.
Fluency
Test for Factors
64 = 16 x 4
= (8 x 2) x 4
= 8 x (2 x 4)
Lesson 25
• Prove that both 4
and 2 are factors of
64 using the
associative property.
Fluency
•
•
•
We will
Multiples
aremake
Infinite
Let’s share our
results!
groups
of four.
Could you have kept counting after I told
you to stop?
We now know the multiples for
ANY
I will
give you a
number are infinite – it goes number
on forever.
to count
How is that different from thebyfactors
of at
a 0.
starting
number?
Every number has a certain amount of
factors, but an unlimited number of
multiples.
Group 1, count by 3s
The
number of factors is finite, but the
Group 2 – 5s
multiples
are infinite. You will count for
Group 3 – 2s
two minutes.
Go!
•
•
Group 4 – 4s
Lesson 25
Multiples are Infinite!
Fluency
Lesson 25
List Multiples and Factors
List as many multiples of 3 as you can in 20 seconds.
Take your mark; get set – go!
3,
6,
27,
30,
9,
List the factors
of 3.
12,
33,
15,
36,
18,
39,
1,
21,
24,
42,
45
3
Fluency
Lesson 25
List Multiples and Factors
List as many multiples of 4 as you can in 20 seconds.
Take your mark; get set – go!
4,
8,
36,
12,
16,
40,
44,
List the factors
of 4.
20,
24,
48,
1,
28,
52,
2,
4
32,
56
Fluency
Lesson 25
List Multiples and Factors
List as many multiples of 5 as you can in 20 seconds.
Take your mark; get set – go!
5,
10,
45,
15,
20,
50,
55,
List the factors
of 5.
25,
60,
1,
30,
35,
65,
5
40,
70
Concept Development (Use Problem Set)
Lesson 25
Problem 1
• Let’s take a look at the number chart in front of
you. What is the smallest prime number you see
on the chart?
• Two.
• How do you know what is the greatest composite
number you see?
• 100, because it is even. All even numbers greater
than 2 have 2 as a factor, so they have to be
composite numbers.
• Now, working with your partner, read and follow
all of the directions at the top of the first page of
the Problem Set. Be sure to follow the directions
in order, and check with each other to see that
you complete each activity the same way. If you
find that you have different responses at times,
talk about it to see what the correct thing to do is.
Concept Development (Use Problem Set)
Lesson 25
Problem 1
• After you marked off multiples of 7, what was the
next number that you circled?
• Were there any multiples of 11 that hadn’t been
crossed out already?
• What about 13? Are there any multiples of 13 that
still need to be crossed off?
• They’re already crossed off from before.
• I wonder if that’s true of the rest? Go back to 11.
Let’s see if we can figure out what happened.
Count by elevens within 100 using the chart.
• 99 is how many elevens?
• 9 elevens.
• So, by the time we circled 11, is it true that we’d
already marked all of the multiples of 2, 3, all the
way up to 10?
Concept Development (Use Problem Set)
Lesson 25
Problem 1
• Yes; we circled 2, 3, 5, and 7, and crossed off their
multiples. We didn’t have to do fours, because the
fours got crossed out when we crossed out
multiples of 2. The same thing happened with the
sixes, eights, nines, and tens.
• So we had already crossed out 2 × 11, 3 × 11, all
the way up to 9 × 11. I wonder if the same thing
happens with 13. Discuss with a partner: will
there be more or fewer groups of 13 than groups
of 11 within a hundred?
• Who thought more because it is a bigger number?
• Actually, it is fewer because it is a larger number
so fewer will fit in 100. Fewer because 9 × 11 is 99,
so maybe 7 or 8 times 13 will be less than 100. 9
× 13 is more than 100, so fewer groups.
Concept Development (Use Problem Set)
Problem 1
Take a moment to figure out
how many multiples of 13 are
within 100.
How many multiples of 13 are
less than 100?
Lesson 25
Concept Development (Use Problem Set)
Problem 1
7 x 13 is 91
Lesson 25
Concept Development (Use Problem Set)
Problem 1
.
• We already marked off 91 because it is a multiple of 7. The
same is true for 6 × 13, 5 × 13, and so on. Do we need to
mark of multiples of 17?
• No, because there will be even fewer groups and we
already marked off those factors.
• The highest multiple of 17 on the hundreds chart is 85. 5
seventeens is 85. We already marked 2 × 17 up to 5 × 17.
Continue to page 2!
Lesson 25
Concept Development (Use Problem Set)
Problem 1
.
Lesson 25
Problem Set
10 Minutes
Problem Set
10 Minutes
We started this
Which
Problem Set by
numbers
are
coloring
number
1
red and
beginning
circled?
our work with the
Which
multiples of 2. Why
numbers
didn’t
we cross are
out
thecrossed
multiples out?
of 1?
Problem Set
10 Minutes
Problem Set
10 Minutes
Debrief
Lesson Objective:
Explore properties of
prime and composite
numbers to 100 by
using multiples.
• Are any prime numbers even? Are all
odd numbers prime?
• We crossed off multiples of 2, 3, 5,
and 7. Why didn’t we have to cross
off multiples of 4 or 6?
• How did you know some of the larger
numbers, like 53 and 79, were prime?
• How can we find the prime numbers
between 1 and 200?
• The process of crossing out multiples
to find primes is called the Sieve of
Eratosthenes. Eratosthenes was an
ancient Greek mathematician. Why
do you think this is called a sieve?
Exit Ticket
Lesson 1