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U n t er r i ch t spl a n
M ul t ip l e s o n t he Numb e r Line
Altersgruppe: 3 r d Gr ade
Virginia - Mathematics Standards of Learning (2009): 3 .5 , 3 .6
Virginia - Mathematics Standards of Learning (2016): 3 .4 .a, 3 .4 .b,
3 .4 .c , 3 .4 .d
Fairfax County Public Schools Program of Studies: 3 .5 .a.1, 3 .5 .a.2,
3 .6.a.3
Online-Ressourcen: T o e t he L i ne
Opening
T eacher
present s
St udent s
pract ice
Mat h
Pract ice
Mat h
Worksheet
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M at h Obj e c t i v e s
E x pe r i e nc e skip counting on a number line
P r ac t i c e multiples of numbers between 2 and 10
L e ar n to identify values on a number line
De v e l o p number sense
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Closing
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Ope ni ng | 3 min
Display the following:
S ay : We want to figure out what numbers belong at the question
marks. What should we do first?
A possible response: First let’s write 40 where it belongs.
A sk : How do we determine what numbers belong at the question
marks?
A possible response: We can count backwards from 50 to
determine the missing number on the right and count backwards
from 40 to find the other two missing numbers.
A sk : What numbers belong at the question marks?
The missing numbers are 36, 39, and 47.
S ay : Here, we are counting by ones as we move right on the number
line. In today’s episode, we will be counting by larger numbers.
T e ac he r pr e se nt s M at h game : T o e t he L i ne - M ul t i pl e s o n
N umbe r L i ne | 12 min
Present Matific ’s episode T o e t he L i ne - M ul t i pl e s o n
N umbe r L i ne to the class, using the projector.
The goal of the episode is to fill in missing numbers on a number line. The tick
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marks on the number line are multiples of a number between 2 and 10.
S ay : Please read the instructions.
Students can respond based on the episode.
S ay : Let’s look at the tick marks on the number line. What number is
on the left of the number line? What number is on the right of the
number line? By what number are we counting?
The number 0 is on the left. The number on the right and the
interval between tick marks will vary each time the episode is
opened.
Depending on the episode’s problem, ask : How can we determine
how to fill in the missing numbers? o r How can we determine
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where to place the tags?
Responses may vary. Some students may suggest skip counting.
Others may suggest determining location using multiplication.
Still others may determine a value by noticing its location
relative to another number – for example, that the number in the
middle of the number line will be half the number on the right.
Ask the students to answer the problem that the episode presents.
Enter the students’ answers, and click on
.
If the answers are correct, the episode will proceed to the next question.
If the answers are incorrect, the instructions will wiggle. For a missing
numbers question, the incorrect entries will turn brown. For a question with
tags, the incorrect tags will wiggle and fall from the number line.
The episode will present a total of six problems.
S t ude nt s pr ac t i c e M at h game : T o e t he L i ne - M ul t i pl e s o n
N umbe r L i ne | 12 min
Have the students play T o e t he L i ne - M ul t i pl e s o n N umbe r
L i ne on their personal devices. Circulate, answering questions as
necessary.
M at h P r ac t i c e : M ul t i pl e s o n t he N umbe r L i ne W o r kshe e t |
12 min
Display the following number lines:
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Distribute graph paper, rulers, and colored pencils.
Ask the students to make nine number lines on the graph paper,
using the display as a guide. On the first number line, they should
count by twos up to 40. On the next number line, they should count
by threes up to 39. They should continue in this way up to counting
by tens. They will need to make the tick marks on the number line
and ensure that they are properly spaced.
When the students are done working, discuss. S ay : Use the number
lines to name the mul t i pl e s of 6 up to 36.
The multiples of 6 up to 36 are 6, 12, 18, 24, 30, and 36.
S ay : Look at the other number lines. Is there another that also has 6,
12, 18, 24, and 36? If so, which one?
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There are two numbers lines where 6, 12, 18, 24, and 36 appear.
They appear on the number line with multiples of 2 and on the
number line with multiples of 3.
A sk : Why does it make sense that every multiple of 6 is also a
multiple of 2? Why does it make sense that every multiple of 6 is
also a multiple of 3?
Six goes into any multiple of 6. Two goes into 6. Therefore, 2
must fit inside any multiple of 6 because it fits inside 6 and 6 fits
inside any multiple of 6. Likewise, 3 goes into 6. So 3 will also go
into any multiple of 6.
A sk : Is the reverse true? Is every multiple of 2 also a multiple of 6?
Is every multiple of 3 also a multiple of 6?
No. For example, 10 is a multiple of 2 that is not a multiple of 6,
and 9 is a multiple of 3 that is not a multiple of 6.
S ay : Let’s look at the multiples of 8. Any multiple of 8 must also be
a multiple of what other numbers? How do you know?
Any multiple of 8 is also a multiple of 2 and of 4. Since 2 and 4
are f ac t o r s of 8, they are also factors of all multiples of 8.
M at h W o r kshe e t P r ac t i c e : A r i t hme t i c P r o gr e ssi o ns - S ki p
C o unt up t o 100 | 5 min
For extra practice with skip counting, have the students work on the
following worksheets: A r i t hme t i c P r o gr e ssi o ns - S ki p
C o unt up t o 100 and A r i t hme t i c P r o gr e ssi o ns ( 5 ) - S ki p
C o unt Up T o 1000 . It is worth noting that the numbers in the
worksheets are not necessarily multiples of their common
difference, as opposed to the numbers on the tick marks in the
episode which are multiples.
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C l o si ng | 3 min
Display the following:
A sk : What numbers belong on the other tick marks? How do you
know?
The tick marks increase by 8. The leftmost tick mark should be
labeled 24. The missing tick mark between 32 and 48 should be
labeled 40. The rightmost tick mark should be labeled 56. We can
tell that we are counting by eights because the difference
between 48 and 32 is 16. There is 1 tick mark between 32 and 48,
so it must be half the distance from 32 to 48. Half of 16 is 8.
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