SCUSD Common Core Mathematics Lesson Planning Guide
Unit Title: Place Value and Multi-Digit
Arithmetic
Lesson 5 D: Adding and Subtracting Using
The Number Line
Approx. time:
45 Minutes
A. Focus and Coherence
Students will know…
 the identity property of addition a+0=a 0+a=a
 the identity property of subtraction a-0=a
Students will be able to…
 Represent numbers on a number line
 Add and subtract numbers within 1000 by using
number lines
Student prior knowledge:
 Commutative property of addition
 Place value, ones tens, hundreds
 Concept of an interval (the space between 1 and 2
equals the space between 3 and 4)
 Greater than less than
Which math concepts will this lesson lead to?
 Identity property of multiplication

CCSS-M Standards:
3NBT.2 Fluently add and subtract within 1000 using
strategies and algorithms based on place value, properties
of operations, and/or the relationship between addition
and subtraction.
B. Evidence of Math Practices
What will students produce when they are making sense,
persevering, attending to precision and/or modeling, in
relation to the focus of the lesson?
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Discuss attributes of the digits (1,2,3,4,5,6,7,8,9,0,)
Draw number lines starting at 0
Draw number lines that don’t start at 0.
Draw vertical number lines.
Draw horizontal lines.
Use straight edges (rulers, cubes, yardsticks, etc) to
draw lines.
Orally guess missing numbers on a number line.
Important vocabulary
Starting point, midpoint, end point
Halfway, digits, numbers
Less than, greater than
Sum always
Order of operations
Essential Question(s)
 Why is place value important?
 Why is there only one digit in each place of a multi-digit number?
 How can a number line help you?
 How do you select an appropriate interval for a number line?
 What is an interval?
 How is subtraction related to addition?
Formative Assessments
Anticipated Student Preconceptions/Misconceptions
 All number lines must start at zero
 Number line intervals are not uniform
 You can only use one property in each problem
Materials/Resources pencils, paper, finger spaces
Optional cubes, rulers, yardsticks
Supplemental materials
Macmillan/McGraw-Hill Reteach page 8 Commutative, associative, Identity Properties
Grade:3
Unit: Place Value and Multi-Digit Arithmetic
Lesson 5D, Pg. 1
www.Mathcafe.com 0-9 subtraction facts
C. Rigor: fluency, deep understanding, application and dual intensity
What are the learning experiences that provide for rigor? What are the learning experiences that provide for evidence of
the Math Practices? (Detailed Lesson Plan)
Warm Up
Ask the students to think of their favorite digit (0, 1, 2, 3, 4, 5, 6, 7, 8, 9,) and tell their partner/group why they picked
that number. Everyone (teacher and student) makes a number line (0-9) and the students record the student choices in
their math notebooks. Ask the students if they notice anything interesting about their favorite digits. Ask the student s
to put the digits in groups. Share with the class why you put the digits in groups.
Save the teacher copy of favorite numbers for display in the classroom.
Lesson
Show the students a number line such as 0-10. Cover a number (3) and ask the students what is three more than
the covered number? (6) Ask them how they know that is correct? What about if your favorite number is 9 can’t you
just make the covered number plus 3 equal nine. Why not?
Repeat with covering other numbers and asking them what the sum is if you added 3 (or another number) to the
starting number?
Repeat with a different number line 0-100 by tens. Add a (single digit or) multiple of ten to the starting number and
ask the students what the sum is.
Repeat with a number line 100 to 1000 by hundreds. Add a (single digit, multiple of 10 or) multiple of 100 to the
starting point. What is the sum?
Ask them if addition always makes the sum larger than the starting number?
Don’t tell them the answer. If they say “yes” the sum is always bigger than the starting number just continue.
Have student’s predict if subtraction always makes the difference smaller than the starting number.
Make a number line 0-10. Cover a staring number subtract a single digit and ask the students what is the difference.
Repeat with 0-100 by tens. Cover the starting number subtract a number ask the students what the difference is.
Make a number line 0-1000 by 100s. Cover the starting number subtract a number ask the student what the
difference is.
Again ask if subtraction always makes the difference smaller than the starting number. Hopefully they discover the
identity property of subtraction and addititon.
What a minute… we only tried it (addition and subtraction) horizontally. What if we tried vertically?
Repeat the procedure with a vertical number line.
Again ask if addition and subtraction always makes the result different from the start.
Independent practice with Themathworksheetsite.com number line.
Put a dot on the starting point and an X on the ending point.
1 You start with two legs and get zero more legs. How many legs do you have?
2 You have five fingers on your right hand and get zero more fingers. How many fingers on your right hand?
3 Four players are in the game. Zero players get out. How many players are still in the game?
4 Nine students are in the lunch line. Zero students leave the line. Now how many students are in the line?
5 Roger has sixty lizards. He gets zero lizards for his birthday. Now how many lizards does he have?
6 Roxanne has seventy sisters. She loses zero sisters. Now how many sisters does she have?
Grade:3
Unit: Place Value and Multi-Digit Arithmetic
Lesson 5D, Pg. 2
7 Ronald has four hundred facebook friends. He gets zero more friends. How many friends does he have?
8 Rose has three hundred facebook friends. He gets zero more friends. How many friends does she have
Closure
Talk to the students about doing math without a digit. If we didn’t have a ___ digit could we still do math? Would it be
harder or easier to do math without the zero digit. Find a short video to show how people did math a long time
ago/before they invented the zero digit.
Look on www.Learn360.org
Suggested Homework/Independent Practice
Ask three people to each tell you one thing that they add nothing to each day.
Record each answer on a number line. For example, I add nothing to the height of the flag pole each day.
10 feet
flag pole
30 feet
Ask three people to each tell you one thing that they subtract nothing from each day. For example I subtract nothing
from the height of the ball wall each day.
5 feet
ball wall
15 feet
Record each answer on a number line.
Hugo Guinan-Blaney
Grade:3
Unit: Place Value and Multi-Digit Arithmetic
Lesson 5D, Pg. 3