Place Value Slides Lesson 1 • Number Sense Power
Foundations
Mastering Place Value:
Whole Numbers & Decimals
Every digit has a home, and every home has a specific value! Learn how to read, build, and compare numbers like a pro.
1
Name the Places
2
Find the Value
3
Compare & Order
Middle School Math Support Slide 1 of 5
Anchor Concept
The Place Value Chart
Notice the decimal point!
Hundreds 100
3
300
Tens 10
5
50
Ones 1
2
2
Dot "AND"
Decimal
Tenths 1/10 (0.1)
7
0.7
Hundredths 1/100 (0.01)
4
0.04
How to read this number: "Three hundred fifty-two AND seventy-four hundredths"
Rule: The decimal point separates WHOLE numbers (left) from PARTS (right). Slide 2 of 5
Key Distinction
Digit vs. Value
Position changes everything!
What is a DIGIT?
A digit is just the single symbol or number (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
In the number 46.8
The digit in the tenths place is 8
What is its VALUE?
The value is how much that digit is actually worth because of its place.
In the number 46.8
The value of that 8 is 8 tenths (0.8)
Remember: Decimals end in -THS (tenths, hundredths). They are small pieces less than 1 whole!
Place Value Power • Middle School Slide 3 of 5
Strategy
Comparing Decimals: Line Up the Dots!
Step-by-Step Method
1
Stack & Line Up
Put one number on top of the other with decimals matched up.
4.72
4.80
2
Fill Empty Spots
Add a "helper zero" at the end so both numbers have equal length.
4.72
4.80
3
Compare Left to Right
Start at the biggest place. Look for the first place that is different!
4 = 4 (Same)
7 is LESS than 8!
4.72 < 4.8
Common Trap: 4.72 looks bigger than 4.8 because 72 is bigger than 8. But 4.8 is really 4.80! 80 hundredths is greater than 72 hundredths!
Remember: More digits does NOT always mean a bigger number! Slide 4 of 5
Check Your Understanding
Show What You Know!
Classroom Challenge
A
Find the Place & Value
Look at the underlined digit:
63.95
What place is the 3 in? Ones Place
What is the value of 3? 3 (or 3 ones)
B
Compare with <, >, or =
Choose the correct symbol:
0.6
?
0.59
Helper Step: Turn 0.6 into 0.60.
Since 60 hundredths > 59 hundredths, 0.6 > 0.59!
Great job! Ready for the practice worksheet! Slide 5 of 5
Place Value Practice Sheet Lesson 1 • Student Practice
Place Value Power
Name:
Date:
Quick Reference Anchor
Hundreds
100
Tens
10
Ones
1
• DOT •
"and"
Tenths
0.1
Hundredths
0.01
1 Identify the Place and Value
Use the reference chart above to help.
54.72
Place: Tenths place
Value: 7 tenths or 0.7 (Example)
82.64
PLACE OF UNDERLINED DIGIT:
VALUE OF UNDERLINED DIGIT:
19.35
PLACE OF UNDERLINED DIGIT:
VALUE OF UNDERLINED DIGIT:
407.8
PLACE OF UNDERLINED DIGIT:
VALUE OF UNDERLINED DIGIT:
2 Match the Description to the Number
Write the letter of the correct matching number on each line.
A number with 6 in the tenths place.
A number with 9 in the hundredths place.
A number with 4 in the tens place.
A. 42.18
B. 15.63
C. 7.09
Turn over for decimal comparisons → Page 1 of 2
Lesson 1 • Student Practice
Comparing & Ordering Decimals
Strategy: Line up the dots!
Golden Rule: Write the numbers stacked on top of each other. Add a helper zero if one number is shorter! Example: 0.5 = 0.50.
3 Compare Using < , > , or =
Stack each pair in the work space, then write the correct symbol in the circle.
3.45
3.5
Work Space (Stack & Add Zero):
0.78
0.72
Work Space (Stack & Compare):
12.40
12.4
Work Space (Stack & Compare):
5.09
5.90
Work Space (Stack & Compare):
4 Real-World Runner Challenge
Three students ran the 50-meter dash in gym class. Here are their times:
Maya: 8.65 sec
Alex: 8.7 sec
Jordan: 8.59 sec
Who ran the fastest time? (Hint: The smallest time wins!)
How do you feel about place value and decimals today? (Circle one)
Integer Line Slides Lesson 2 • Number Sense Power
Integers & Lines
Integer Explorers:
Positive & Negative Numbers
Numbers don't stop at zero! Discover how numbers move in both directions on the number line and in our everyday world.
0
Zero Anchor
The center point
Positives
Right & Up
-
Negatives
Left & Down
Middle School Math Support Slide 1 of 5
Visual Model
The Number Line Map
Zero is neither positive nor negative
NEGATIVE NUMBERS (Left of 0) ZERO IS THE ANCHOR POSITIVE NUMBERS (Right of 0)
-5
-4
-3
-2
-1
0
+1
+2
+3
+4
+5
Negative Numbers (-)
Values LESS than zero. Move to the left or down.
Positive Numbers (+)
Values GREATER than zero. Move to the right or up.
Opposites are numbers that are the exact same distance from 0! (Like -4 and +4) Slide 2 of 5
Real-World Math
Where Do We See Integers?
Clue Words Matter!
Temperature
Above zero: Warm (+)Below zero: Freezing (-)
"8 degrees below zero"
-8°
Sea Level
Above sea level: Mountains (+)Below sea level: Deep ocean (-)
"A submarine at 40 ft deep"
-40 ft
Money & Bank
Deposit / Earn: Gain (+)Withdraw / Debt: Loss (-)
"Spent $15 on lunch"
-$15
Zero is sea level, 0° temperature, or an empty bank balance! Slide 3 of 5
Master Rule
Comparing Integers: The Right-Hand Rule
Don't get tricked!
Whichever number is further to the RIGHT is ALWAYS BIGGER!
On a vertical line: Whichever number is HIGHER UP is ALWAYS BIGGER!
The Trick Question
Which is greater: -2 or -8?
Students often think: "8 is bigger than 2, so -8 must be bigger!"
× False! Think about temperature or debt!
The True Reality
Integer Line Worksheet Lesson 2 • Student Practice
Integer Explorers
Name:
Date:
NEGATIVE (LESS) ZERO (ANCHOR) POSITIVE (GREATER)
-5
-4
-3
-2
-1
0
+1
+2
+3
+4
+5
1 Real-World Integer Detective
Read each real-world clue. Write the signed integer (like +4 or -4 ).
CLUE A 5 degrees below zero
CLUE B Earned $12 for chores
CLUE C Football loss of 6 yards
CLUE D Submarine at 30 ft depth
2 Plot the Integers
Draw a large dot on the number line for each letter location.
Point A = -3
Point B = +4
Point C = -1
Point D = 0
-5
-4
-3
-2
-1
0
+1
+2
+3
+4
+5
Turn over to compare & order integers → Page 1 of 2
Lesson 2 • Student Practice
Comparing & Ordering Integers
Reminder: Further RIGHT = BIGGER!
Tip: Find both numbers on the line. The number further to the RIGHT is always the greater number!
3 Compare Integers Using < , > , or =
-4
2
-1
-6
0
-3
-7
-7
4 Order from Least to Greatest
Start with the most negative number (furthest left).
Set 1: 4, -3, 0
Least to Greatest:
Set 2: -2, 5, -8, 1
Least to Greatest:
5 Winter Weather Report
A winter storm hit four cities overnight. Here were the recorded low temperatures:
Denver: -4°F
Chicago: -9°F
Dallas: 8°F
Seattle: 2°F
Which city was the COLDEST?
Which city was the WARMEST?
How confident do you feel locating and comparing integers?
😎 Super clear!
🙂 Getting there
🤔 Need practice
Middle School Mathematics • Integer Explorers Page 2 of 2
Absolute Value Slides Lesson 3 • Number Sense Power
Distance & Magnitude
Absolute Value Journey:
Distance From Zero!
Have you ever walked negative steps? Of course not! Learn why absolute value is always positive or zero.
Count Steps
Distance to 0
|x|
The Symbol
Straight bars
Always Positive
No negative distance
Middle School Math Support Slide 1 of 5
Core Concept
Absolute Value Means DISTANCE
How many jumps to reach Zero?
Frog starts at -4 (Jumps 4 steps right →)
TARGET: ZERO (0)
(← Jumps 4 steps left) Frog starts at +4
-5
-4
-3
-2
-1
0
+1
+2
+3
+4
+5
Distance from -4 to 0 is:
4 units
Distance from +4 to 0 is:
4 units
Both -4 and +4 are the EXACT SAME distance (4) away from zero!
Distance can never be negative. An odometer always counts forward! Slide 2 of 5
Math Notation
The Absolute Value Bars: | x |
Two straight vertical lines
How to Read the Bars
When you see two straight vertical lines around a number, it asks:
"How far is this number from zero?"
| -7 | read as: "the absolute value of -7"
| 7 | read as: "the absolute value of 7"
The "Car Wash" Analogy
Think of the absolute value bars like a car wash! Any number that goes inside comes out clean and positive.
| -9 | → 9
| 15 | → 15
| 0 | → 0
Zero is already at zero, so its distance is 0!
Never make a number negative when taking its absolute value! Slide 3 of 5
Real-World Magnitude
Sea Level Mystery: Who is Further?
Distance vs Direction
Scuba Diver Sam
Underwater explorer
Sam is swimming at an elevation of -35 ft .
DISTANCE FROM SEA LEVEL:
| -35 | = 35 ft
Seagull Bella
Sky glider
Bella is flying at an elevation of +35 ft .
DISTANCE FROM SEA LEVEL:
Absolute Value Worksheet Lesson 3 • Student Practice
Absolute Value Journey
Name:
Date:
Absolute Value = Distance from Zero Distance is ALWAYS positive!
NEGATIVE NUMBER EXAMPLE | -5 | = 5 (5 steps away from 0)
POSITIVE NUMBER EXAMPLE | +5 | = 5 (5 steps away from 0)
1 Count the Jumps to Zero
Count how many units each number is away from 0.
How far is -3 from 0?
Start at -3 → Jump to -2, -1, 0
| -3 | =
How far is +6 from 0?
Start at +6 → Jump backwards to 0
| +6 | =
2 Evaluate Each Absolute Value
Remember: distance is never negative! Write the answer in the box.
| -8 | =
| 14 | =
| -25 | =
| 0 | =
| -1 | =
| -100 | =
Turn over for comparison showdown → Page 1 of 2
Lesson 3 • Student Practice
Magnitude vs. Direction
Double check: Look for the bars!
Watch Out: -9 < 2, BUT with absolute value bars: |-9| = 9, so |-9| > 2!
3 Compare Using < , > , or =
First simplify any absolute value, then choose the correct symbol.
| -7 | (= 7)
4 (= 4)
| -5 | (= 5)
| 5 | (= 5)
-10 (no bars)
| -10 | (= 10)
| -3 | (= 3)
| -9 | (= 9)
4 Ocean & Mountain Adventure
A marine biologist is in a submarine at an elevation of -45 feet . A bird watcher is on a cliff at an elevation of +60 feet .
A. How far is the submarine from sea level (0)?
B. How far is the bird watcher from sea level (0)?
C. Who is further away from sea level? Explain how you know.
Sequence Wrap-Up: How confident do you feel with Number Sense overall?
🏆 Math Champion!
👍 Strong Progress
🔄 Need Review
Middle School Mathematics • Absolute Value Journey Page 2 of 2
Number Sense Assessment Cumulative Summative Assessment
Number Sense Showdown
Name:
Date:
Score ____ / 28
Directions: Read each question carefully. Write your answers clearly in the spaces provided. Part 1 & 2
1 Place Value & Decimals (8 pts)
2 pts each
1. Look at the number 64.38.
Which digit is in the tenths place?
Digit:
2. In the number 91.75:
What is the actual value of the digit 5?
Value:
3. COMPARE (<, >, =) 0.7 [ ] 0.68
4. COMPARE (<, >, =) 4.52 [ ] 4.6
2 Integers & Number Lines (10 pts)
2 pts each
5. WRITE THE INTEGER 8 degrees below zero
6. WRITE THE INTEGER Deposit of $20 in bank
7. Plot each point with a clear dot on the number line: Point A = -3 | Point B = +2
-4
-3
-2
-1
0
+1
+2
+3
+4
8. COMPARE (<, >, =) -6 [ ] 2
9. COMPARE (<, >, =) -1 [ ] -7
Turn page over for Absolute Value & Word Problem → Page 1 of 2
Summative Assessment • Part 3 & 4
Absolute Value & Real-World Math
Reminder: Distance is always positive!
3 Absolute Value & Distance (6 pts)
2 pts each
10. EVALUATE | -14 | =
11. EVALUATE | 23 | =
12. EVALUATE | 0 | =
13. COMPARE (<, >, =) | -9 | [ ] 5
14. COMPARE (<, >, =) | -8 | [ ] | 8 |
4 Real-World Application Challenge (4 pts)
2 pts each
Sea Level Expedition:
A diver is at an elevation of -28 feet (below sea level). A drone is flying at an elevation of +35 feet (above sea level). Sea level is at 0 feet .
A. Write an absolute value equation to show the diver's distance from sea level:
B. Which object is further away from sea level (0)?
Student Check-In: How did you do on this assessment?
😎 I did my best!
🙂 Felt pretty good
🤔 Need a review
Middle School Number Sense • Summative Assessment Page 2 of 2
Number Sense Scoring Guide Teacher Resource • Scoring Guide
Number Sense Assessment Key
Total Points 28 Points
Part 1: Place Value & Decimals (8 pts total • 2 pts each)
Standard: 6.NS.B
1. In 64.38, tenths place digit: 3
2. In 91.75, value of 5: 0.05 or 5 hundredths
3. 0.7 > 0.68 (0.70 > 0.68): >
4. 4.52 < 4.6 (4.52 < 4.60): <
Part 2: Integers & Number Lines (10 pts total • 2 pts each)
Standard: 6.NS.C.5, 6.NS.C.6
5. 8 degrees below zero: -8
6. Deposit of $20: +20 or 20
7. Number Line Plotting: Point A plotted exactly at -3; Point B plotted exactly at +2.
8. -6 < 2: < (positive is always greater)
9. -1 > -7: > (-1 is further right)
Part 3 & 4: Absolute Value & Application (10 pts total)
Standard: 6.NS.C.7
10. |-14| = 14
11. |23| = 23
12. |0| = 0
13. |-9| > 5 (since 9 > 5): >
14. |-8| = |8| (since 8 = 8): =
15A. Diver distance: |-28| = 28 ft (Accept 28 or |-28|=28).
15B. Further object: The drone (35 ft > 28 ft).
Turn page over for accommodations & error analysis → Page 1 of 2
Teacher Resource • Instructional Supports
Special Ed Accommodations & Rubric
Tier 2 / Tier 3 Guidance
Recommended IEP / 504 Testing Accommodations
Visual / Structural
Provide desktop color-coded place value charts, dry-erase number lines with sliders, and scratch paper folded into boxes.
Presentation & Pacing
Read word problems aloud (verbatim), chunk test into two 15-minute sittings (Page 1 on Day 1, Page 2 on Day 2), allow frequent breaks.
Response Format
Allow verbal explanations for #15B, scribe support for student writing, and acceptance of drawn number lines as valid scratch work.
Common Error Analysis & Quick Fixes
Error: Student says 4.52 > 4.6 because "52 is bigger than 6."
Remediation: Revisit the "Helper Zero" strategy. Have student append a zero to make 4.60, then compare using base-ten grid blocks.
