A cohesive 3rd-grade mathematics sequence focusing on foundational NBT and NF standards. Students develop deep conceptual understanding through visual models, interactive tasks, and targeted intervention strategies.
Solve 458 + 274 using expanded form. Hint: You will need to regroup!
458 →
400 + 50 + 8
+ 274 →
200 + 70 + 4
Raw Sum →
Final regrouped answer:
Case #4: Word Problem Application
The Mystery of the Missing Artifacts: A museum has 524 Roman coins on display. The chief curator removes 182 of them for an exclusive study session. How many coins remain on display?
1. Estimate First
Round to nearest Ten:
2. Decompose to Solve
Decompose 524 - 182:
Show your final subtraction difference below:
coins
Case Verification Check
How can you use addition to verify your Roman coins difference? Write out the inverse operation check that proves your subtraction is correct:
Distance traveled: 1/4 + 1/4 + 1/4 = 3/4 of the destination!
Always count the intervals (jumps), not the ticks, to find distance! Slide 5 of 10
Precision Landing
NC.3.NF.2
Navigating Sixths and Eighths
As the denominator gets larger, the segments get smaller because we divide the same space into more parts!
The 6-Segment Runway (Sixths)
3/6
Three jumps of 1/6 lands exactly on 3/6 (which is half the runway!).
The 8-Segment Runway (Eighths)
5/8
Five jumps of 1/8 lands exactly on 5/8.
Compare 3/6 and 5/8. Which landing point is further down the runway? Slide 6 of 10
Co-Pilot Mission
NC.3.NF.2
Let's Co-Pilot! Partition a Runway
With your partner, solve this challenge: Partition a runway into 6 equal parts and locate 4/6.
Active Flight Plan
0
? ? ? ? ?
1
Question 1:
How many tick marks do we need to draw?
Question 2:
How many unit jumps to reach 4/6?
Remember, 6 parts means we draw exactly 5 ticks between 0 and 1! Slide 7 of 10
Flight Danger Zone
NC.3.NF.2
Danger: Unequal Intervals!
If the spaces between ticks are not equal sizes, the landing coordinates are invalid!
BROKEN LANDING (Unequal)
unequal!
The intervals are different sizes. These do NOT represent a true fraction!
SAFE LANDING (Equal)
All spaces are exactly the same. Each segment represents a perfect 1/4.
Check twice: Always measure your intervals before plotting fractions! Slide 8 of 10
Advanced Flight Paths
NC.3.NF.2.b
Can a Fraction go Beyond 1?
Yes! If a flight path continues to airport 2, our coordinates can keep climbing.
Let's plot 5/4 on an extended runway!
0
1/4
2/4
3/4
1 (4/4)
5/4
6/4
7/4
2 (8/4)
5/4 means we have 5 unit parts of size 1/4. It is greater than 1 whole runway!
Keep counting standard unit intervals even after passing 1! Slide 9 of 10
Flight Certified
NC.3.NF.2
Pilot Certified!
You are now equipped to navigate any fraction runway in the sky:
1. Define Limits
Locate start (0) and destination (1)
2. Partition
Split into equal distance segments
3. Count Intervals
Count jumps from left to right
4. Plot Target
Mark the point with a secure dot
Unlock your pilot navigation journals to begin flight practice! Slide 10 of 10
3/2
EXTENDED RUNWAY F
0
1st half
1 (2/2)
2nd half
2 (4/2)
Mission #7: Navigator Story Problem
Aviation Navigation: A helicopter flight path starts at 0 miles and ends at the main landing pad at 1 mile. The emergency helipads are placed exactly at every 1/3 of a mile interval.
A helicopter is forced to land at an emergency pad located at 2/3 of a mile. Draw the helicopter flight line, partition it into thirds, and place a dot where the emergency landing occurred.
Draw helicopter path & plot 2/3 here:
0
1
Pilot Certification Question:
In your own words, explain how you know that the point 4/4 on a runway number line is exactly equal to the whole number 1:
RUNWAY RADARS • PAGE 3 NC.3.NF.2
Runway Radars Task Cards
Flight Log Worksheet
10 MIN
Debrief & Certification
Discuss Slide 9 (beyond 1 whole). Collect Page 3 of the worksheet as graduation proof for the cadet flight license!
4. Center Organization Guide
Setup instructions for Task Cards station:
Print and laminate the 8 pilot flight cards.
Provide standard rulers or plastic faction bars so students can measure segments.
Provide student co-pilots with scratch paper or dry-erase boards to draw their partitioned runway lines.
Use Card 4 (Error Analysis) as a talking point for student partner pairs.
TEACHER GUIDE • PAGE 2 RUNWAY RADARS
Runway Radars Answer Keys
Teacher Resource • Official Keys
ANSWER KEYS
Practice Sheet Answer Key
Page 1 (Guided Log)
Runway A: Draw 1 tick mark exactly in the middle of 0 and 1. Plot a dot on it and label it 1/2.
Runway B: Draw 3 equal-distance ticks. Label them 1/4, 2/4, 3/4 from left to right. Plot dots on each.
Page 2 (Independent)
Runway C Dot: 3/6 (which is equivalent to 1/2).
Runway D (Thirds): Draw 2 ticks. Plot dot on the 2nd tick (2/3).
Runway E (Eighths): Draw 7 ticks. Plot dot on the 5th tick (5/8).
Page 3 (Navigator)
Extended Runway F: Draw 1 tick in the middle of 0 and 1 (1/2), and 1 tick in the middle of 1 and 2 (3/2). Plot a dot at 3/2.
Story problem: Draw 2 ticks. Plot dot at 2/3.
Cert Question: 4/4 means you counted 4 intervals of size 1/4. This covers the entire distance from 0 to 1.
Task Cards Answer Key
Card 1 (Partition): Draw 5 tick marks.
Card 2 (Identify): Star is at 2/3.
Card 3 (Unit): Each unit segment is 1/8.
Card 4 (Error): Fractions must represent equal parts. If intervals are unequal, the coordinates do not show real mathematical fraction measurements.
Card 5 (Beyond 1): Count 5 jumps from 0.
Card 6 (Plot): Star must be placed on the middle tick [2/4].
Card 7 (Concept): Counting spaces measures the distance traveled. Counting ticks can confuse kids (since the 0 tick isn't an interval distance).
Card 8 (Whole): Plotting 6/6 lands exactly on the whole number 1.
Slide 7 Partner Challenge Key:
Question 1: Draw exactly 5 tick marks between 0 and 1.
Question 2: Count 4 equal jumps from 0 to locate the point 4/6.
