Open Line Hops Slides
Grade 2 Math Adventures Place Value & Number Line Hops
Open Line Hops!
Learn how to place numbers, make hops of 10 and 1, and count the distance between numbers!
1
Landmarks (0-100)
2
Spotting Numbers
3
Hopping Between Numbers
Step 1
Ruler vs. Open Number Line
Big Idea
Closed Number Line
Every single tick mark is already printed. It can feel crowded and tight!
0 5 10
Super Flexible!
Open Number Line
An empty line with no tick marks! You choose which numbers to put on it!
◀
▶
Empty and ready for your thinking!
Mathematician Secret: We only write the numbers that help us solve the problem!
Step 2
Use "Friendly Landmark" Numbers
The Power of 50
When placing 2-digit numbers from 0 to 100, start by marking the halfway point!
0 Start
HALFWAY!
50 Landmark
100 End
Numbers Less Than 50
(1 through 49 live on the left!)
Numbers Greater Than 50
(51 through 99 live on the right!)
Quick Check: Is the number 32 on the left or right of 50? Left side! (Less than 50)
Question
Where Does 45 Belong?
Think & Predict
On your whiteboard or with a partner: Where would you place 45 on this line?
0
?
?
50
?
100
Is 45 to the left or right of 50?
Is 45 close to 50 or far from 50?
Solution
Solved: 45 is Just Left of 50!
Answer Reveal
1
Compare to 50
45 is less than 50, so it stays on the left side of 50.
2
Check Distance
45 is only 5 steps away from 50! It is very close.
3
Place the Hop!
Place 45 just a little to the left of 50!
0
45
50
100
45 is close to 50 because 45 + 5 = 50!
Question 1
Which Letter Marks 75?
Student Vote
Look at the open number line below. Where does 75 belong?
0
A
50
B
C
100
Hold up your whiteboards: Is it A, B, or C?
Vote Now!
Solution 1
Letter B Marks 75!
Answer Reveal
0
A
≈ 20
50
B
75!
C
≈ 95
100
Why B? 75 is right in the middle between 50 and 100!
A is too small (<50) and C is too close to 100!
Question 2
Which Spot Marks 23?
Student Vote
Where does 23 land on this line?
Hint: Halfway to 50 is 25!
0
X
Y
50
Z
100
Write your choice: X, Y, or Z?
Decide Now!
Solution 2
Spot Y Marks 23!
Answer Reveal
0
X
≈ 8
Y
23!
50
Z
≈ 65
100
Why is Spot Y Correct?
Halfway between 0 and 50 is 25. Number 23 is just a tiny hop before 25!
Spot Y Wins!
Next Level
Open Lines Can Zoom In!
Any Start & End
You don't always have to start at 0! You can start and end at any friendly tens!
Goal: Place 58 on this zoomed-in line! Middle Landmark = 50
30
40
50
58
60
70
58 is just 2 hops behind 60! Zooming in makes placing numbers super clear.
Turn and Talk: Why is 58 closer to 60 than to 50? Only 2 away!
New Skill
Big Hops of 10 & Little Hops of 1
Frog Power!
On an open number line, we don't have to count by ones! We can make giant leaps of 10 and tiny steps of 1!
Giant Hop +10
Hops of Ten (+10)
Changes the tens digit by 1! The ones digit stays the exact same!
+10 34 44
Tiny Hop +1
Hops of One (+1)
Changes only the ones digit! Used for our precise little landings.
+1 44 45
Pro Strategy: Always hop your big tens first, then finish with your little ones!
Model
Let's Solve: 34 + 23
Decompose & Leap!
Starting Spot
34
Mark on the left side!
Hop the Tens
+20
2 big hops of 10!
Hop the Ones
+3
3 tiny hops of 1!
Open Number Line: Starting at 34 Goal: Where do we land?
+10 +10 +1 +1 +1 34 44 54 57
34 + 23 = 57!
34 ➔ 44 ➔ 54 ➔ 55 ➔ 56 ➔ 57
Your Turn
Start at 52: Hop +34!
Whiteboard Challenge
34
Solve on your open number line:
52 + 34 = ?
Hop Tens First, Then Ones!
Draw this on your whiteboard: How many tens? How many ones?
52 Start
hop...
hop...
?
Landing?
Make your hops! What number did you land on?
Work Together!
Solution
Hops Revealed: 52 + 34 = 86!
Answer Reveal
86
The 3 Tens & 4 Ones Plan:
3 Hops of 10 (+30) then 4 Hops of 1 (+4)
Landed on 86!
+10 +10 +10 +4 52 62 72 82 86
Count along:
52 ➔ 62 ➔ 72 ➔ 82 ➔ 86!
52 + 34 = 86
Frog Challenge
Where Did Freddy Frog Land?
Student Question
Freddy started at 47. He hopped +10, then +10, then +5!
+10 +10 +5 47 57 67 ?
Choice A 70
Choice B 72
Choice C 75
Solution
Freddy Landed on 72!
Answer Reveal
+10 +10 +5 47 57 67 72
Choice A 70
Winner! Choice B
72 67 + 5 = 72!
Choice C 75
Distance 1
How Many Hops from 30 to 70?
Count the Tens
Start at 30. Hop forward to 70. How many total hops?
30 Start
How many hops of 10?
70 Goal
Choice A 30
Choice B 40
Choice C 50
Solution
It Takes 40 Hops! (4 Tens)
Answer Reveal
+10 +10 +10 +10 30 40 50 60 70
Choice A 30
Winner! Choice B
40 4 hops of 10 = 40!
Choice C 50
Distance 2
How Many Hops from 25 to 48?
Tens & Ones
Hop from 25 to 48! How many tens and ones did you hop?
25 Start
Hop big tens... then little ones!
48 Goal
Choice A 13
Choice B 23
Choice C 33
Solution
23 Hops: 2 Tens + 3 Ones!
Answer Reveal
+10 +10 +3 25 35 45 48
Choice A 13
Winner! Choice B
23 +10 +10 +3 = 23 hops!
Choice C 33
Distance 3
How Many Hops from 41 to 76?
Student Whiteboards
Start at 41 and leap to 76! What is the total distance?
41 Start
3 hops of 10... plus how many ones?
76 Goal
Choice A 35
Choice B 25
Choice C 45
Solution
35 Hops: 3 Tens + 5 Ones!
Answer Reveal
+10 +10 +10 +5 41 51 61 71 76
Winner! Choice A
35 30 + 5 = 35 hops!
Choice B 25
Choice C 45
Distance 4
How Many Hops from 38 to 62?
Friendly 10s Strategy
Secret trick: Hop +2 to reach 40 first! How many hops to reach 62?
38 Start
40 Friendly 10!
62 Goal
Choice A 14
Choice B 34
Choice C 24
Solution
24 Hops Total! (+2, +20, +2)
Answer Reveal
+2 +20 +2 38 40 60 62
Choice A 14
Choice B 34
Winner! Choice C
24 2 + 20 + 2 = 24 hops!
Distance 5
How Many Hops from 54 to 89?
Fast Leap
Start at 54. Leap forward to 89. How many hops total?
54 Start
Hop from 54 to 84 (+30)... then +5 to 89!
89 Goal
Choice A 25
Choice B 35
Choice C 45
Solution
35 Hops Total! (+30, then +5)
Answer Reveal
+30 +5 54 84 89
Choice A 25
Winner! Choice B
35 30 + 5 = 35 hops!
Choice C 45
Grand Challenge
How Many Hops from 29 to 73?
Master Level
Hop +1 to reach 30! Then hop the tens to 70, and finish at 73!
29 Start
30 +1 Hop
73 Goal
Choice A 44
Choice B 54
Choice C 34
Solution
44 Hops Total! (+1, +40, +3)
Answer Reveal
+1 +40 +3 29 30 70 73
Winner! Choice A
44 1 + 40 + 3 = 44 hops!
Choice B 54
Choice C 34
Review
Your Number Line Superpowers!
Ready to Leap!
1
Pick Landmarks
Use friendly numbers like 0, 50, and 100 to estimate where numbers land.
50 is always in the middle!
2
Big Hops of 10
Leap fast by hopping tens first. Only the tens digit changes!
34 ➔ 44 ➔ 54 (+10)
3
Hop Between Numbers
Hop to friendly tens, leap across the distance, and count your total hops!
Smart leaps win!
Grab your whiteboards! You are Number Line Champions!
2nd Grade Number Masters
Open Line Leaps Practice Sheet
Grade 2 Math • Number Lines
Open Line Leaps!
Name:
Date:
1
Landmark Detectives: Place each number!
Tip: Mark 50 in the middle first!
A. Place 45 on the line: Is it closer to 0 or 50?
0
50
100
B. Place 80 on the line: Is it before 50 or after 50?
0
50
100
C. Place 22 on the line: Half of 50 is 25! Where is 22?
0
50
100
2
Draw the Hops & Find the Sum!
Hop big tens (+10), then little ones (+1)!
A. 36 + 23 = Break apart 23: 2 tens and 3 ones
36
B. 52 + 35 = Break apart 35: 3 tens and 5 ones
52
Remember: Big hops change the tens digit. Little hops change the ones digit! Page 1 of 2
Part 2 • Hop Distance Detectives
How Far is the Leap?
Name:
3
Count the Hops Between Numbers
Draw your hops and add them up!
A. How many hops to get from 30 to 70? Total Hops: ______
30
70
B. How many hops to get from 25 to 48? Total Hops: ______
25
48
C. Hop from 38 to 62! (Hint: Hop +2 to 40 first!) Total Hops: ______
38
62
4
Freddy Frog's Big Pond Leap
Freddy Frog sits on lily pad 44. He takes 3 giant hops of 10 and 4 tiny hops of 1. Where does Freddy land? Draw his hops on the open line below!
44
Number Sentence: 44 + _____ = _____ Freddy lands on: ________
Self-Check: How do you feel about open lines?
I need a little help
I can do it!
I can teach a friend!
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