Single Hops Teacher Guide Lesson 1: Teacher Resource
Single Hops Teacher Guide
Focus: Adding 1-Digit Numbers to 2-Digit Numbers (Open & Closed Number Lines)
Grade 5 Self-Contained CRA Math Framework
Target Learning Objective
When given a two-digit plus one-digit equation, the student will locate the larger addend, draw sequential forward hops of 1, and identify the landing number as the sum with 80% accuracy across 3 consecutive probes.
Concrete & Visual Manipulatives
Desktop printed number line strip (20–50)
Dry-erase counter token or mini jumping toy
Colored highlighters (Green: start / Red: stop)
The 3-Step "Hop Forward" Routine
1
Find the Big Number
Circle the 2-digit number and put your finger or token on that mark.
2
Count & Hop (+1s)
Draw one arc for each hop while counting aloud: "+1, +2, +3..."
3
Circle the Landing
The line mark you land on is your final sum. Write it in the box.
Scripted Teacher Talk (Example: 34 + 5)
Model ("I Do"): "Watch my pencil. The equation is 34 + 5. 34 is the bigger number, so I start there. I place my green dot on 34. Now I look at the second number: 5. That tells me to make 5 small hops to the right because adding means getting bigger. Watch me hop: 1 (lands on 35), 2 (36), 3 (37), 4 (38), 5 (39). I landed right on 39! So, 34 + 5 = 39."
Guided Practice ("We Do"): "Now do 27 + 4 with me. Touch 27. How many hops will we take? Yes, 4 hops! Let's jump together: 1... 2... 3... 4. What number did your pencil land on?"
Anticipated Errors & Quick Corrections
Counting Start as Hop 1:
Student points to 34 and counts "1" before hopping. Correction: "Hop first, then say the number!"
Hopping Left (Subtle Reversal):
Student moves backward on line. Correction: Cue with green forward arrow: "Add means jump up/right!"
Number Line Leaps • Multi-Day Sequence Page 1 of 2: Instruction Guide
Lesson 1: Data Collection
Prompt Hierarchy & Progress Tracker
Daily Special Education IEP Monitoring Sheet
Student: ___________________
Date: ___________________
Prompt Level Coding Legend
IND (4)
Independent
Completes all hops and writes sum with no assistance.
VER (3)
Verbal Prompt
Needs verbal cue: "Where do we start? How many hops?"
GES (2)
Gestural Prompt
Teacher points to starting number or taps arc paths.
MOD (1)
Direct Model
Teacher models jump or provides hand-under-hand guide.
Daily Trial Tracking Log (2-Digit + 1-Digit Addition) Target: 4/5 Correct Independently
Trial Equation Locate Start Accurate Hops Correct Sum Prompt Level 1 24 + 3 + / − + / − + / − IND • VER • GES • MOD 2 41 + 6 + / − + / − + / − IND • VER • GES • MOD 3 35 + 4 + / − + / − + / − IND • VER • GES • MOD 4 52 + 5 + / − + / − + / − IND • VER • GES • MOD 5 63 + 7 + / − + / − + / − IND • VER • GES • MOD
Observational Notes & Accommodations Used
Number Line Leaps • Multi-Day Sequence Page 2 of 2: Progress Monitoring
Single Hops Practice Worksheet Math Practice • Level 1
Single Hops Practice Worksheet
Adding 1-Digit Numbers on a Number Line
Name:
Date:
My Steps: 1 Circle big number • 2 Put dot on line • 3 Hop forward & count
1
[ ] IND [ ] VER [ ] GES [ ] MOD
24 + 3 =
Start at 24. Trace the 3 hops.
+1 +1 +1
23
24
25
26
27
28
29
30
2
[ ] IND [ ] VER [ ] GES [ ] MOD
41 + 5 =
Put your dot on 41. Draw 5 hops forward (+1 each).
40
41
42
43
44
45
46
47
48
3
[ ] IND [ ] VER [ ] GES [ ] MOD
35 + 4 =
Put your dot on 35. Draw 4 hops forward.
34
35
36
37
38
39
40
41
42
Lesson 1: Guided Practice Page 1 of 2
Math Practice • Level 2
Independent Single Hops
Draw your start point and forward hops!
Name:
4
[ ] IND [ ] VER [ ] GES [ ] MOD
52 + 5 =
Start at 52. Hop forward 5 times.
51
52
53
54
55
56
57
58
59
5
[ ] IND [ ] VER [ ] GES [ ] MOD
63 + 7 =
Start at 63. Count carefully as you jump 7 times.
62
63
64
65
66
67
68
69
70
71
72
6
[ ] IND [ ] VER [ ] GES [ ] MOD
Sam had 45 stickers. His teacher gave him 4 more stickers. How many stickers does Sam have in all?
45 + 4 =
44
45
46
47
48
49
50
How did I do today?
Single Hops Answer Key Teacher Resource • Solutions
Single Hops Answer Key
Scoring Guide & Solutions for Lesson 1 Worksheet
Total Points: 6 pts Passing Criterion: 5/6 (83%)
1 24 + 3 = 27
Jump Steps: Starts at 24 → hops 25 (+1), 26 (+1), 27 (+1). Lands on 27 .
2 41 + 5 = 46
Jump Steps: Starts at 41 → hops 5 single units (42, 43, 44, 45, 46). Lands on 46 .
3 35 + 4 = 39
Jump Steps: Starts at 35 → hops 4 single units (36, 37, 38, 39). Lands on 39 .
4 52 + 5 = 57
Jump Steps: Starts at 52 → hops 5 single units (53, 54, 55, 56, 57). Lands on 57 .
5 63 + 7 = 70
Jump Steps: Crosses the ten benchmark: 63 → 64, 65, 66, 67, 68, 69, 70. Lands on 70 .
6 45 + 4 = 49
Word Problem: Identifies 45 as starting value, adds 4 hops → lands on 49 stickers .
IEP Scoring & Diagnostic Protocol
If Student Answers 1 Less (e.g. 26 instead of 27):
Check if student counted the starting tick as hop 1. Prompt: "Touch the start number, say 'ready', then jump and count '1'!"
If Student Needs Physical Prompting:
Use a physical tactile marker (foam frog or counting bear) to hop along the printed line before using a pencil.
Lesson 1: Answer Key • Number Line Leaps Page 1 of 1
Tens First Teacher Guide Lesson 2: Teacher Resource
Tens First Teacher Guide
Focus: Adding 2-Digit Numbers using Big Tens Leaps & Small Ones Hops
Grade 5 Self-Contained Strategy: Decompose & Leap
Lesson Objective
Given a two-digit plus two-digit addition problem (e.g., 32 + 24), the student will decompose the second addend into tens and ones, make large leaps of 10, then small hops of 1 on an open number line with 75% independence .
Color-Coded Visual Anchor
10 Blue Arc: Big Leap (+10)
1 Green Arc: Small Hop (+1)
The 4-Step Routine
1
Set First Number
Write the first number at the start of your number line.
2
Break Apart
Split second number into Tens & Ones boxes (e.g. 23 → 20 & 3).
3
Jump Tens (+10)
Make big leaps of 10. (e.g., 32 → 42 → 52).
4
Hop Ones (+1)
Take small hops for the ones. Circle your landing sum.
Scripted Modeling Routine (Example: 35 + 23)
Step 1 (Anchor): "We are adding 35 + 23. Let's start with 35. I write 35 on the left end of my open number line."
Step 2 (Decompose): "Look at 23. How many tens? 2 tens, which is 20! How many ones? 3 ones. So 23 is two tens and three ones."
Step 3 (Leap Tens): "Instead of hopping 23 tiny times, we make 2 BIG LEAPS of 10. Watch: 35 plus 10 is 45. 45 plus 10 is 55! That was so fast!"
Step 4 (Hop Ones): "Now we just need 3 small hops of 1: 56, 57, 58. We landed on 58! So 35 + 23 = 58."
Error Handling Routine
Error: Changing the ones place when leaping 10 (e.g., student jumps from 35 to 40 instead of 45).
Correction: Point to the tens digit. "When we leap by 10, only the front tens number changes. 3 tens becomes 4 tens. The 5 ones stay exactly the same: 35 → 45!"
Number Line Leaps • Multi-Day Sequence Page 1 of 2: Instruction Guide
Lesson 2: Data Collection
Tens First Progress Log
Special Education Independence & Strategy Tracker
Student: ___________________
Observer: ___________________
4 Key Observable Behaviors
1. Decomposing: Correctly identifies number of tens & ones before drawing line.
2. Size Discrimination: Draws visibly larger arcs for +10 and smaller arcs for +1.
Tens First Practice Worksheet Math Practice • Level 2
Tens First Practice Worksheet
Adding 2-Digit Numbers: Jump Tens, Then Hop Ones
Name:
Date:
Strategy: 1 Break second number into Tens & Ones • 2 Big leaps of 10 • 3 Small hops of 1
1
[ ] IND [ ] VER [ ] GES [ ] MOD
32 + 23 =
Break 23: 2 Tens (+10, +10) + 3 Ones (+1, +1, +1)
+10 Leap +10 Leap +1, +1, +1
32
42
52
55
2
[ ] IND [ ] VER [ ] GES [ ] MOD
45 + 24 =
Break 24:
2 tens (20)
4 ones (4)
Start at 45. Jump 2 tens (+10, +10), then hop 4 ones.
45
→
Lesson 2: Guided Practice Page 1 of 2
Math Practice • Level 2
Independent Tens & Ones
Decompose the second number and jump forward on the line.
Name:
3
[ ] IND [ ] VER [ ] GES [ ] MOD
26 + 32 =
Break 32: tens + ones
26
→
4
[ ] IND [ ] VER [ ] GES [ ] MOD
53 + 24 =
Break 24: tens + ones
53
→
5
[ ] IND [ ] VER [ ] GES [ ] MOD
Maya has 34 toy cars. Leo brings 25 toy cars. How many toy cars do they have altogether?
34 + 25 =
Break 25: tens + ones
34
→
Self Check:
I jumped my tens first. I counted all my ones.
Lesson 2: Independent Practice Page 2 of 2
Tens First Answer Key Teacher Resource • Solutions
Tens First Answer Key
Scoring Guide & Solutions for Lesson 2 Worksheet
Total Items: 5 items Passing Criterion: 4/5 (80%)
1 32 + 23 = 55
Decomposition: 20 + 3
Jumps: Start at 32 → leap +10 (42) → leap +10 (52) → hop +1, +1, +1 (53, 54, 55). Lands on 55 .
2 45 + 24 = 69
Decomposition: 20 + 4
Jumps: Start at 45 → leap +10 (55) → leap +10 (65) → hop 4 ones (66, 67, 68, 69). Lands on 69 .
3 26 + 32 = 58
Decomposition: 30 + 2
Jumps: Start at 26 → leap 3 tens: 36, 46, 56 → hop 2 ones: 57, 58. Lands on 58 .
4 53 + 24 = 77
Decomposition: 20 + 4
Jumps: Start at 53 → leap 2 tens: 63, 73 → hop 4 ones: 74, 75, 76, 77. Lands on 77 .
5 34 + 25 = 59
Decomposition: 20 + 5
Word Problem: Start at 34 → leap 2 tens (44, 54) → hop 5 ones (55, 56, 57, 58, 59). Total: 59 toy cars .
Strategy Mastery Scoring Scale
Mastery (4-5 items) Decomposes tens/ones and leaps tens accurately with IND or VER prompts only.
Approaching (3 items) Leaps tens accurately but loses count of ones; needs gestural prompt on ticks.
Emerging (0-2 items) Attempts to hop all numbers by ones. Reintroduce base-10 block physical track.
Lesson 2: Answer Key • Number Line Leaps Page 1 of 1
Double Digit Practice Worksheet Math Practice • Level 3
Double Digit Practice Worksheet
Mastering Open Number Lines with Tens & Ones
Name:
Date:
Pro Tip: Start with the biggest number • Leap tens (+10) • Hop ones (+1) to your answer Always hop forward!
1
[ ] IND [ ] VER [ ] GES [ ] MOD
38 + 25 =
Break 25: 2 Tens (20) + 5 Ones (5)
Start at 38. Leap two tens (+10, +10), then hop 5 ones.
38
→
2
[ ] IND [ ] VER [ ] GES [ ] MOD
47 + 34 =
Break 34:
3 tens
4 ones
Start at 47. Leap 3 tens, then hop 4 ones.
47
→
Lesson 3: Guided Mastery Page 1 of 2
Math Practice • Level 3
Open Line Challenges
Draw your own starting point and leaps!
Name:
3
[ ] IND [ ] VER [ ] GES [ ] MOD
56 + 23 =
Break 23: 2 tens and 3 ones
56
→
4
[ ] IND [ ] VER [ ] GES [ ] MOD
64 + 28 =
Break 28: 2 tens and 8 ones
64
→
5
[ ] IND [ ] VER [ ] GES [ ] MOD
The school library had 48 science books. The librarian bought 33 new science books. How many science books are there now?
48 + 33 =
Break 33 = 30 + 3
48
→
Goal Reflection:
I can use an open number line! I am ready for the progress check.
Lesson 3: Independent Practice Page 2 of 2
Addition Progress Monitoring Tracker IEP Progress Monitoring • Probe A
Addition Progress Monitoring Tracker
Standards-Based Assessment of Number Line Addition • 4 Target Items
Student: ___________________
Date: ___________________
Evaluator: ___________________
1 2-Digit + 1-Digit 54 + 5 =
Prompt: [ ] IND [ ] VER [ ] GES [ ] MOD • Accuracy: [ ] + [ ] −
54 →
2 Tens & Ones Leaps 43 + 32 =
Prompt: [ ] IND [ ] VER [ ] GES [ ] MOD • Accuracy: [ ] + [ ] −
43 →
3 Crossing Tens 37 + 26 =
Prompt: [ ] IND [ ] VER [ ] GES [ ] MOD • Accuracy: [ ] + [ ] −
37 →
4 Word Problem
Prompt: [ ] IND [ ] VER [ ] GES [ ] MOD • Accuracy: [ ] + [ ] −
David read 52 pages on Saturday and 27 pages on Sunday. How many pages did he read in all?
52 + 27 =
52 →
Probe Total Score: / 4 Correct Percentage: %
Independence Level:
Progress Monitoring • Addition Probe Page 1 of 2
Special Education IEP Tool
Multi-Trial Progress Log
Longitudinal Accuracy, Strategy Use & Independence Tracking
Student ID: ___________________
Grade: 5 • Self-Contained
Sample Standardized IEP Goal Statement
"By September 2027, when presented with two-digit addition equations, the student will independently decompose addends and utilize an open number line (jumping tens and hopping ones) to solve equations with at least 80% accuracy across 4 consecutive weekly probes at the Independent (IND) or Verbal (VER) prompt level."
Weekly Progress Monitoring Data Log Target Mastery: 80%+ with IND/VER
Trial Date Raw Score % Accuracy Dominant Prompt Instructional Action / Notes 1 ____/____ ___ / 4 ____% IND • VER • GES • MOD Baseline probe administered. 2 ____/____
Double Digit Answer Key Teacher Resource • Solutions
Double Digit Answer Key
Solutions & Scoring Criteria for Lesson 3 Worksheet & Progress Probe
Mastery Benchmark: 80% Prompt: IND or VER
Lesson 3 Practice Worksheet Solutions
1. 38 + 25 = 63
Start at 38 → leap +20 (48, 58) → hop +5 (59, 60, 61, 62, 63). Lands on 63 .
2. 47 + 34 = 81
Start at 47 → leap +30 (57, 67, 77) → hop +4 (78, 79, 80, 81). Lands on 81 .
3. 56 + 23 = 79
Start at 56 → leap +20 (66, 76) → hop +3 (77, 78, 79). Lands on 79 .
4. 64 + 28 = 92
Start at 64 → leap +20 (74, 84) → hop +8 (to 92). Lands on 92 .
5. 48 + 33 = 81
Word Problem: Start at 48 → leap +30 (78) → hop +3 (81). Total: 81 science books .
Progress Monitoring Probe A Solutions
Probe 1: 54 + 5 59
Start 54 → 5 single hops: 55, 56, 57, 58, 59.
Probe 2: 43 + 32 75
Start 43 → leap 3 tens: 53, 63, 73 → 2 hops: 74, 75.
Probe 3: 37 + 26 63
Start 37 → leap 2 tens: 47, 57 → 6 hops to 63.
Probe 4: 52 + 27 79
Start 52 → leap 2 tens: 62, 72 → 7 hops: 79 pages.
IEP Reporting Conversion: 4/4 = 100% (Mastered) • 3/4 = 75% (Target Progressing) • 2/4 = 50% (Instructional Level) • 1/4 = 25% (Reteach Required)
Lesson 3: Answer Key • Number Line Leaps Page 1 of 1
