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Math Goal Mastery

A targeted sequence of progress monitoring assessments and evaluation guides designed to measure and document key IEP mathematics benchmarks, including multi-step word problems and multi-digit operations.

JDJenny Daniels

Problem Detectives

A targeted assessment and progress monitoring unit focused on multi-step word problem analysis. Students develop skills in determining what is being asked, filtering relevant details from distractors, and selecting sequential operations to solve real-world problems.

Division Masters

A progress monitoring lesson focusing on multi-digit whole number division with dividends up to four digits. Students demonstrate conceptual understanding and computational fluency using visual models, partial quotients, or the standard algorithm.

Math Goal Mastery

A targeted sequence of progress monitoring assessments and evaluation guides designed to measure and document key IEP mathematics benchmarks, including multi-step word problems and multi-digit operations.

JDJenny Daniels

Problem Detective Assessment

Problem Detective: Multi-Step Word Problems

IEP Progress Assessment • Target Date: October 2026 • Goal Mastery Monitoring

Cases 1 – 3 of 6

Student Name:

Date:

Total Score: / 24

CASE #1: Book Fair Budget

1. Question: [ ] 2. Info: [ ] 3. Operation: [ ] 4. Solve: [ ]

Leo brought $35 to the school book fair. The fair had 140 books on display. Leo bought 3 graphic novels that cost $8 each, and he also bought a bookmark for $2. How much money did Leo have left?

1. What is the question asking you to find?

2. Relevant Information vs. Extra Info

Needed numbers:

Extra/distractor number to ignore:

3. Select Operations & Plan

Step 1: [ + − × ÷ ] Step 2: [ + − × ÷ ]

4. Show Work & Solution

Answer:

CASE #2: Apple Orchard Harvest

1. Question: [ ] 2. Info: [ ] 3. Operation: [ ] 4. Solve: [ ]

Maya picked 45 red apples and 39 green apples on Saturday. Her brother picked apples for 3 hours. Maya packed all of her picked apples equally into 7 gift baskets. How many apples did Maya put in each basket?

1. What is the question asking you to find?

2. Relevant Information vs. Extra Info

Needed numbers:

Extra/distractor number to ignore:

3. Select Operations & Plan

Step 1: [ + − × ÷ ] Step 2: [ + − × ÷ ]

4. Show Work & Solution

Answer:

CASE #3: Bakery Muffin Boxes

1. Question: [ ] 2. Info: [ ] 3. Operation: [ ] 4. Solve: [ ]

Chef Marco baked 80 blueberry muffins in an oven set at 375°F. During the morning rush, customers bought 32 muffins. Marco packed all the remaining muffins into bakery boxes that hold 6 muffins each. How many boxes did Marco fill?

1. What is the question asking you to find?

2. Relevant Information vs. Extra Info

Needed numbers:

Extra/distractor number to ignore:

3. Select Operations & Plan

Step 1: [ + − × ÷ ] Step 2: [ + − × ÷ ]

4. Show Work & Solution

Answer:

PART 2

Problem Detective: Multi-Step Word Problems

Student: Cases 4 – 6 of 6

CASE #4: Soccer Car Wash Fundraiser

1. Question: [ ] 2. Info: [ ] 3. Operation: [ ] 4. Solve: [ ]

The soccer team won their match 4 to 1 on Saturday. To buy new practice jerseys, 6 players each washed 5 cars. They charged $8 for each car washed. Then, the coach donated $40 to their fund. What was the total amount of money raised?

1. What is the question asking you to find?

2. Relevant Information vs. Extra Info

Needed numbers:

Extra/distractor info:

3. Select Operations & Plan

Step 1: [ + − × ÷ ] Step 2: [ + − × ÷ ]

4. Show Work & Solution

Answer:

CASE #5: Art Studio Markers

1. Question: [ ] 2. Info: [ ] 3. Operation: [ ] 4. Solve: [ ]

In art room 14, Ms. Rivera had 96 new colored markers. She distributed them equally across 8 student tables. At Table 2, students discovered that 3 markers were completely dried out and had to be thrown away. How many usable markers remained at Table 2?

1. What is the question asking you to find?

2. Relevant Information vs. Extra Info

Needed numbers:

Extra/distractor number to ignore:

3. Select Operations & Plan

Step 1: [ + − × ÷ ] Step 2: [ + − × ÷ ]

4. Show Work & Solution

Answer:

CASE #6: Museum Field Trip Bus

1. Question: [ ] 2. Info: [ ] 3. Operation: [ ] 4. Solve: [ ]

The 5th grade classes are traveling 18 miles to the science museum. Class A has 24 students, Class B has 27 students, and 5 parent chaperones are joining them. The chartered bus has 64 passenger seats. How many empty seats will be left on the bus?

1. What is the question asking you to find?

2. Relevant Information vs. Extra Info

Needed numbers:

Extra/distractor number to ignore:

3. Select Operations & Plan

Step 1: [ + − × ÷ ] Step 2: [ + − × ÷ ]

4. Show Work & Solution

Answer:

IEP Progress Summary Checklist

Target Criterion: 80% accuracy across 3 consecutive trials

Determine Goal: ___ / 6

Identify Info: ___ / 6

Select Ops: ___ / 6

Calculation: ___ / 6

Problem Detective Answer Key

Problem Detective: Teacher Answer Key

IEP Evaluation Guide

Target Goal: Read & analyze multi-step word problems (Question, Relevant Info, Operations)

Cases 1 – 3 Answers

1. Question: 1 pt

2. Filter Info: 1 pt

3. Operation Plan: 1 pt

4. Correct Solve: 1 pt

CASE #1: Book Fair Budget — Exemplar Key Total Points: 4 / 4

Leo brought $35. Display had 140 books. Leo bought 3 novels at $8 each and a bookmark for $2. How much left?

1. What is being asked: (1 pt)

The amount of money Leo has remaining after purchasing 3 graphic novels and 1 bookmark.

2. Relevant Info vs. Distractor: (1 pt)

Needed: $35 starting, 3 books, $8 each, $2 bookmark.
Distractor: 140 books on display (not needed).

3. Operations & Plan: (1 pt)

Step 1: Multiplication (\(\times\)) and Addition (\(+\)) to find total spent.
Step 2: Subtraction (\(-\)) from starting total.

4. Calculation & Final Solution: (1 pt)

3 × $8 = $24
$24 + $2 = $26 total spent
$35 − $26 = $9

Correct Answer: $9 left

CASE #2: Apple Orchard Harvest — Exemplar Key Total Points: 4 / 4

Maya picked 45 red and 39 green apples. Brother picked for 3 hours. Maya packed all into 7 baskets.

1. What is being asked: (1 pt)

The number of apples packed into each gift basket.

2. Relevant Info vs. Distractor: (1 pt)

Needed: 45 red apples, 39 green apples, 7 baskets.
Distractor: 3 hours spent by brother (not needed).

3. Operations & Plan: (1 pt)

Step 1: Addition (\(+\)) to find total apples collected.
Step 2: Division (\(\div\)) to partition into 7 baskets.

4. Calculation & Final Solution: (1 pt)

45 + 39 = 84 total apples
84 ÷ 7 = 12

Correct Answer: 12 apples per basket

CASE #3: Bakery Muffin Boxes — Exemplar Key Total Points: 4 / 4

Chef Marco baked 80 muffins at 375°F. Sold 32 in morning. Packed remaining muffins into boxes of 6.

1. What is being asked: (1 pt)

How many boxes Chef Marco filled with the leftover muffins.

2. Relevant Info vs. Distractor: (1 pt)

Needed: 80 baked, 32 sold, 6 per box. Distractor: 375°F oven temperature (not needed).

Division Mastery Assessment

Multi-Digit Division Mastery Assessment

IEP Progress Assessment • Target Date: October 2026 • Dividends up to 4 Digits

Problems 1 – 3 of 6

Student Name:

Date:

Total Score: / 24

Problem 1 582 ÷ 6

Method used: [ ] Area Model [ ] Partial Quotients [ ] Algorithm

Show your work using a visual model or standard algorithm: Align digits by place value

Quotient: Remainder:

Check with ×:

Problem 2 3,248 ÷ 4 4-digit dividend

Method used: [ ] Area Model [ ] Partial Quotients [ ] Algorithm

Show your work using a visual model or standard algorithm: Watch for zeros in the quotient

Quotient: Remainder:

Check with ×:

Problem 3 4,595 ÷ 7 With remainder

Method used: [ ] Area Model [ ] Partial Quotients [ ] Algorithm

Show your work using a visual model or standard algorithm: Ensure remainder is less than divisor

Quotient: Remainder:

Check with ×:

PART 2

Multi-Digit Division Mastery Assessment

Student: Problems 4 – 6 of 6

Problem 4 1,728 ÷ 12 2-digit divisor

Method used: [ ] Area Model [ ] Partial Quotients [ ] Algorithm

Show your work using a visual model or standard algorithm: Tip: List multiples of 12 (12, 24, 36, 48...)

Quotient: Remainder:

Check with ×:

Problem 5 3,548 ÷ 24 2-digit divisor with remainder

Method used: [ ] Area Model [ ] Partial Quotients [ ] Algorithm

Show your work using a visual model or standard algorithm: Remainder must be less than 24

Quotient: Remainder:

Check with ×:

Problem 6 Real-World Application

Method: [ ] Model [ ] Algorithm

A food distribution warehouse received 2,160 cans of soup. Workers packed the cans equally into 18 large crates to ship to neighborhood shelters. How many cans of soup were placed in each crate?

Answer with unit label:

Check with ×:

Multi-Digit Division IEP Progress Tracker

Target Criterion: 80% accuracy (19+ / 24 total points)

Visual Model: ___ / 6

Standard Alg: ___ / 6

Remainders: ___ / 6

Verification: ___ / 6

Division Mastery Answer Key

Multi-Digit Division: Teacher Answer Key

IEP Scoring & Diagnostic Guide

Goal: Multi-digit division with up to 4-digit dividends using visual models, partial quotients, or standard algorithm.

Problems 1 – 3 Answers

Model / Setup: 1 pt

Place Value / Steps: 1 pt

Correct Quotient: 1 pt

Check / Verification: 1 pt

Problem 1 Key 582 ÷ 6 = 97 (Remainder: 0)

4 / 4 Points

Method A: Partial Quotients / Area Model

6 × 90 = 540 → 582 − 540 = 42
6 × 7 = 42 → 42 − 42 = 0
Sum of parts: 90 + 7 = 97

Area Model Dimensions: Width 6, sub-lengths 90 and 7; sub-areas 540 and 42.

Method B: Standard Algorithm

58 ÷ 6 = 9 (tens), 9 × 6 = 54
58 − 54 = 4; bring down 2 → 42
42 ÷ 6 = 7 (ones), 7 × 6 = 42 (rem 0)

Check: 97 × 6 = 582 ✓

Common IEP Misconception: Forgetting that 58 represents 58 tens, resulting in misaligned quotient digits.

Problem 2 Key 3,248 ÷ 4 = 812 (Remainder: 0)

4 / 4 Points

Method A: Partial Quotients / Area Model

4 × 800 = 3,200 → Remainder: 48
4 × 10 = 40 → Remainder: 8
4 × 2 = 8 → Remainder: 0
Sum: 800 + 10 + 2 = 812

Method B: Standard Algorithm

32 ÷ 4 = 8 (hundreds), 32 − 32 = 0
Bring down 4 → 4 ÷ 4 = 1 (ten)
Bring down 8 → 8 ÷ 4 = 2 (ones)

Check: 812 × 4 = 3,248 ✓

IEP Diagnostic Check: Ensure student correctly recognizes place value in 4-digit dividends (8 in hundreds place = 800).

Problem 3 Key 4,595 ÷ 7 = 656 R 3

4 / 4 Points

Method A: Partial Quotients

7 × 600 = 4,200 → 4,595 − 4,200 = 395
7 × 50 = 350 → 395 − 350 = 45
7 × 6 = 42 → 45 − 42 = 3 (Remainder)
Quotient: 600 + 50 + 6 = 656 R 3

Method B: Standard Algorithm

45 ÷ 7 = 6 (hundreds), 45 − 42 = 3
Bring down 9 → 39 ÷ 7 = 5 (tens), 39 − 35 = 4
Bring down 5 → 45 ÷ 7 = 6 (ones), 45 − 42 = 3

Check: (656 × 7) + 3 = 4,592 + 3 = 4,595 ✓

Remainder Rule: Verify student confirms remainder (3) is strictly smaller than the divisor (7).

PART 2

Multi-Digit Division: Teacher Answer Key & Rubric

3. Operations & Plan: (1 pt)

Step 1: Subtraction (\(-\)) to find remaining muffins.
Step 2: Division (\(\div\)) by 6 muffins per box.

4. Calculation & Final Solution: (1 pt)

80 − 32 = 48 remaining muffins
48 ÷ 6 = 8

Correct Answer: 8 boxes filled

PART 2

Teacher Answer Key & IEP Scoring Decision Matrix

Cases 4 – 6 • Rubric Breakdown

CASE #4: Soccer Car Wash Fundraiser Total Points: 4 / 4

Won 4 to 1. 6 players washed 5 cars each at $8/car. Coach donated $40. Total money raised?

1. Question & 2. Info:

Target: Total money raised for the soccer team.
Needed: 6 players × 5 cars, $8/car, $40 donation.
Distractor: Game score 4 to 1.

3. Operations & 4. Solution:

6 × 5 = 30 cars total
30 × $8 = $240 from car wash
$240 + $40 = $280 total raised

CASE #5: Art Studio Markers Total Points: 4 / 4

Room 14. 96 markers shared among 8 tables. Table 2 had 3 dried markers discarded. Remaining usable?

1. Question & 2. Info:

Target: Usable markers remaining at Table 2.
Needed: 96 markers, 8 tables, 3 dried out.
Distractor: Room number 14.

3. Operations & 4. Solution:

96 ÷ 8 = 12 markers per table
12 − 3 = 9 usable markers
Answer: 9 usable markers

CASE #6: Museum Field Trip Bus Total Points: 4 / 4

Traveling 18 miles. 24 students (Class A), 27 (Class B), 5 chaperones. 64 bus seats. Empty seats left?

1. Question & 2. Info:

Target: Number of empty seats left on bus.
Needed: 24 + 27 students, 5 adults, 64 seats.
Distractor: 18 miles distance.

3. Operations & 4. Solution:

24 + 27 + 5 = 56 passengers total
64 − 56 = 8 empty seats
Answer: 8 empty seats

IEP Progress Decision Matrix (Goal Target: 80% / 19+ pts) Scoring: 1 pt per component × 4 components × 6 cases = 24 pts

19 – 24 pts (80% – 100%) GOAL MASTERED

Demonstrates consistent independence in identifying targets, isolating distractors, and selecting multi-step operations.

15 – 18 pts (60% – 79%) PROGRESSING

Understands target question and operations, but occasionally incorporates distractor numbers or miscalculates multi-step arithmetic.

< 15 pts (< 60%) NEEDS TARGETED INTERVENTION

Requires explicit instruction with highlighting tape, graphic organizers, and single-to-multi-step bridging scaffolds.

Problems 4 – 6 • Rubric

Problem 4 Key: 1,728 ÷ 12 = 144 (Remainder: 0) 4 / 4 Points

Step-by-Step Breakdown:

12 × 100 = 1,200 → 1,728 − 1,200 = 528
12 × 40 = 480 → 528 − 480 = 48
12 × 4 = 48 → 48 − 48 = 0
Total Quotient: 100 + 40 + 4 = 144

Algorithm Steps & Verification:

17 ÷ 12 = 1 (rem 5); bring down 2 → 52
52 ÷ 12 = 4 (rem 4); bring down 8 → 48
48 ÷ 12 = 4 (rem 0)

Check: 144 × 12 = 1,728 ✓

Problem 5 Key: 3,548 ÷ 24 = 147 R 20 4 / 4 Points

Step-by-Step Breakdown:

24 × 100 = 2,400 → 3,548 − 2,400 = 1,148
24 × 40 = 960 → 1,148 − 960 = 188
24 × 7 = 168 → 188 − 168 = 20 (rem)
Quotient: 100 + 40 + 7 = 147 R 20

Algorithm Steps & Verification:

35 ÷ 24 = 1 (rem 11); bring down 4 → 114
114 ÷ 24 = 4 (rem 18); bring down 8 → 188
188 ÷ 24 = 7 (rem 20)

Check: (147 × 24) + 20 = 3,528 + 20 = 3,548 ✓

Problem 6 Key: Real-World Food Warehouse Application 4 / 4 Points

Problem Interpretation & Math:

Total items: 2,160 cans • Crates: 18
Equation: \(2,160 \div 18\)
18 × 100 = 1,800 → 2,160 − 1,800 = 360
18 × 20 = 360 → 360 − 360 = 0
Quotient: 120 cans per crate

Label & Verification:

Correct final response must include the units (120 cans of soup or 120 cans/crate).

Check: 120 × 18 = 2,160 cans ✓

Division IEP Mastery Matrix (Target Goal: 80% / 19+ pts) Scoring: 4 pts per problem × 6 problems = 24 total pts

19 – 24 pts (80% – 100%) GOAL MASTERED

Accurately applies visual models or standard algorithm to 3- and 4-digit dividends. Correctly identifies and interprets remainders.

15 – 18 pts (60% – 79%) PROGRESSING

Success with 1-digit divisors; experiences minor place value alignment errors or multi-step subtraction mistakes with 2-digit divisors.

< 15 pts (< 60%) NEEDS TARGETED INTERVENTION

Requires structured graph paper for place value alignment and scaffolded partial quotients ("Big 7") using familiar benchmark multiples (10×, 5×, 2×).

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