Table Detectives Review Packet
TEKS 3.5E Review Grade 3 Mathematics
TABLE DETECTIVES
Name:
Date:
Teacher:
Score:
Sleuth Field Guide: Cracking Table Rules
Rule Check: Look ACROSS, not DOWN!
Additive Relationship Input + n = Output
Add or subtract the same constant number to each input.
Ex: Age difference. If Leo is 4 years older: Age + 4.
Multiplicative Relationship Input × n = Output
Multiply each input by the same constant group size.
Ex: Wheels on cars. Each car has 4 wheels: Cars × 4.
Golden Detective Rule: A rule is only correct if it works for EVERY single row in the table, not just the first one!
Part 1: Warm-Up Case Files
Find the rule, write the equation, and fill in the missing numbers.
Case #1: Bicycles and Wheels Multiplicative
| Bicycles (\(b\)) |
Wheels (\(w\)) |
| 2 |
4 |
| 5 |
10 |
| 8 |
16 |
| 11 |
? |
Rule: Multiply bicycles by ________
Missing value: 11 bicycles = ________ wheels
Case #2: Board Game Points Additive
| Round 1 (\(r\)) |
Total Score (\(t\)) |
| 3 |
10 |
| 6 |
13 |
| 9 |
16 |
| 14 |
? |
Rule: Add ________ to Round 1 score
Missing value: Round 1 of 14 = ________ total
Case #3: Insect Observation Find Relationship
| Number of Beetles |
Total Legs |
| 3 |
18 |
| 4 |
24 |
| 7 |
? |
| 10 |
60 |
Verbal description: The number of legs is ____________________
Missing value: 7 beetles have ________ legs
Case #4: Maya's Savings Bank Work Backwards
| Weeks Saved (\(w\)) |
Total Dollars (\(d\)) |
| 2 |
10 |
| 4 |
20 |
| ? |
45 |
| 12 |
60 |
Rule: Multiply weeks by ________ to get dollars
Missing value: $45 saved in ________ weeks
TEKS 3.5E Mastery Target: Number Pairs & Tables Page 1 of 3
2
CASE FILES: REAL-WORLD PROBLEM SOLVING
Analyze tables and represent real-world situations
5 Sweet Treats Bakery packs 8 muffins into every display box. Table & Description
Complete the table below showing the relationship between boxes and total muffins.
| Boxes (\(b\)) |
Total Muffins (\(m\)) |
| 3 |
24 |
| 5 |
40 |
| 7 |
|
| 9 |
|
Verbal Rule:
To find the total muffins, __________________________________.
Number Sentence:
Boxes = Total Muffins
6 Elena is 6 years older than her brother Mateo. Additive Table
The table shows the relationship between Mateo's age and Elena's age over several years.
| Mateo's Age (\(m\)) |
Elena's Age (\(e\)) |
| 2 |
8 |
| 5 |
11 |
| 8 |
14 |
| 12 |
|
A. How old will Elena be when Mateo is 12? _________
B. When Elena is 25, how old will Mateo be? _________
C. Why is this additive instead of multiplicative?
7 In a science experiment, Mr. Davis records seed packets and total seeds. Missing Inputs & Outputs
| Packets (\(p\)) |
Total Seeds (\(s\)) |
| 3 |
27 |
| 5 |
45 |
| 6 |
|
|
81 |
A. Rule: Packets \(\times\) _______ = Total Seeds
B. How many seeds in 6 packets? _________
C. For 81 seeds, how many packets are needed? _________
8 Create Your Own Table: Carnival Ring Toss Table Construction
Each ring toss win awards 5 prize tickets. Complete the table to represent the relationship.
| Wins (\(w\)) |
Tickets Won (\(t\)) |
| 1 |
5 |
| 2 |
|
| 4 |
|
| 10 |
|
Explain the relationship rule in words:
Application & Construction of Paired Data Page 2 of 3
3
STAAR MISSION CHALLENGE
Test-format multiple choice & detective audit
9 A calendar company knows that there are 7 days in 1 week. Which table represents the relationship between the number of weeks and the total number of days?
A
| Weeks |
Days |
| 1 |
7 |
| 2 |
14 |
| 3 |
21 |
| 4 |
28 |
B
| Weeks |
Days |
| 1 |
7 |
| 2 |
8 |
| 3 |
9 |
| 4 |
10 |
C
| Weeks |
Days |
| 7 |
1 |
| 14 |
2 |
| 21 |
3 |
| 28 |
4 |
D
| Weeks |
Days |
| 1 |
7 |
| 2 |
14 |
| 3 |
17 |
| 4 |
24 |
10 The table below shows the relationship between the number of red apples picked and the total number of apples in a basket.
| Red Apples (\(r\)) |
Total Apples (\(t\)) |
| 4 |
12 |
| 7 |
15 |
| 10 |
18 |
| 15 |
23 |
Which rule describes the relationship between the number of red apples and the total number of apples?
F Multiply the number of red apples by 3 to get total apples
G Add 8 to the number of red apples to get total apples
H Add 3 to the number of red apples to get total apples
J Multiply the number of red apples by 8 to get total apples
11 Art Class Supply Packs Multi-Step
Mrs. Gomez puts 4 paintbrushes and 1 palette into each art kit. The table shows the total paintbrushes for different numbers of kits.
| Art Kits |
Paintbrushes |
| 2 |
8 |
| 5 |
20 |
| 8 |
32 |
If Mrs. Gomez prepares 12 art kits, how many paintbrushes will she need in all? Show your strategy:
Answer: paintbrushes
Case #12 Detective Audit: Error Analysis Crack the Case
| Input |
Output |
| 2 |
10 |
| 3 |
15 |
| 6 |
30 |
Sleuth Sam said: "The rule is Add 8 because \(2 + 8 = 10\)."
Why is Sam's rule incorrect, and what is the true rule?
Detective Certification Completed! Page 3 of 3
Table Detectives Answer Key
Teacher Resource TEKS 3.5E Answer Key & Guide
TABLE DETECTIVES: ANSWER KEY (PAGES 1 & 2)
Standards Alignment
TEKS 3.5(E) Readiness
Page 1: Warm-Up Case Files (Cases 1–4) Focus: Determining Additive vs. Multiplicative Rules
Case #1: Bicycles & Wheels Multiplicative
Rule: Multiply bicycles by 2 (\(b \times 2 = w\))
Missing value: 11 bicycles = 22 wheels (\(11 \times 2 = 22\))
Check: \(2\times2=4\), \(5\times2=10\), \(8\times2=16\). Rule verified.
Case #2: Board Game Points Additive
Rule: Add 7 to Round 1 score (\(r + 7 = t\))
Missing value: Round 1 of 14 = 21 total (\(14 + 7 = 21\))
Check: \(3+7=10\), \(6+7=13\), \(9+7=16\). Rule verified.
Case #3: Insect Observation Multiplicative
Verbal description: The number of legs is 6 times the number of beetles.
Missing value: 7 beetles have 42 legs (\(7 \times 6 = 42\))
Check: \(3\times6=18\), \(4\times6=24\), \(10\times6=60\). Rule verified.
Case #4: Maya's Savings Bank Inverse Operation
Rule: Multiply weeks by 5 (\(w \times 5 = d\))
Missing value: $45 saved in 9 weeks (\(45 \div 5 = 9\))
Check: \(2\times5=10\), \(4\times5=20\), \(12\times5=60\). Rule verified.
Page 2: Case Files Real-World Problem Solving (Problems 5–8) Focus: Verbal Descriptions & Equations
Problem 5: Sweet Treats Bakery (Muffins in Boxes) Rule: \(b \times 8 = m\)
Completed Table Entries:
• Row 3: 7 boxes \(\rightarrow\) 56 muffins (\(7 \times 8\))
• Row 4: 9 boxes \(\rightarrow\) 72 muffins (\(9 \times 8\))
Verbal Rule: "Multiply the number of boxes by 8 to get the total number of muffins."
Number Sentence: Boxes \(\times\) 8 = Total Muffins (or \(b \times 8 = m\))
Problem 6: Mateo and Elena's Ages Rule: \(m + 6 = e\)
Completed Table Entry:
• Row 4: Mateo 12 \(\rightarrow\) Elena 18 (\(12 + 6\))
Part A: Elena will be 18 years old.
Part B: When Elena is 25, Mateo is 19 years old (\(25 - 6 = 19\)).
Part C Explanation: It is additive because their age difference is always a constant 6 years apart. As years pass, both people age by 1 year, so the difference never multiplies.
Problem 7: Science Lab Seed Packets Rule: \(p \times 9 = s\)
Completed Table Entries:
• Row 3: 6 packets \(\rightarrow\) 54 seeds
• Row 4: 9 packets \(\rightarrow\) 81 seeds
Part A: Rule: Packets \(\times\) 9 = Total Seeds
Part B: 6 packets = 54 seeds (\(6 \times 9 = 54\))
Part C: For 81 seeds, need 9 packets (\(81 \div 9 = 9\))
Problem 8: Carnival Ring Toss Prize Tickets Rule: \(w \times 5 = t\)
Completed Table Entries:
• 2 wins \(\rightarrow\) 10 tickets | 4 wins \(\rightarrow\) 20 tickets
• 10 wins \(\rightarrow\) 50 tickets
Sample Student Explanation:
"Each win gives 5 tickets, so the total number of prize tickets is always equal to the number of ring toss wins multiplied by 5."
TEKS 3.5E Complete Answer Key Answer Key • Page 1 of 2
Assessment Analysis STAAR Rationale & Rubric
STAAR MISSION SOLUTIONS & DIAGNOSTIC GUIDE
Page 3 Solutions
Problem 9: Weeks to Days Table Correct: A
Rule: Weeks \(\times 7 =\) Days (\(1\times7=7, 2\times7=14, 3\times7=21, 4\times7=28\)).
Distractor Analysis:
B is incorrect: Follows an additive pattern (+6, +6, etc. but adds +1 down days: 7, 8, 9, 10). Misinterprets 1 week = 7 days as adding 1 each time.
C is incorrect: Inverts input and output (days in input column, weeks in output column).
D is incorrect: Matches row 1 (\(1 \times 7 = 7\)) and row 2 (\(2 \times 7 = 14\)), but rows 3 and 4 have arbitrary numbers (17 and 24). Tests whether students check every row!
Problem 10: Apples in Basket Rule Correct: G
Rule: Red Apples \(+ 8 =\) Total Apples (\(4+8=12, 7+8=15, 10+8=18, 15+8=23\)).
Distractor Analysis:
F is incorrect: Works ONLY for the first row (\(4 \times 3 = 12\)), but fails for row 2 (\(7 \times 3 = 21 \neq 15\)). Common single-row trap.
H is incorrect: Subtracted 4 from 7 down the input column (+3 down) instead of across rows.
J is incorrect: Used multiplication instead of addition (\(4 \times 8 = 32 \neq 12\)).
Problem 11: Art Supply Kits Answer: 48 brushes
Rule: Art Kits \(\times 4 =\) Paintbrushes.
Accepted Strategies:
• Multiplication equation: \(12 \times 4 = 48\).
• Decomposition / doubling: 10 kits = 40, 2 kits = 8; \(40 + 8 = 48\).
• Repeated addition / skip counting by 4s to 12 groups.
Problem 12: Sleuth Sam Error Audit Error Analysis
True Rule: Input \(\times 5 =\) Output (Multiplicative).
Key Explanation Elements:
1. Sam only tested row 1 (\(2 + 8 = 10\)).
2. The rule failed row 2: \(3 + 8 = 11\), but output is 15.
3. The true relationship is multiplying by 5: \(2\times5=10\), \(3\times5=15\), \(6\times5=30\).
TEKS 3.5E Common Misconception Matrix & Instructional Interventions
1. Looking DOWN instead of ACROSS
Students find the pattern down one column (+3, +3) rather than identifying how input transforms to output. Intervention: Have students draw an arrow across each row with a rule box in the center.
2. First-Row Confirmation Bias
Finding a rule that works for row 1 and immediately choosing it without testing rows 2 and 3. Intervention: Require students to write checkmarks next to all pairs before accepting a rule.
3. Additive vs. Multiplicative Mix-Up
Confusing groups of items (wheels, legs) with additive scenarios (ages, heights). Intervention: Use equal group imagery to distinguish equal sets from constant differences.
Review Packet Scoring Rubric Total Points: 20
Part 1: Cases 1–4
4 points (1 pt each)
Rule & missing value
Part 2: Cases 5–8
8 points (2 pts each)
Table + explanation
Part 3: Questions 9–11
6 points (2 pts each)
STAAR questions
Part 4: Audit Case 12
2 points
Error explanation
Comprehensive Instructional & Diagnostic Tool Answer Key • Page 2 of 2
