A comprehensive 3rd-grade mathematics sequence guiding students from concrete and pictorial arrays to repeated addition and multiplication fact mastery. Students construct, analyze, and connect rows and columns through blueprint-themed visual models and differentiated problem-solving.
Why: It has 3 equal rows with 4 dots in each row. Total: 12. No missing dots or uneven columns.
Problem 2: Correct: NO
Why: The rows are not equal. Row 1 has 4, Row 2 has 2, and Row 3 has 3. Arrays must have equal rows.
Problem 3 (Stars):
Rows: 2
In each row: 5
Columns: 5
Total: 10
Problem 4 (Squares):
Rows: 4
In each row: 3
Columns: 3
Total: 12
Problem 5 (Circles):
Rows: 3
In each row: 3
Columns: 3
Total: 9
PAGE 2 SOLUTIONS
Blueprint Builders
Problem 6 (3 rows of 5):
Drawing should show 3 horizontal rows, each containing exactly 5 items.
Rows: 3 • Columns: 5 • Total: 15
5 + 5 + 5 = 15
Problem 7 (4 rows of 4):
Drawing should show a square array with 4 rows and 4 columns.
Rows: 4 • Columns: 4 • Total: 16
4 + 4 + 4 + 4 = 16
Problem D: 12 Bricks Two Ways (Accept any two valid pairs):
3 rows of 4
4 rows of 3
2 rows of 6
6 rows of 2
Exit Ticket Exemplar Answer
"Yes, Maya is correct because both equal 10. 2 rows of 5 is 5 + 5 = 10, and 5 rows of 2 is 2 + 2 + 2 + 2 + 2 = 10. Rotating an array changes the rows and columns, but the total number of objects stays exactly the same!"
Complete Solutions & Model Responses • Pages 1 & 2
Scoring Guide
PAGE 1 SOLUTIONS
Array to Equation Translation
Problem 1 (3 rows of 5 dots):
Rows: 3 • Columns: 5 • Total: 15
Addition: 5 + 5 + 5 = 15
Multiplication: 3 × 5 = 15
Problem 2 (4 rows of 3 squares):
Rows: 4 • Columns: 3 • Total: 12
Addition: 3 + 3 + 3 + 3 = 12
Multiplication: 4 × 3 = 12
Problem 3 (2 rows of 6 circles):
Rows: 2 • Columns: 6 • Total: 12
Addition: 6 + 6 = 12
Multiplication: 2 × 6 = 12
PAGE 2 SOLUTIONS
Reverse Blueprints & Word Problems
Problem 4 (\(6 + 6 + 6 = 18\)):
Array should show 3 rows with 6 items in each row.
Rows: 3 • Columns: 6 • 3 × 6 = 18
Problem 5 (\(2 + 2 + 2 + 2 + 2 = 10\)):
Array should show 5 rows with 2 items in each row.
Rows: 5 • Columns: 2 • 5 × 2 = 10
Problem 6 (Cookie Tray):
Array shows 3 horizontal rows of 6 cookies.
Repeated addition: 6 + 6 + 6 = 18
3 × 6 = 18 cookies
Problem 7 (Classroom Desks):
Array shows 4 horizontal rows of 5 desks.
Repeated addition: 5 + 5 + 5 + 5 = 20
4 × 5 = 20 desks
Exit Ticket Exemplar Answer
"Multiplication is faster because \(4 \times 5\) is a shortcut for adding 5 four times. Instead of writing out a long chain of plus signs (\(5 + 5 + 5 + 5\)), multiplication lets us write just two numbers: the number of rows and how many are in each row to get 20."
Lesson 2 Assessment Rubric
Level 4 (Advanced): Translates fluently between arrays, repeated addition, and multiplication; solves word problems independently.
Level 3 (Proficient): Accurately writes row addition and multiplication sentences with correct totals.
Level 2 (Approaching): Understands repeated addition but occasional errors counting rows or addends.
Level 1 (Emerging): Adds dimensions (\(3 + 5 = 8\)) rather than equal groups; needs physical counters.
