Grade Six Math Benchmarks

Model Calculation (+1 pt): \(A = b \cdot h\)
\(A = 14 \text{ cm} \times 6 \text{ cm} = 84 \text{ cm}^2\)

Final Answer (+1 pt): 84 \(\text{cm}^2\)

Q4 Exemplar Triangle: Half Base Times Height

[ 4 Points ]

b = 16 m ✔ h = 9 m ✔ 10 m ✗ Distractor: 10 m outer side

Base (\(b\)) = 16 m (+1 pt) Height (\(h\)) = 9 m (+1 pt)

Model Calculation (+1 pt): \(A = \frac{1}{2} b h = \frac{1}{2} \times 16 \times 9\)
\(A = 8 \times 9 = 72 \text{ m}^2\)  (or \(144 \div 2 = 72\))

Final Answer (+1 pt): 72 \(\text{m}^2\)

Misconception & Partial Credit Guide:

• Q3 Slant Error: Student writing \(14 \times 8 = 112\text{ cm}^2\) awards 0 pts for calculation & answer, but award 1 pt for recognizing base = 14 cm.
• Q4 Forgotten Half: Student calculating \(16 \times 9 = 144\text{ m}^2\) without dividing by 2 awards 2/4 pts (identified base & height).

Grade 6 Math Exemplar • Page 2 of 4 Part 2 Cont. Solutions on Page 3 →

Teacher Key

Composite Figure Decomposition Solutions

PAGE 3 SCORE: 6 / 6 PTS

Q5 Exemplar Community Garden Decomposition (6 Pts)

[ 6 Points Total ]

Shape 1: Rectangle 10 ft × 8 ft = 80 sq ft Shape 2: Triangle ½ (6 × 8) = 24 sq ft 10 ft 8 ft Total Base = 16 ft b = 16 − 10 = 6 ft

Step 1: Rectangle (+2 pts) \(l \times w\)

\(A_1 = 10 \text{ ft} \times 8 \text{ ft} = 80 \text{ ft}^2\)
(1 pt for formula/work, 1 pt for 80)

Area 1 = 80 \(\text{ft}^2\)

Step 2: Triangle (+2 pts) \(\frac{1}{2} b h\)

\(b = 16 - 10 = 6 \text{ ft}\),  \(h = 8 \text{ ft}\)
\(A_2 = \frac{1}{2} \times 6 \times 8 = 24 \text{ ft}^2\)

Area 2 = 24 \(\text{ft}^2\)

Step 3 (+2 pts) Total Sum: \(A_1 + A_2 = 80 + 24\)

104 \(\text{ft}^2\)

Scoring Rubric Breakdown:

• Full Credit (6 pts): Step 1 = 80 (2 pts), Step 2 = 24 (2 pts), Step 3 = 104 with correct square feet units (2 pts).
• Partial Credit: Award follow-through credit in Step 3 if student correctly sums their incorrect sub-areas.

Grade 6 Math Exemplar • Page 3 of 4 Part 3 Solutions on Page 4 →

Teacher Key

Part 3: 3D Prism Surface Area Solutions

PAGE 4 SCORE: 6 / 6 PTS

Q6 Exemplar Rectangular Prism Net Surface Area

[ 3 Points Total ]

Top: 6×4 = 24 Back: 6×3 = 18 Bottom: 6×4 = 24 Front: 6×3 = 18 4×3=12 4×3=12 Total: 24+24+18+18+12+12

Top & Bottom: \(2 \times (6 \times 4)\) 48 \(\text{in}^2\) (+0.5 pt)

Front & Back: \(2 \times (6 \times 3)\) 36 \(\text{in}^2\) (+0.5 pt)

Left & Right: \(2 \times (4 \times 3)\) 24 \(\text{in}^2\) (+0.5 pt)

Total Surface Area (+1.5 pts): 108 \(\text{in}^2\)

Q7 Exemplar Triangular Prism Camping Tent

[ 3 Points Total ]

• 2 Triangular Ends (+1 pt): \(2 \times \left(\frac{1}{2} \times 6 \times 4\right) = 2 \times 12 = \mathbf{24 \text{ ft}^2}\)

• 3 Rectangular Faces (+1 pt): Slant Roofs: \(2 \times (5 \times 10) = 100 \text{ ft}^2\)
Floor: \(1 \times (6 \times 10) = 60 \text{ ft}^2\)  →  Total Rectangles = \(\mathbf{160 \text{ ft}^2}\)

Summing All 5 Faces: \(24 + 160 = 184\)

Tent Surface Area (+1 pt): 184 \(\text{ft}^2\)

Comprehensive Score Conversion Matrix: Total: 30 Points

Exceeds (Level 4):
27 – 30 pts (90–100%)

Meets (Level 3):
21 – 26 pts (70–89%)

Approaching (Level 2):
15 – 20 pts (50–69%)

Needs Support (Level 1):
< 15 pts (< 50%)

Look-Fors:

• • Multiply \(364 \times 5\) ones first.
• • Write the placeholder 0 in the ones column before multiplying by 2 tens.
• • Add carefully and regroup into thousands.

Product:

\(364 \times 25 =\)

Q4 Multi-Step Real World Context

A concert hall has 148 rows of seats. Each row has 32 seats. If all seats are filled for a Friday night performance, how many total people are seated?

[ 3 pts ]

Show your complete multiplication work:

Calculation: \(148 \times 32 = ?\)

Total People: people

Grade 6 Math Assessment • Page 2 of 4 Go to Page 3 →

Part 2: Fractions

Fraction Addition & Subtraction (Unlike Denominators)

Student: Page 3: / 7

Rule: Find a Common Denominator first before adding or subtracting numerators!

Q5 Adding Fractions with Unlike Denominators

Find a common denominator, rewrite equivalent fractions, and solve in simplest form.

[ 4 pts ]

Problem: \(\frac{3}{4} + \frac{2}{5}\)

Step 1: Common Denominator

Least Common Denominator of 4 and 5 is: ____

\(\frac{3}{4} =\) /

\(\frac{2}{5} =\) /

Step 2: Add and Simplify

Sum (improper or mixed):

Q6 Subtracting Fractions (Baking Context)

Maya has \(\frac{5}{6}\) cup of sugar. She uses \(\frac{1}{4}\) cup to make lemon cookies. How much sugar does Maya have left?

[ 3 pts ]

Show equivalent fractions and subtraction steps:

Expression: \(\frac{5}{6} - \frac{1}{4} = ?\)

Sugar Remaining: cup(s)

Grade 6 Math Assessment • Page 3 of 4 Go to Final Page 4 →

Part 3: Fraction Operations

Multiplication & Division of Fractions

Student: Page 4: / 8

Q7 Multiplying Fractions

Multiply straight across (numerator × numerator, denominator × denominator). Simplify your answer.

[ 2 pts ]

Evaluate Expression: \(\frac{4}{7} \times \frac{3}{8}\)

Product (Simplest Form):

Q8 Dividing Fractions (Keep, Change, Flip)

Divide fractions by multiplying by the reciprocal of the divisor.

[ 3 pts ]

Evaluate Expression: \(\frac{5}{6} \div \frac{2}{3}\)

Quotient (Simplest Form):

Q9 Fraction Division Application

A woodworker has a board that is \(\frac{7}{8}\) meter long. He cuts the board into smaller craft strips that are each \(\frac{1}{4}\) meter long. How many craft strips can he make?

[ 3 pts ]

Show your division equation and reciprocal steps:

Equation: \(\frac{7}{8} \div \frac{1}{4} = ?\)

Number of Strips: strips

Self-Check: 😀 Multiplication Master 🌟 Fraction Pro 📚 Need Practice

Teacher Feedback:

Scoring Criteria: • +1 pt: \(364 \times 5 = 1,820\)
• +1 pt: Zero placeholder in ones place
• +1 pt: \(364 \times 20 = 7,280\)
• +1 pt: Final sum = \(9,100\)

Final Product: 9,100

Q4 Solution: Concert Hall Seating (\(148 \times 32\)) [ 3 Points Total ]

Algorithm Work (+2 pts):

    148
 ×  32
——————
    296  ← \(148 \times 2\) (+1 pt)
+  4440  ← \(148 \times 30\) (+1 pt)
——————
   4736  ← Sum

Correct Answer (+1 pt): 4,736 people seated

Grading & Partial Credit:

• Regrouping in Addition: In Q3, adding \(1820 + 7280\): students must regroup \(2 + 8 = 10\) tens into 1 hundred, yielding \(8 + 2 + 1 = 11\) hundreds. Award partial credit if steps are shown.

Grade 6 Math Exemplar • Page 2 of 4 Part 2 Fraction Solutions on Page 3 →

Teacher Key

Part 2: Fraction Add & Subtract Solutions

PAGE 3 SCORE: 7 / 7 PTS

Target Standard: 5.NF.A.1 / 6.NS Extension (Add/subtract fractions with unlike denominators) Total: 7 Points

Q5 Solution: \(\frac{3}{4} + \frac{2}{5}\) [ 4 Points Total ]

Step 1: Common Denominator (+2 pts)

Least Common Denominator of 4 and 5 = 20 (+1 pt)

\(\frac{3 \times 5}{4 \times 5} = \mathbf{\frac{15}{20}}\)  and  \(\frac{2 \times 4}{5 \times 4} = \mathbf{\frac{8}{20}}\) (+1 pt)

Step 2: Add Numerators (+1 pt): \(\frac{15}{20} + \frac{8}{20} = \mathbf{\frac{23}{20}}\)  or  \(\mathbf{1\frac{3}{20}}\)

Accepted Answers (+1 pt): \(\frac{23}{20}\)  or  \(1\frac{3}{20}\)

Q6 Solution: Baking Sugar Remaining (\(\frac{5}{6} - \frac{1}{4}\)) [ 3 Points Total ]

Model Solution (+2 pts):

• Common denominator of 6 and 4 is 12 (or 24):
  \(\frac{5 \times 2}{6 \times 2} = \frac{10}{12}\)  and  \(\frac{1 \times 3}{4 \times 3} = \frac{3}{12}\) (+1 pt)
• Subtract numerators: \(\frac{10}{12} - \frac{3}{12} = \mathbf{\frac{7}{12}}\) (+1 pt)
(If using 24: \(\frac{20}{24} - \frac{6}{24} = \frac{14}{24} = \frac{7}{12}\). Both full credit.)

Remaining Sugar (+1 pt): \(\frac{7}{12}\) cup

Critical Look-Fors:

• Adding Denominators Error: Watch for \(\frac{3}{4} + \frac{2}{5} = \frac{5}{9}\) or \(\frac{5}{6} - \frac{1}{4} = \frac{4}{2} = 2\). Students adding/subtracting straight across earn 0 credit for conversion.
• Acceptable Equivalents: Accept unsimplified \(\frac{14}{24}\) with 2.5/3 pts if simplest form was not reached.

Grade 6 Math Exemplar • Page 3 of 4 Part 3 Mult & Div on Page 4 →

Teacher Key

Part 3: Fraction Mult & Div Solutions

PAGE 4 SCORE: 8 / 8 PTS

Q7 Solution: \(\frac{4}{7} \times \frac{3}{8}\) [ 2 Points Total ]

Method 1 (Multiply Straight Across): \(\frac{4 \times 3}{7 \times 8} = \frac{12}{56}\) → divide by 4: \(\mathbf{\frac{3}{14}}\) (+1 pt work, +1 pt answer)
Method 2 (Cross-Cancel): \(\frac{1 \times 3}{7 \times 2} = \mathbf{\frac{3}{14}}\)

Product (+1 pt): \(\frac{3}{14}\)

Q8 Solution: \(\frac{5}{6} \div \frac{2}{3}\) [ 3 Points Total ]

Reciprocal Multiplication (+2 pts): • Keep \(\frac{5}{6}\), Change \(\div\) to \(\times\), Flip \(\frac{2}{3}\) to \(\frac{3}{2}\) (+1 pt)
• \(\frac{5}{6} \times \frac{3}{2} = \frac{15}{12}\) → divide by 3: \(\mathbf{\frac{5}{4}}\) or \(\mathbf{1\frac{1}{4}}\) (+1 pt)

Quotient (+1 pt): \(\frac{5}{4}\)  (or \(1\frac{1}{4}\))

Q9 Solution: Woodworking Strips (\(\frac{7}{8} \div \frac{1}{4}\)) [ 3 Points Total ]

Model Solution (+2 pts): • Equation: \(\frac{7}{8} \div \frac{1}{4} = \frac{7}{8} \times \frac{4}{1}\) (+1 pt)
• Multiply: \(\frac{28}{8} = \frac{7}{2} = \mathbf{3\frac{1}{2}}\) strips (+1 pt)
(Also accept 3 full strips with \(\frac{1}{2}\) strip remaining)

Strips (+1 pt): \(3\frac{1}{2}\) strips

Score Scale (30 Points Total): Grade 6 Computation Benchmark

Exceeds (4):
27 – 30 pts (90–100%)

Meets (3):
21 – 26 pts (70–89%)

Approaching (2):
15 – 20 pts (50–69%)

Needs Support (1):
< 15 pts (< 50%)