Troy School District · Mathematics · Grade 6 · Form B
Standards Drill · 120 minutes · 100 points

Grade 6 Mathematics — Standards-Aligned Skills Examination

A calculation-focused, standards-walkthrough exam covering the CCSS-M Grade 6 standards (6.RP, 6.NS, 6.EE, 6.G, 6.SP). Each problem cites the standard(s). Form B complements Form A.

Student Name
Proctor
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Instructions

1. 6.RP.A · Ratios and unit rates 10 points
  1. Express each ratio in simplest form:

    (i) \(18 : 24\)    (ii) \(45 : 30\)    (iii) \(2 : 4 : 6\)

  2. Find each unit rate:

    (i) 240 miles in 4 hours    (ii) $36 for 8 lbs    (iii) 360 words in 5 minutes

  3. Use a ratio table to solve: a recipe uses 3 cups flour for every 2 cups sugar. How much sugar for 21 cups of flour?
  4. Compare unit prices to identify the better buy. Show your work:

    (i) 12 oz for $3.60 vs. 18 oz for $4.95
    (ii) 5 lbs for $9.50 vs. 8 lbs for $14.40

  5. A car travels 65 mph. How far does it go in 2.5 hours? In 4 hours 30 minutes?
2. 6.RP.A.3 · Percent 10 points
  1. Convert each:

    (i) 0.45 to a percent    (ii) 7/20 to a percent    (iii) 175% to a decimal    (iv) 8% to a fraction in simplest form

  2. Find each:

    (i) 25% of 84    (ii) 60% of 130    (iii) 12% of 250

  3. Find each missing value:

    (i) What percent of 60 is 15?    (ii) 36 is 40% of what number?    (iii) What percent of 200 is 50?

  4. A $80 jacket is on sale at 20% off. Find the sale price and the savings.
  5. A $50 meal includes a 18% tip. Find the tip and the total.
3. 6.NS.A · Fraction division 8 points
  1. Compute each (reciprocal method):

    (i) \( \dfrac{2}{3} \div \dfrac{4}{5} \)    (ii) \( \dfrac{5}{6} \div \dfrac{1}{2} \)    (iii) \( \dfrac{7}{8} \div 4 \)    (iv) \( 6 \div \dfrac{3}{5} \)    (v) \( 2\dfrac{1}{4} \div \dfrac{3}{4} \)    (vi) \( 1\dfrac{1}{3} \div 2\dfrac{2}{3} \)

  2. Word problem: A board is \(3\dfrac{1}{2}\) ft long. It is cut into pieces, each \( \dfrac{1}{4} \) ft long. How many pieces? Show the division.
  3. Word problem: A pitcher holds \(5\) cups. If each glass holds \( \dfrac{2}{3} \) cup, how many glasses does the pitcher fill? Show the division and interpret any remainder.
4. 6.NS.B · Multi-digit decimals, GCF, LCM 10 points
  1. Compute (decimal operations):

    (i) \(34.56 + 7.892\)    (ii) \(50.4 - 18.93\)    (iii) \(2.4 \cdot 1.25\)    (iv) \(15.6 \div 0.4\)    (v) \(0.36 \cdot 0.05\)

  2. Compute long division: \(2{,}916 \div 27\). State quotient and remainder.
  3. Find the GCF of each pair: 24 and 36; 18 and 45; 60 and 84.
  4. Find the LCM of each pair: 6 and 9; 8 and 12; 10 and 15.
  5. The distributive property: rewrite \(48 + 36\) as \(12 \cdot (\square + \square)\). Show how the GCF gives the factorization.
5. 6.NS.C · Integers, absolute value, coordinate plane 10 points
  1. Order from least to greatest: \(-7,\ 4,\ -2,\ 0,\ 3,\ -5\).
  2. Compute each absolute value:

    (i) \(|-9|\)    (ii) \(|7 - 12|\)    (iii) \(|-3| + |-8|\)    (iv) \(|-4 + 11|\)

  3. Plot \( A(-3, 4), B(2, 4), C(2, -1), D(-3, -1) \) on a coordinate plane. Find the perimeter and area of the quadrilateral.
  4. Find the distance between each pair of points (horizontal or vertical only):

    (i) \( (-2, 5) \) and \( (4, 5) \)    (ii) \( (3, -2) \) and \( (3, 7) \)    (iii) \( (-1, 3) \) and \( (-1, -6) \)

  5. Reflect each point over the named axis and state the new coordinates:

    (i) \( (-3, 5) \) over \(x\)-axis    (ii) \( (4, -2) \) over \(y\)-axis    (iii) \( (5, 5) \) over \(x\)-axis

6. 6.EE.A · Expressions and equivalent expressions 10 points
  1. Write an algebraic expression:

    (i) "5 less than twice a number \(n\)"    (ii) "the sum of 3 and \(x\), divided by 4"    (iii) "8 more than the product of 2 and \(y\)"

  2. Evaluate each when \(x = 5,\ y = -2,\ z = 3\):

    (i) \(2x + 3y\)    (ii) \(z^2 - x\)    (iii) \( \dfrac{4x - y}{z + 1} \)

  3. Combine like terms:

    (i) \(3a + 4 - a + 7\)    (ii) \(5x + 2y - 3x + 8y\)    (iii) \(7m - 4n - 3m + 2n + 5\)

  4. Apply the distributive property and simplify:

    (i) \(4(2x + 3)\)    (ii) \(-3(y - 5)\)    (iii) \(5(2a + 1) - 2(3a - 4)\)

7. 6.EE.B · One-step equations and inequalities 12 points
  1. Solve each one-step equation:

    (i) \(x + 12 = 27\)    (ii) \(y - 8 = -3\)    (iii) \(6m = 42\)    (iv) \( \dfrac{n}{4} = 9 \)    (v) \(-3z = 24\)    (vi) \(p + 7 = 2\)

  2. Solve each two-step equation:

    (i) \(2x + 5 = 13\)    (ii) \(3y - 7 = 14\)    (iii) \( \dfrac{x}{2} - 4 = 6 \)    (iv) \(-4m + 9 = 17\)

  3. Write and solve a one-step inequality. Graph the solution on a number line:

    (i) \(x + 7 \le 15\)    (ii) \(y - 4 > 6\)    (iii) \(3z \ge 18\)

8. 6.EE.C · Independent and dependent variables 5 points
  1. A taxi charges $4 plus $2 per mile. Let \(C\) be the cost in dollars and \(m\) be the miles. Write an equation \(C = ?\). Identify the independent and dependent variables.
  2. Make a table of values for the equation in (a) for \(m = 1, 2, 3, 4, 5\).
  3. Sketch the graph of \(C\) vs. \(m\) on a labeled coordinate plane.
9. 6.G · Area, surface area, volume, polygons on the coordinate plane 12 points
  1. Find the area of each:

    (i) parallelogram, base 8, height 5    (ii) triangle, base 14, height 6    (iii) trapezoid, parallel sides 7 and 11, height 4    (iv) composite figure: rectangle 6 × 8 plus a triangle on top with base 8 and height 3

  2. Find the volume of a rectangular prism with dimensions \(2\dfrac{1}{2}\) by \(1\dfrac{1}{2}\) by 4 (fractional edges).
  3. How many \(\dfrac{1}{2}\)-foot cubes fit inside a 3 × 2 × \(1\dfrac{1}{2}\) ft box? Show your work.
  4. Find the total surface area of a rectangular prism with dimensions 3 × 4 × 5. Show all six face areas as a sum.
  5. Plot the polygon with vertices \( A(-2, 1), B(3, 1), C(5, -2), D(-2, -2) \) on a coordinate plane. Find the area by decomposing into a rectangle and a triangle.
10. 6.SP · Statistical questions, measures, displays 13 points

Daily reading minutes for 12 students: \(15, 20, 22, 25, 30, 30, 32, 35, 40, 45, 50, 90\).

  1. Compute the mean. Round to one decimal.
  2. Find the median.
  3. Find the mode.
  4. Find the range.
  5. Find Q1 and Q3, then compute the IQR.
  6. Sketch a box plot above a number line. Label all five summary values.
  7. Sketch a dot plot or histogram (bins of width 10).
  8. Identify whether 90 is an outlier by inspection and justify in one sentence (e.g., it is far above the rest of the data). If 90 is removed, recompute the mean. Comment in one sentence on which measure of center (mean or median) is more affected by outliers.
  9. Identify which of the following are statistical questions (questions that anticipate variability in answers):

    (i) "How tall am I?"    (ii) "How tall are 6th-graders at our school?"    (iii) "What is the temperature outside right now?"    (iv) "How long does it take 6th-graders to run the mile?"