Grade 6 Math Worksheets for 11-Year-Olds: Fractions, Ratios, Data Handling & Geometry

Instructions

Welcome to your math adventure! Read each question carefully and show your work where needed. Use the coordinate grid for the last section. Good luck!

Section 1: Fraction Frenzy

Solve the following fraction problems. Write your answers in the simplest form.

1. 2/5 + 1/2 =


2. 4 1/3 - 1 3/4 =


3. (3/4 - 1/8) ÷ 1/2 =

Section 2: Ratio & Proportion Puzzles

Use your knowledge of ratios and proportions to find the answers.

1. Complete the equivalent ratio:   4 : 7 = ___ : 21


2. A recipe for 12 cookies requires 2 cups of flour. How much flour is needed to make 18 cookies?

Section 3: Data Detective

Put on your detective hat and analyze the data to solve the mysteries.

1. The number of goals scored by a soccer team in its last 7 games were: 3, 2, 0, 2, 5, 1, 2.
   Find the:
   • Mean: _______________
   • Median: ______________
   • Mode: _______________
   • Range: _______________
2. A class of 30 students voted for their favorite subject. Math received 15 votes. If this data were displayed on a pie chart, what angle in degrees would the "Math" section represent?


3. Describe the pattern and find the next two numbers in the sequence:   1, 4, 9, 16, ___, ___.

Section 4: Grid Adventures

Use the coordinate grid below to answer the questions. The center of the grid is the origin (0,0).

1. Plot and label the points: P(-4, 4), Q(1, 4), and R(1, -1). Connect the points in order from P to Q to R. What type of triangle is PQR?


2. Translate the shape PQR from the previous question 2 units to the right and 3 units down. What are the new coordinates of point P (we'll call it P')?


3. Reflect the original shape PQR across the x-axis. What are the new coordinates of point Q (we'll call it Q')?


4. Rotate the point S(3, 2) 90° clockwise around the origin (0,0). What are the new coordinates of S'?


5. An equilateral triangle is rotated around its center point. What is its order of rotational symmetry?

Answer Key

Check your answers below.

Section 1: Fraction Frenzy

1. 9/10   (2/5 + 1/2 = 4/10 + 5/10 = 9/10)
2. 2 7/12   (4 1/3 - 1 3/4 = 13/3 - 7/4 = 52/12 - 21/12 = 31/12)
3. 1 1/4   ((6/8 - 1/8) ÷ 1/2 = 5/8 × 2/1 = 10/8 = 5/4)

Section 2: Ratio & Proportion Puzzles

1. The missing number is 12.   (To get from 7 to 21, you multiply by 3. So, 4 × 3 = 12)
2. 3 cups of flour are needed.   (The ratio is 12 cookies to 2 cups, or 6 cookies per cup. 18 cookies / 6 = 3 cups)

Section 3: Data Detective

1. Data set: 0, 1, 2, 2, 2, 3, 5
   • Mean: 2.14 (or 15/7)   (Sum is 15, divided by 7)
   • Median: 2   (The middle number in the ordered set)
   • Mode: 2   (The most frequently occurring number)
   • Range: 5   (Highest minus lowest: 5 - 0 = 5)
2. 180°   (Math is 15 out of 30 students, which is 1/2. A full circle is 360°, so 1/2 of 360° is 180°.)
3. The pattern is square numbers (1², 2², 3², 4²...). The next two numbers are 25 (5²) and 36 (6²).

Section 4: Grid Adventures

1. It is a right-angled triangle.
2. P' is at (-2, 1).   (Original P(-4, 4) -> (-4+2, 4-3))
3. Q' is at (1, -4).   (Original Q(1, 4) reflected across the x-axis changes the sign of the y-coordinate)
4. S' is at (2, -3).   (When rotating 90° clockwise, the rule is (x,y) becomes (y,-x))
5. The order of rotational symmetry is 3. (It looks the same after rotations of 120°, 240°, and 360°).