Grade 6: Multi-Step Mixed Challenges
These original challenges combine several skills in one story. Record intermediate results, include units, draw a model or route when useful, and check the final result. Teachers can reveal answers using the existing hidden-answer controls.
Prerequisites: first-quadrant coordinates, central tendency, median-of-halves quartiles, basic probability and decimal money. IQR and monetary token exchange are original extensions.
Journey log: coordinates and statistics
Draw a grid from x = 0 to 20 and y = 0 to 16. Start at (2, 2). Travel east 4, north 6, east 6, south 8, east 8, and north 10 blocks. Record each legโs length as data. For quartiles use medians of lower and upper halves; exclude the overall median if the count is odd.
- Give the location after every leg and the final coordinates.
- Find total distance and shortest horizontal/vertical return distance.
- Find the mean, median and mode of leg lengths.
- Find the range, Q1, Q3 and IQR.
- Add a seventh leg of 30 blocks east. Find the new mean and median.
- Use the original IQR to test whether the 30-block leg is an outlier.
Festival games: probability and money
A fair spinner has 8 equal sectors: 3 red, 3 blue and 2 green. Red wins 2 tokens, blue wins 1 and green wins 0. One spin costs $1. A visitor makes 16 spins: 7 red, 5 blue and 4 green. Tokens can be exchanged at 4 tokens per $1.
- Find theoretical P(red), P(blue) and P(green).
- Find P(at least 1 token) in one spin.
- Find the experimental red probability and compare it with theoretical red probability.
- Find total tokens won and their exchange value.
- Find the visitorโs net money change.
- Would the next spin have to be green to balance the results? Explain.
Source notes
Inspired by the themed, mixed-skill activities in Evan-Moorโs Skill Sharpeners Math series. Stories, values and questions above are original.
- Grade 4: Getting to the Park, PDF page 9 (printed page 7), and the operation path on PDF page 10.
- Grade 5: Contents, PDF pages 3โ4; fraction, decimal, percent, function-table and multistep problems.
- Grade 6: Whatโs Your Range?, PDF page 56; mean, median, mode and range. Quartiles and IQR extend that activity.