Differentiate with 3 versions of one mystery picture
Give each student the same picture at the level they are ready for: integers in the first quadrant, integers in all four quadrants, or decimals and fractions. Everyone draws the same picture, so the reveal is shared and one answer key checks every sheet.
Last updated 19 October 2026. Written by the Plotpicture team.
The 3 versions
- Version A, integers in the first quadrant. Whole numbers, both positive. The level of the first quadrant standards: grade 5 in the US, year 4 in England.
- Version B, integers in four quadrants. The same picture moved so it sits across the axes, so about half the pairs have a negative x, a negative y or both. Grade 6 in the US, year 6 in England.
- Version C, decimals or fractions. The same picture with each square worth 0.5, 0.25, a half, a quarter or an eighth, in one quadrant or four. Good practice in placing rational numbers for grades 6 to 8.
Worked example: one point of the house
The house starter has 44 points. Its second point reads:
- Version A: (20, 2)
- Version B: (8, −10)
- Version C at 0.25 a square, first quadrant: (5, 0.5)
- Version C in halves, four quadrants: (4, −5)
All four land on the same spot of the picture. In version B the picture is moved 12 squares left and 12 squares down so it sits across the axes, x from −12 to 12 and y from −12 to 12. Each square is 1.
Running a mixed lesson
- Print all 3 versions from one drawing; a single PDF can hold them in order.
- Hand out the versions by need, or let students pick and move up if they find it easy.
- Give one shared instruction about order and Lift pen; the lists have the same Lift pen marks in the same places.
- Check the first 3 points of every sheet against the answer key for its version.
- Reveal together: every student has the same picture, whatever the numbers were.
The next time you use a picture, move each student up one version if their first sheet was clean. Over a term, the same handful of pictures can carry a class from first quadrant integers to fractions in four quadrants, and students who finish early always have a next step that uses the picture they already know.
Common mistakes
- Checking a version B sheet against the version A key. Each version has its own key; the grids are labelled differently.
- Moving a student to decimals before four quadrants are secure. Two new things at once is twice the confusion.
- Drawing on half squares and expecting integers. Points between grid lines are flagged in A and B; snap them or keep them for C.
- Forgetting the label spacing. Fractions take room, so a large grid may need labels every 2 lines; the maker says when.
Sources
- Grade 5, Geometry: graph points on the coordinate plane, Common Core State Standards Initiative. Last reviewed 19 October 2026.
- Grade 6, The Number System: points in all four quadrants, Common Core State Standards Initiative. Last reviewed 19 October 2026.
- National curriculum in England: mathematics programmes of study, Department for Education. Last reviewed 19 October 2026.
Frequently asked questions
Do students notice they have different sheets?
Some do. The version letter is printed small at the top of each page. Many teachers let students choose, or move a student up a version partway through the term.
Is the picture really the same in every version?
Yes. Every version is made from the same drawing, point for point, so the pictures match line for line. Version B is the same picture moved; version C is the same picture with each square worth less.
Which version should I give a student who finishes early?
The next one up. They already know the picture, so the new challenge is only the numbers.
Make the worksheet
The mystery picture maker draws, traces and prints all 3 versions; the rules it follows are on how it works, and the other guides cover the rest of the lesson.