Illustrative Mathematics Grade 5, Unit 7: Shapes on the Coordinate Grid
In this unit, your child plots points on the coordinate grid and uses it for real situations, compares two number patterns by graphing pairs of their terms, and classifies quadrilaterals and triangles by their properties. A recurring question: which shapes always belong to a category, and which only sometimes? It follows the decimal and whole-number unit and leads into a final unit that puts the year together.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
What is my child learning in Unit 7?
- Graphing pairs of terms from two patterns, like add 4 and add 2, and describing how the patterns relate. Learn more: Comparing two number patterns on a grid
- Plotting points and drawing shapes on the coordinate grid, using ordered pairs to name each vertex. Learn more: Finding points on a grid, like (6, 3)
- Using the coordinate grid to solve real problems, like plotting distance and time, and explaining each point. Learn more: Plotting real-life points on a grid
- Reasoning that if all rhombuses have four equal sides, then every square, being a rhombus, does too. Learn more: Why a square is also a rectangle
- Sorting quadrilaterals and triangles by sides and angles, deciding which shapes always or sometimes belong to a category. Learn more: Sorting four-sided shapes into a family tree
Sample questions to try together
These are real questions from our practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
Ana and Luis both start with $0. Each week, Ana saves $5 and Luis saves $10. When Ana has $15, how much does Luis have?
- $25
- $40
- $30
How you can help
- Give your child ordered pairs to connect on graph paper, like (1, 1), (5, 1), (5, 4), and (1, 4). Ask what shape it makes and how they know.
- Ask “always, sometimes, or never?” on a walk or ride: Is a rhombus a square? Is a square a rhombus? Let your child explain each answer using sides and angles.
- Make two lists with your child, adding 4 and adding 2 from 0. Plot pairs like (4, 2) and (8, 4), and ask how each first number compares with its partner.
Where kids can get stuck
- Saying a rhombus is always a square because both have four equal sides.
- Plotting a shape's vertices with the coordinates swapped, so the rectangle lands in the wrong place.
- Ignoring the scale on an axis, so a line marked in 10s is read as counting by 1s.
Practice makes perfect
Bobby's Math Club has practice problems that adapt to your child’s level, each with a detailed explanation and an easy-to-follow video, so your child can build confidence in these skills one step at a time.
Words your child will hear
- coordinate grid
- Graph paper with an x-axis and a y-axis for naming locations.
- ordered pair
- Two numbers in parentheses, like (3, 5), that name one point on a grid.
- vertex
- A corner point where two sides of a shape meet.
- quadrilateral
- Any flat shape with four straight sides.
- rhombus
- A parallelogram with four equal sides, which may or may not have right angles.
- parallelogram
- A four-sided shape with two pairs of parallel sides.
- trapezoid
- A four-sided shape with at least one pair of parallel sides.
- category
- A group of shapes that share the same properties.
- corresponding terms
- Numbers in the same position in two patterns, like the third number in each list.
Ready to build your child’s confidence with shapes on the coordinate grid?
In Bobby's Math Club, your child practices these skills at just the right level, with a hint when they need one, a clear explanation after every question, and kid-friendly videos. Unlimited practice is free.
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Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
Which math standards does Illustrative Mathematics Grade 5 Unit 7 cover?
Illustrative Mathematics Grade 5 Unit 7 covers these math standards. Each one links to what it means, sample questions, and teaching strategies.
- 5.OA.B.3: Make two number patterns from two rules, and compare them.
- 5.G.A.1: Find and plot points on a coordinate grid, like (6, 3).
- 5.G.A.2: Graph points on a coordinate grid to solve real-life problems.
- 5.G.B.3: Know that a square has everything a rectangle has, because it is one.
- 5.G.B.4: Sort shapes into families by their sides and angles.
For teachers: Unit names and order vary between editions and districts, so your school’s own materials have the exact sequence. Learn how Bobby's Math Club can help your students grow.