Saxon Math Grade 5, Section 5: Expressions Patterns & Coordinate Geometry
In this unit, your child ends the year with algebra-flavored work. They evaluate expressions with parentheses and brackets, build and compare two number patterns, and plot points on a coordinate grid, including the pairs formed from those patterns. Following the geometry and measurement unit, it is where many children first see a pattern turn into a straight line on a graph, a big idea for next year.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
What is my child learning in Section 5?
- Evaluating expressions with parentheses and brackets, like 2 × [12 − (4 + 3)] = 10. Learn more: Solving number sentences with parentheses
- Building two patterns from rules like add 3 and add 9, and comparing how the corresponding terms relate. Learn more: Comparing two number patterns on a grid
- Plotting and naming points on a coordinate grid, reading across to the x-coordinate and up to the y-coordinate. Learn more: Finding points on a grid, like (6, 3)
- Graphing pairs from patterns and real situations, and seeing how the points line up in a straight line. Learn more: Plotting real-life points on a grid
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
Work out (25 - 5) × 3.
- 10
- 70
- 60
How you can help
- Write 2 × [12 − (4 + 3)] on a napkin and ask your child to solve it from the inside out, 10. Then move the brackets and see what changes.
- Build two lists with your child, adding 3 and adding 9 from 0. Ask how each pair compares, then plot pairs like (3, 9) to see a straight line.
- Track something that grows steadily, like reading 10 pages a day. Plot (day, pages) together and ask your child what the point (5, 50) means.
Where kids can get stuck
- Working left to right and ignoring the brackets, so 2 × [12 − (4 + 3)] becomes 23 instead of 10.
- Swapping the order in an ordered pair, so the pattern pair (3, 9) is plotted at (9, 3).
- Starting one list at 1 instead of 0, so the pairs no longer line up term by term.
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
- expression
- Numbers and operation signs written together to show a calculation, like 3 × (4 + 2).
- brackets
- The square symbols [ ] that group part of an expression, often around parentheses.
- pattern
- Numbers that change in a steady, predictable way.
- rule
- What you do to get from one number in a pattern to the next.
- corresponding terms
- Matching partners from two patterns, paired up to compare or graph.
- ordered pair
- Two numbers in parentheses, like (3, 5), that name one point on a grid.
- coordinate grid
- Graph paper with an x-axis and a y-axis for naming locations.
- x-coordinate
- In (4, 7), the 4: the distance along the x-axis.
- y-coordinate
- In (4, 7), the 7: the distance along the y-axis.
Ready to build your child’s confidence with expressions and graphing?
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.
Join the club
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 Saxon Math Grade 5 Section 5 cover?
Saxon Math Grade 5 Section 5 covers these math standards. Each one links to what it means, sample questions, and teaching strategies.
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.