Balance Scale Equations Worksheet – Visual Algebra
- Grades
- Grades 6–7, Middle School
- Pages
- 4
- File type
- Answer key
- Included
- Subject
- Math, Algebra
- Topic
- hands-on math, equations
- Resource types
- Worksheets & Printables, Worksheets
- Answer key
- Included
About this resource
What's inside this resource
This balancing algebraic equations worksheet uses a hanging balance scale to show grades 6 and 7 why solving an equation means doing the same thing to both sides. Lidded boxes labeled x and round counters worth 1 sit on each pan, so students can see, count and cross off their way to the value of x.
A worked example on page 1 walks through 2x + 3 = 11 with a four-row frame: write the equation, record what is left after removing counters, find x, then check. Students then move through six short parts that change the kind of thinking each time.
What students do
- Part A: read four one-step scales, write each equation and find x
- Part B: solve three two-step scales using the equation, after-removing, x and check rows
- Part C: decide whether four moves on 2x + 6 = 14 keep the beam level or tip it, then explain one
- Part D: draw boxes and counters on empty scales to match two equations, then solve
- Part E: find the step where a student subtracted 4 instead of dividing by 4, and correct it
- Part F: a challenge scale with boxes on both pans, 3x + 1 = x + 11
Format: 4 pages (3 student pages and 1 answer key) with 16 tasks. You get two files: a full color copy and a black and white copy that prints cleanly on any printer. The answer key follows the same part names and item numbers and lists every equation, value of x and check.
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In the classroom
Teaching tips & learning objectives
Learning objectives
Write the equation shown by a balance scale with boxes and counters, such as x + 5 = 9 or 3x = 18.
Solve two-step equations like 3x + 2 = 17 by removing equal counters from both pans and then sharing the rest among the boxes.
Judge whether a proposed move keeps an equation balanced and explain why an unequal change tips the scale.
Teaching tips
Go through the page 1 worked example together so students see every row of the four-row frame filled in before they start Part A.
Ask students to cross off counters on the printed pans in Part A and Part B; the crossed-off picture makes the matching step easy to check.
Point out that a scale may show the box on the right pan, as in item 2 (12 = x + 7), and that the equation can be written either way round.
Skills covered
Modeling equations: students turn a picture of boxes and counters into a written equation, then into a value of x.
Inverse operations: two-step items have students take away equal counters first and then share what is left, which mirrors subtracting and then dividing.
Reasoning about equality: Part C asks which moves keep the beam level, so students explain the rule rather than just apply it.
Good to know
Questions teachers ask about this resource
What grade levels is this balance scale worksheet for?
It is written for grades 6 and 7, when students first solve one-step and two-step equations. The picture model also makes it a good reteach for older students who need a visual approach.
How many problems are included?
There are 16 tasks plus a worked example: four one-step scales, three two-step scales, four keep-level judgments with one explanation, two draw-the-scale items, one find-the-mistake item and one challenge with boxes on both pans.
Is there an answer key?
Yes. Page 4 gives the equation, the value of x and the check for every item, using the same part names and numbering as the student pages.
What formats are included?
Two printable PDFs: one in full color and one in print-friendly black and white. Students work on paper, which suits the two drawing items in Part D.
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Curriculum
Standards, concepts & topics
Standards
Standards
- 6.EE.B.7 — Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers
- 7.EE.B.4 — Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
Core concepts
Core concepts
balance model of equality
inverse operations
one-step equations
two-step equations
variables on both sides
Topics
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