Math Foundations
Strengthen number sense, fractions, ratios, expressions, equations, geometry, and data—the bridge from middle-school math to high-school success.
- Problem types
- 634
- Practice variants
- 2,536
Page 10 of 18
Each problem type has four distinct practice variants. Open a preview to move among all four.
Compare cases by evaluating an expression
Evaluate algebraic expressions correctly using substitution and order of operations.
Apply the same cost rule separately to each customer rather than comparing drink counts alone. Substitute each input, multiply by the per-drink amount, and include the fixed charge in both …
Preview problemEvaluate from a variable-value table or key
Evaluate algebraic expressions correctly using substitution and order of operations.
Read each table row as a precise variable assignment before substituting. Put seven in a’s position and five in b’s position, preserving the coefficient and subtraction in the original expression. …
Preview problemTurn an algebraic expression into arithmetic form
Evaluate algebraic expressions correctly using substitution and order of operations.
Keep the negative replacement intact by writing it in parentheses wherever x appears. The coefficient still means multiplication, so evaluate that signed product before carrying out the subtraction. Report the …
Preview problemTranslate structured variable information into evaluation work
Evaluate algebraic expressions correctly using substitution and order of operations.
Match each letter to its own value card entry, keeping q’s negative sign in parentheses and retaining its coefficient of three. Write the full numerical substitution before calculating, then multiply …
Preview problemScreen a mixed set for correct evaluation work
Evaluate algebraic expressions correctly using substitution and order of operations.
First establish the correct chain from substitution through the intermediate arithmetic to the final value. Test every labeled line against that chain: a line may be valid at any stage, …
Preview problemChoose a valid first step and evaluate
Evaluate algebraic expressions correctly using substitution and order of operations.
A valid first step replaces x inside the existing parenthesized difference while leaving the outside factor and separate constant where they began. Compare each candidate by that structural test before …
Preview problemCombine like variable terms
Combine like terms and simplify expressions while preserving structure.
Both terms count copies of the same variable quantity, so they are like terms. Add only their coefficients and keep the shared x factor unchanged; addition does not multiply the …
Preview problemCombine variable terms and constants
Combine like terms and simplify expressions while preserving structure.
Sort the expression into two like-term groups before calculating: terms carrying x belong together, while plain numbers belong together. Add the x-coefficients and the constants separately, then keep those two …
Preview problemCombine like terms with negatives
Combine like terms and simplify expressions while preserving structure.
Carry every sign with the term that follows it before regrouping. The two x-terms have matching variable parts, while the two subtracted numbers are negative constants in a separate group. …
Preview problemPreserve unlike terms while simplifying
Combine like terms and simplify expressions while preserving structure.
Classify terms by their complete variable part: x-terms combine only with x-terms, y-terms only with y-terms, and the constant remains separate. Keep the subtraction signs attached, including the understood coefficient …
Preview problemModel and simplify a context expression
Combine like terms and simplify expressions while preserving structure.
Model each sales source exactly once before simplifying: lunch and after-school sales produce two like x-terms, while the door contributes a fixed count. Add all three contributions, combine only the …
Preview problemSimplify a total measure expression
Combine like terms and simplify expressions while preserving structure.
The total path includes every listed section, so begin by adding all four measures. Regroup the two variable lengths and the two fixed lengths, then combine each pair separately. A …
Preview problemBuild a simplified expression from a table
Combine like terms and simplify expressions while preserving structure.
Translate every location into one term before combining. The two room entries share the x variable and can be combined by adding coefficients, while the office’s seven folders form a …
Preview problemTranslate term cards into a simplified expression
Combine like terms and simplify expressions while preserving structure.
Write the five cards as an addition expression exactly as given before simplifying. Group the three variable cards and total their coefficients, remembering that the two-x card represents two copies, …
Preview problemTranslate a term description into a simplified expression
Combine like terms and simplify expressions while preserving structure.
Translate the description term by term: the two groups of x-copies form like variable terms, followed by a separate subtraction of two. Add the coefficients on the x-terms, but keep …
Preview problemCheck which simplified forms are truly equivalent
Combine like terms and simplify expressions while preserving structure.
Group the two x-terms with their signs and combine the constants in a separate group. After simplifying both, check the stronger requirement that the form is fully simplified: no like …
Preview problemChoose a valid like-term move and simplify
Combine like terms and simplify expressions while preserving structure.
Treat each proposed first move as a claim about structure: terms belong together only when their variable parts match exactly. Once a valid grouping is identified, reorganize the entire expression …
Preview problemExpand with distribution
Use the distributive property to expand and factor simple linear expressions.
Think of the outside factor as counting three identical copies of everything inside the parentheses. That means it creates one product with the variable term and another with the constant …
Preview problemExpand and simplify
Use the distributive property to expand and factor simple linear expressions.
Use two stages here: first remove the parentheses by multiplying the outside factor by both terms inside, while carrying along the separate x-term. Then scan the expanded expression for like …
Preview problemFactor out a common factor
Use the distributive property to expand and factor simple linear expressions.
Factoring runs distribution backward. Since six is the required common factor, place it outside a pair of parentheses and divide each original term by six to determine what remains inside. …
Preview problemFill in a missing distribution or factoring step
Use the distributive property to expand and factor simple linear expressions.
The displayed variable term accounts for one of the two products created by distribution. Trace the blank back to the other term inside the parentheses: the outside four must multiply …
Preview problemUse distribution in a repeated-groups context
Use the distributive property to expand and factor simple linear expressions.
Model one bag as a single grouped package containing both its variable number of candies and its two stickers. Because there are five identical bags, five multiplies that whole package. …
Preview problemConnect area and distribution
Use the distributive property to expand and factor simple linear expressions.
Read the diagram as one rectangle split into two side-by-side pieces. Both pieces share the height of three, so that height multiplies each width section and creates two partial areas. …
Preview problemUse factoring to show shared structure in context
Use the distributive property to expand and factor simple linear expressions.
The total is built from four equal bundles, so four should be the common factor that sits outside the group. Divide each term of the total by four to recover …
Preview problemTranslate an area model into symbolic form
Use the distributive property to expand and factor simple linear expressions.
The two colored sections are parts of one rectangle, so first combine their side-by-side widths into one grouped total width. Then use rectangle area: the shared height multiplies that entire …
Preview problemTranslate grouped language into symbolic form
Use the distributive property to expand and factor simple linear expressions.
Start by keeping one group's variable and constant together inside parentheses. Four groups means the four multiplies that entire quantity, not just its first term. Distribution then turns the repeated …
Preview problemCheck which forms are equivalent
Use the distributive property to expand and factor simple linear expressions.
Create one dependable comparison form by distributing the three across the original group. Then test every labeled expression against the entire structure, remembering that reordering addends does not change a …
Preview problemChoose the best direction for the distributive property
Use the distributive property to expand and factor simple linear expressions.
Let the desired form determine which way to use the distributive property. The expression begins as a sum, but the goal is to reveal five equal groups, so look for …
Preview problemUndo addition or subtraction in one step
Solve one-step equations and interpret the solution in context.
View the equation as a balanced statement with seven added to the unknown. Isolate the unknown by undoing that addition, and perform the same subtraction on both sides so the …
Preview problemUndo multiplication or division in one step
Solve one-step equations and interpret the solution in context.
The coefficient means the unknown has been multiplied by four, not increased by four. Use the inverse operation by dividing both sides by that coefficient; this leaves one copy of …
Preview problemSolve one-step equations with negatives
Solve one-step equations and interpret the solution in context.
Keep the negative sign attached to the number on the right as you work. Since five is subtracted from the unknown, add five to both sides to undo that operation …
Preview problemSolve and check a one-step equation
Solve one-step equations and interpret the solution in context.
First undo the added nine with equal subtraction on both sides to isolate the variable. The verification is a separate step: replace the variable in the original equation with the …
Preview problemSolve an additive context equation
Solve one-step equations and interpret the solution in context.
Separate the story into a starting amount, a change of six more stickers, and a final total of fourteen. Write the unknown start plus the increase as equal to the …
Preview problemSolve a framed multiplicative context equation
Solve one-step equations and interpret the solution in context.
The total comes from four equal boxes, so model it as four times an unknown per-box amount. To recover one box's share, divide the total equally among the four boxes. …
Preview problemSelect and solve a one-step context equation
Solve one-step equations and interpret the solution in context.
Define the unknown as the class size before anyone joined. Because four students join and the count then reaches eighteen, the valid equation must show the start increasing by four, …
Preview problemJudge a solution check
Solve one-step equations and interpret the solution in context.
Evaluate the claim by replacing x with Mia's stated value in the original equation and comparing the two sides numerically. If they differ, the claim is invalid regardless of how …
Preview problem