Which expression is the prime factorization of 72?
Choose an answer to see the worked solution.
Worked solution72 = 8 × 9 = (2 × 2 × 2)(3 × 3) = 23 × 32. Check: 8 × 9 = 72. The option 22 × 33 evaluates to 4 × 27 = 108, not 72.
Grade 7 ILEARN Math Checkpoint 1 Practice
What Checkpoint 1 covers in grade 7, items to try, the mistakes students make most, and the practice that goes with it.
Designed, reviewed, and checked by Greg · 25+ years in the classroom · Updated for 2026-27 · Window Sept 14 – Nov 13, 20266standards
120practice items
24item mock form
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What Checkpoint 1 covers
6 standards, 2 marked essential. Short names in our own words.
- 7.NS.1Additive inverses; sums of rationals
- 7.NS.2Distance as absolute value of a difference
- 7.NS.3Distributive property; signed productsEssential
- 7.NS.4Signed quotients and equivalent formsEssential
- 7.NS.5Prime factorization with exponents
- 7.NS.6Squaring and square roots
Try three items
Pick an answer to see the worked solution.
Evaluate: 6 − (−15)
Choose an answer to see the worked solution.
Worked solutionSubtracting a negative is the same as adding its opposite: 6 + 15 = 21. On a number line, 6 and −15 are 21 units apart.
Which number is a perfect square?
Choose an answer to see the worked solution.
Worked solutionA perfect square is a whole number times itself. 64 = 8 × 8, so 64 is a perfect square. None of 50, 60, or 70 can be written that way.
Where students go wrong
The most common mistake on each standard, and what to do about it, from the teacher pages in the Checkpoint 1 intervention.
Adding magnitudes and attaching a sign afterwards
- What it looks like
- −32 + 19 answered as −51, or as 51. The student adds the two numerals and then decides a sign by which one “looks bigger”, so the size is wrong as well as the sign.
- What to do
- Put both moves on a line before computing. Start at −32 and travel 19 to the RIGHT, because adding a positive moves right. You land at −13. The answer is always between the two numbers when the signs differ, which rules out 51 immediately.
Adding the two values instead of subtracting them
- What it looks like
- The distance between −12 and −5 given as 17. The student reads “both are negative” as “add them” and reports a distance larger than either number is from zero.
- What to do
- Distance is |a − b| — always a SUBTRACTION, whatever the signs. |−12 − (−5)| = |−7| = 7. Sanity-check on a line: two points both left of zero and close together cannot be 17 apart.
Distributing the negative to the first term only
- What it looks like
- −6(2n − 4) simplified as −12n − 24, or −5(2x − 3) as −10x − 15. The multiplier reaches the first term with its sign and the second term keeps the sign it had.
- What to do
- The factor outside multiplies EVERY term, sign included. A negative times a negative is positive, so the −4 becomes +24. Check with a number: at n = 1 the original is −6(−2) = 12, and −12 − 24 is −36.
Making both parts of a quotient negative
- What it looks like
- −(p/q) written as (−p)/(−q). The single minus in front is copied onto the top AND the bottom, which cancels it and silently changes the sign of the value.
- What to do
- One minus sign, one place to put it. −(p/q) equals (−p)/q and equals p/(−q) — three ways to write ONE negative quotient. Putting it in both places makes two negatives, which is a positive.
Stopping before every factor is prime
- What it looks like
- 100 factored as 4 × 52, or 48 as 6 × 8. The product is correct and at least one factor is composite, so it is not a prime factorization.
- What to do
- After writing a factorization, point at each factor and ask “can this be split?” 4 can, into 2 × 2. Keep splitting until every factor is prime: 100 = 22 × 52.
Reading a square root as a halving
- What it looks like
- √100 answered as 50, with the explanation that a root “cuts the number in half”. It agrees with the truth at no value at all, and survives because the answer looks reasonable.
- What to do
- A square root asks “what times ITSELF gives this?” Test the answer by squaring it: 50 × 50 = 2,500, not 100. 10 × 10 = 100, so √100 = 10. Squaring the answer is the whole check.
Get the Checkpoint 1 practice
120 items · 39 pagesCheckpoint 1 Practice + Mock Form
120 practice items at three levels, plus a 24-item mock form.
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72 items · 46 pagesCheckpoint 1 Intervention & Reteach
A teacher page, reteach page, practice, error analysis and exit ticket for each standard.
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See inside the Checkpoint 1 practice
Press play for a 20-second look at the real pages.
Grade 7, window by window
Independent practiceIndependent practice for the Indiana ILEARN Math assessment. Not affiliated with, sponsored by, or endorsed by the Indiana Department of Education. Standard names are short summaries in our own words; see IDOE for the official text.