Free · Grades 3–4 · 4 sections · 18 questions
Factors, multiples, and the patterns that show they are the same relationship read from two ends.
The answer key prints on a separate page.
Factors and multiples are one relationship, not two, and children who learn them a week apart often never notice: 4 is a factor of 12 and 12 is a multiple of 4 say the same thing. Putting both on one paper is what makes the symmetry visible, and the pattern section is there to make it useful — a child who can continue 4, 8, 12, 16 is listing multiples whether or not the word is on the page.
The reliable diagnostic is a factor list that stops early. Asked for the factors of 36, a child who writes 1, 2, 3, 4, 6 has understood the idea and lost the search: pairs run inward from both ends and meet, and the ones above 6 are just the partners of the ones below it.
Multiplication & division basics On the paper: Multiplication facts · Division with remainders · Word problems. Open this test 
Multi-digit multiplication On the paper: Multi-digit multiplication · Word problems. Open this test 
Decimals unit test On the paper: Decimal place value · Comparing decimals · Decimal arithmetic · Word problems. Open this test