Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
An equation such as 8 × ? = 48 is a small puzzle: the equals sign says both sides have the same value, and one of the three numbers is hidden. Third graders learn to find that hidden whole number in multiplication and division equations, wherever it sits. It might be the product (6 × 6 = ?), a factor (8 × ? = 48), the dividend (5 = ? ÷ 3) or the divisor (36 ÷ ? = 9).
Children solve these by thinking about the three numbers that belong together in a fact family. If 8 and 6 multiply to 48, then 48 divided by 8 is 6 and 48 divided by 6 is 8. An equation written backwards, like 5 = ? ÷ 3, often trips students up, so they need to see that the equals sign means "is the same as" and not "the answer comes next." This work quietly lays the groundwork for algebra, where letters replace the question marks and boxes.
Faced with 5 = ? ÷ 3, some students write 15 = 5 ÷ 3 or decide the problem is impossible. Show balance pictures where each side has the same value.
For 8 × ? = 48 a child may multiply 8 × 48. Ask what number of eights makes 48 instead.
In ? ÷ 4 = 6 the missing number is the total being split, so it must be larger than 4 and 6. Students who answer 24 ÷ 6 = 4 have swapped roles.
Many errors disappear if the student puts the answer back into the equation. Make "substitute and check" a routine step.
Find the unknown number: 5 = ? ÷ 3.
Answer: The unknown number is 15.
Number bonds or triangle fact cards (with the product at the top) make it easy to cover one number and ask what is missing. Pair that with balance scales or "same as" statements to strengthen understanding of the equals sign before introducing equations written in unusual orders.
On assessments, look for items with the unknown in every position and with equations written both ways round. Quick daily warm-ups that mix 6 × ? = 54, ? ÷ 7 = 4 and 9 = 63 ÷ ? build flexibility.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 6
8 × 6 = 48, so the unknown factor is 6.
Answer: 28
The unknown is the total. 4 groups of 7 is 28, and 28 ÷ 4 = 7.
Answer: C) 6
54 divided by 6 is 9, because 6 × 9 = 54. So the unknown is 6.
Answer: 36
6 groups of 6 make 36.
Answer: A) 9
9 × 7 = 63, so the missing factor is 9.
Answer: 6
30 split into some number of equal groups gives 5 in each. 6 × 5 = 30, so the unknown is 6.
Answer: C) 8
Some number divided by 2 equals 4. 2 × 4 = 8, and 8 ÷ 2 = 4, so the unknown is 8, not 2.
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.
A full lesson with slides, activities and an exit ticket on finding the unknown number in an equation, pitched to grade 3 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 3.OA.A.4 with an answer key, ready in about a minute.
Make a worksheet →Turn finding the unknown number in an equation into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Multiplication and division equations with three whole numbers, where any one of them may be unknown. Examples from the standard include 8 × ? = 48, 5 = _ ÷ 3 and 6 × 6 = ?.
Symbols such as ?, a box or a blank are typical in grade 3. Letters appear in 3.OA.D.8 for two-step problems and become standard in middle school.