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To get four squares in a row-vertically, horizontally, or diagonally.

How to Play

1. To begin the game, Player 1 moves a marker (green square) to a number in the factor list of numbers 1-9 along the bottom of the game screen.

2. Player 2 then moves the other marker (green square) to any number in the factor list (including the number marked by Player 1). The product of the two marked numbers is determined, and that product is colored red for Player 2.

3. Player 1 moves either marker to another number, and the new product is colored blue for Player 1.

4. Players take turns moving a marker, and each product is marked red or blue, depending on which player made the product. However, if a product is already colored, the player does not get a square for that turn.

5. Play continues until one player wins, or until all squares have been colored.

Credit

This Product Game Investigation was adapted with permission and guidance from Prime Time: Factors and Multiples, Connected Mathematics Project, G. Lappan, J. Fey, W Fitzgerald, S. Friel and E. Phillips, Dale Seymour Publications (1996), pp. 17‑25.

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This applet is the Product Game: a fun, interactive game that exercises your skill with factors and multiples.

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Puzzles and games on a range of operations

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Figure This! Math Challenges for Families - Challenge Index

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Home · Take a Challenge · Challenge Index · Math Index · Contact Us · About Technical Requirements · Printing the Challenges · Family Corner · Teacher Corner PowerPoint Presentation · Video Presentation · En Español · Purchase the CD

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Practice on a range of topics. Do one page at a time. There may be topics that haven't been covered yet.

Doing a Math Minute each day can help students review skills, build fluency, and practice academic vocabulary. Despite their name, students should NOT race through these problems.

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Practice on a range of topics. Do one page at a time. There may be topics that haven't been covered yet.

Doing a Math Minute each day can help students review skills, build fluency, and practice academic vocabulary. Despite their name, students should NOT race through these problems.

Note: No answer key included

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Not Enough Mashed Potatoes (Fractions and Decimals)

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Not Enough Mashed Potatoes (Fractions and Decimals)

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After the lesson, half the classrooms practiced by reciting equations displayed on a whiteboard: "One times three is three, two times three is six..." through to 10. The other half practiced with flash cards. Students had their own personal sets with answers on the reverse side. Both groups spent five minutes practicing three times during the week for a total of 15 minutes. (More details on the experiment's design .)

When the teachers moved on to multiplication by fours, the groups switched. The chanters quizzed themselves with flash cards, and the flash card kids started chanting. All the students practiced memorizing both ways.

The results added up to a clear winner.

On a pre-test before the lesson, the second graders got an average of three math facts right. Afterwards, the chanters tended to double their accuracy, answering six facts correctly. But the flash card users averaged eight correct. Students were tested again a full week later without any additional practice sessions, and the strong advantage for flash card users didn't fade. It was a sign that flash card practice not only produces better short-term memories, but also better long-term ones - the ultimate goal.

The study, " The effect of retrieval practice on fluently retrieving multiplication facts in an authentic elementary school setting ," was published online in October 2023 in the journal Applied Cognitive Psychology. Though a small study of 48 students, this classroom experiment is a good example of the power of what cognitive scientists call "spaced retrieval practice," in which the act of remembering consolidates information and helps the brain form long-term memories.

Retrieval practice can seem counterintuitive. One might think that students should study before being assessed or quizzing themselves. But there's a growing body of evidence that trying to recall something is itself a powerful tool for learning, particularly when you are given the correct answer immediately after making a stab at it and then get a chance to try again. Testing your memory - even when you draw a blank - is a way to build new memories.

Many experiments have shown that retrieval practice produces better long-term memories than studying. Flash cards are one way to try retrieval practice. Quizzes are another option because they also require students to retrieve new information from memory. Indeed, many teachers opt for speed drills, asking students to race through a page of multiplication problems in a minute.

Flash cards can be less anxiety provoking, provide students immediate feedback with answers on the reverse side and allow students to repeat the retrieval practice immediately, running through the deck more than once. Still, kids are kids and they easily drift off task during independent practice time. With a timed quiz, the teacher can be more confident that everyone has benefited from a round of retrieval practice. I'd be curious to see flash cards and quizzes pitted against each other in a future classroom experiment.

As charming as multiplication songs are - I have a soft spot for School House Rock and my editor fondly recalls her Billy Leach multiplication records - they are unlikely to be as effective as flash cards because they don't involve retrieval practice, according to Gino Camp, a professor of learning sciences at Open University in the Netherlands and one of the researchers on the study.

That doesn't mean we should jettison the songs or all the other memorization methods just because some aren't as effective as others. Researchers may eventually find that a combination of techniques is even more powerful. Still, there are limited minutes in the school day, and knowing which learning methods are the most effective can help everyone - teachers, parents and students - use their time wisely.

This story about multiplication flash cards was written by Jill Barshay and produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the Hechinger newsletter .

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Flash cards prevail over repetition in memorizing multiplication tables | KQED

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A team of learning scientists compared two common methods for learning multiplication facts: chanting and flash cards.