Nancy Anderson, EdD
Mathematics Teacher ~ Author ~ Consultant
1. Focus on one phase at a time. (See "" for more information on the phases of fact fluency.) Print the cards and talk with students about what they notice. Talk about how to read a multiplication expression as number of rows "times" number in each row.
2. Help students write the product on the back of each card.
3. When you get to Phase 2 (or Phase 4), encourage students to notice that the array is split into smaller parts that encourage them to “see” a related well-known fact and use that fact to find the unknown product. Encourage students to rely on the array -- and not memorization or tricks -- to find the product.
4. Note that the “turnaround” fact fluency cards do NOT feature an array because each is the “turnaround fact” for its related fact. Prompt students to connect these facts to ones she or he already knows.
5. The 9× facts are on the same cards as the 10× facts to encourage students to use 10 groups of a number to find 9 groups of a number. For example, we can find 9 × 4 by thinking of 10 groups of 4 minus 1 group of 4 (so, 9 × 4 = 40 - 4 = 36).
6. The arrays on the final four cards are not divided. Students should choose a strategy to find the product. For example, students might compute 5 × 7 by thinking of 4 × 7 plus another group of 7.
For more information, see the article “Fluency without Fear” by Stanford University Professor Jo Boaler. The article is available at the following link: https://www.youcubed.org/fluency-without-fear/