Multiplication strategies seems to be the bulk of third grade math curriculum for my students. They work on understanding the meaning of multiplication and mastering multiplication facts with factors 0-12. Even after students understand multiplication in terms of “equal groups of,” many still need practice to be able to fluently multiply.
Here are some of my students’ favorite multiplication strategies:
1. Use manipulatives to help solidify what multiplication means
I like to use pipe cleaners made into circles to show groups and counters. Students can also put the pipe cleaner circles on white boards and draw in the equal groups. Either way, the pipe cleaners help students clearly see the groups they’ve made. While using manipulatives can take a little bit longer, it is important that students have time to physically demonstrate how multiplication works.
Don’t skip past manipulatives too quickly. When we don’t take the time to make math concepts concrete, misconceptions or misunderstanding can arrive later on. Building a solid foundation will help students moving forward.
Hint: Create a little manipulative bag for students to keep with their supplies. This can save time passing out materials and recollecting them. It can also help students become responsible for their own materials.
2. Focus on one factor at a time
It is important to look at each factor at a time. This allows students to look for patterns and apply certain strategies for each factor. For example, students can look at their 5 facts to see that they always end with a 5 or 0. Students can practice skip counting by 5s to find these answers. I find that this strategy helps students grow their confidence. I like to introduce multiplication factors in this order: 2, 5, 10, 1, 0, 3, 4, 6, 8, 7, 9, 11, 12.
Hint: Use a multiplication chart to take a look at patterns. Use these multiplication chart worksheets for each factor that helps isolate different patterns for each factor. This is a great way for students to practice their facts and discover the patterns on their own.
3. Skip Counting
Skip counting can be a great strategy for students. As mentioned above, many students will skip count to solve for 2,5, or 10 facts. Most students can count by 2s, 5s, and 10s automatically. However, skip counting by 4s, 6s, or 7s can be more challenging. I teach my students that they can skip count one time on the top of their papers or on a sticky note as a resource to take a peek at later. For instance, if students are working on their 7 facts, they can write down how they skip count by 7. Their skip counting list would say” 7, 14, 21, 28, 35, 42, 49, 56, 63, 70. If needed, they can count up on their fingers to figure out what 7 comes next. Once they have their skip count line, they can count over to find the product. For example, for 7 X 6, see which number is 6th on the list.
Hint: Have students recreate their skip counting list to help make the pattern become more automatic. Encourage students to skip count out loud while using their list or notecard. This will help students become more comfortable with the different multiples of a given factor.
4. Decompose, decompose, decompose
Once when students have mastered some of the “easier” facts, decomposing allows students to use their known facts to solve for more difficult problems. This strategy can also be applied to larger numbers past basic facts.
When my students decompose a factor, I have them draw in an “alien head” to show how the number can be decomposed. Students circle the number to decompose and add 2 circle antennas above. Inside the “antenna” circles, students write the 2 numbers that can be added together to equal the original factor. We like to tap on each part of the equation as we rewrite the decomposed equation. I tell students to multiple factor X one alien antenna + factor X the other alien antenna.
Hint: Show students how factors can be decomposed in different ways. Discuss why some ways to decompose numbers are easier than others. For example, decomposing 7 into 5 and 2 might be easier than decomposing as 6 and 1 because 6 facts can be more challenging than 5 and 2 facts.
These are some of my class’s and my favorite multiplication strategies. What ways to do you love? Anything you would add to the list?
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