Welcome to Part 3 of MathBait™ Multiplication, our final installment for students learning and building fluency with one digit products. Don't be too sad! What lies ahead is a treasure trove of 20 activities and 9 digital games! We also have loads of great content on the way as we advance to multi-digit multiplication and prime numbers which continue to aid in fluency as well as support a solid foundation for higher math. Get ready to have an absolute blast learning!
Thus far, students became confident in skip counting before advancing to processing two pieces of information (the number of groups and how many items in each group). Now, we shift our focus to formally multiplying. In the following lessons, students will be introduced to the multiplication symbol and continue to build on their previous understanding to master their multiplication skills.
Prerequisites
Students should complete MathBait™ Multiplication Parts 1 and 2. They should be able to fluently skip count by 2, 3, and 5 and are beginning to strengthen their ability to count by 4, 6, 8, 9, and 10. Students should also be able to answer simple questions such as "if I count by 3's five times what number do I stop on?". It is okay if students are still using their fingers. Finally, students should be familiar with the word multiple and be able to determine if small values are multiples. For instance, is 14 a multiple of 2? Students can confirm 14 is a number said when we skip count by 2's and is thus a multiple of 2.
If students are not ready for Part 3, that is okay! It is better to take it slow than rush things. Spend more time on Part 2 until students feel confident in their skip counting, their ability to recognize multiples, and to determine the total number of items.
Goal
In MathBait™ Multiplication Part 3, students will be introduced to the multiplication symbol. They will continue to build fluency through novel activities. While in some lessons students will multiply directly, many activities build fluency through creating multiple pathways to access products. This not only strengthens student recall of basic facts, but also helps prepare them for algebra and other activities in which they will utilize their multiplication knowledge for problem solving.
It is highly recommended that students play all the games provided here multiple times over a few weeks. Spiraling back to earlier games will help develop a strong fluency and multiple methods of accessing their multiplication facts.
Select a lesson to view details. We recommend students play in the order provided for graduated levels of fluency. Bookmark this page to easily return for spiral review or a fun change of pace.
Symbols and Scale
In this lesson, students will practice finding the missing value. The purpose of these activities is to strengthen fluency by providing different perspectives of multiplication facts.
Warm Up: Using Symbols
Begin by telling students that we often use symbols to avoid having to write so much. Allow students time to think of a symbol they are familiar with. If needed, explain to students that a symbol is a small picture, drawing, or shape that has a meaning. Students may instantly think of emojis which are a great example. Allow students to share a symbol and what it means. For instance a heart can convey love while a knife and fork might indicate a food court or meals nearby. Signs on the road often have symbols. This can be a quick or in-depth conversation depending on where students take it and time available.
Draw out a large X and tell students this is the symbol for multiples. Wait to use the term "multiplication". Explain that when we see something like 3×4, it is asking us the fourth number or the fourth multiple when counting by 3's. Order matters here. Draw back to the Hide and Seek game from MathBait™ Multiplication Part 2. When we move to row 3 we are counting by 3's. In other words, 3×4 is the same as going down to row 3 and counting over 4 spaces. At this time, we recommend calling the × symbol "ex". This avoids confusion and having to process too much information. Some students may already be familiar with the notation, but for students new to multiplying, allow them time first to practice with the notation before introducing terminology.
Ask students to write 3-4 statements like 3×4 and trade with a partner. Students should find the total for each statement. For instance, in 3×4 students will identify the fourth number said when counting by 3's (12). The goal here is to make multiplication easy and approachable by leaning on existing understanding. We are not doing anything new, but rather finding an easier way to communicate. Writing out "what is the 5th number we say when counting by 4's" is a lot. Now, we can simply write 4×5 to mean the same thing.
If time permits, return to MathBait™ Multiplication Part 2 and play a group round of Hide and Seek. Replace each clue the dragon gives with a multiplication statement. For example, if the dragon says, "I start at 5 and hop 4 spaces", have students identify this as 5×4 and find the value of 20.
Activity 1: What's That Called?
In this activity, we will provide students with the terminology for the × symbol. This is an investigation to allow students to feel like they have discovered the name on their own and to help make sense of the new terminology.
Draw out the large X on the board and ask students to share what this means. Drawing on the Warm Up, students should recall this is the symbol we use for skip counting. A statement such as 4×5 tells us to find the 5th number when skip counting by 4's.
In the Warm Up, we called this symbol "ex", because it looks like an X! But, later we will see there are many symbols we can use. Some people use a dot. Write out 4·5. Explain that in middle school, we no longer use the × and instead use a dot. Some people use parentheses like 4(5). While we don't care much about the different ways to write ×, we shouldn't call it "ex" because it doesn't always make an ex!
Provide students with their skip counting chart. Have each student write out a statement like they did in the warm up (such as 3×4). Remind students of the activity in MathBait™ Multiplication Part 2 where they made squares on their chart. This time, we will make rectangles.
With a colored pencil or crayon, ask students to draw out the rectangle that matches their statement. It can be helpful to model for students. For example, if we picked 3×4, I'll go down to row 3 and trace out 4 over. Next, complete the rectangle starting in the top left corner.
Ask students to count the number of small 1-by-1 squares in their rectangle. What do they notice? Here are a few key points to highlight:
There are 12 squares in a 3×4 rectangle and 12 is the 4th number said when skip counting by 3's.
The rectangle is 4 tall and 3 wide, which are the numbers we used.
Explain to students that we often describe a rectangle by how big it is. We would call this rectangle 3-by-4 because it is 3 wide and 4 tall. For this reason, we often call the × symbol "by". Allow students to each say the statement they selected using the word "by".
Another word we can use for the × symbol is "times". If possible, place students in small groups and allow them 5-7 minutes to come up with an idea why we might call this symbol times. After their discussion, ask students what something like 5×6 means. Students should recall this meant the 6th number we say when counting by 5's. It's like we count 5 how many times? "6!".
Conclude by explaining we can say 5×6 as "5 times 6" because it is telling us to count by fives six times. We call this multiplication. Allow students to guess at why we might call this multiplication. Explain or bounce off student comments to note that when we multiply we are finding multiples. Five times six is asking us to find the 6th multiple of 5, so we are multiplying.
If time permits, allow students to practice with a partner. Each student writes a multiplication statement such as 3×6 and they practice saying 3×6 in multiple ways: "3 times 6", "the 6th number counting by 3's", "counting by 3, 6 times", "3 by 6 (like a rectangle)". Explain it is not necessary that students remember all the different ways to say the same thing, our goal is to recognize these words and understand the meaning behind the words. They can pick the way they like best to communicate.
Activity 2: What is Multiplication?
Now that students have been formally introduced to the multiplication symbol as well as the term "multiplication", this is a great time to dive into what multiplication means. Notice we have intentionally held back on this previously. Our program waits to introduce the meaning of multiplication and ways to interpret products until students already feel confident in their skills from building on skip counting. This helps reduce cognitive dissonance and misunderstandings and promotes a positive feeling around fact fluency and multiples.
The best way to explain multiplication is for students to "discover" the meaning on their own. This activity is designed as an exploration; allow students to drive the conversation and share their thoughts.
Provide students with graph paper. This activity can be completed with coloring, cutting, or folding. You may allow students to select their medium or choose a medium that works best for your classroom.
We will be counting by 3's. If coloring, have students color bars of length three to create a graph up to about 12. For cutting, cut out the bars, and if folding, provide students with four bars of length 12 and allow them to fold to create the multiplies of three. (Note: if cutting or folding, little hands may have difficulty with small pieces. You can create wider three-strips to help accommodate developing fine motor skills).
Ask students what they notice and wonder about the bars they have created. They created the bars using skip counting, is there another way they know how to make 3, 6, 9, and 12?
The goal is to lean into repeated addition and help students to see that skip counting is simply adding the same amount each time. When we count by 1's, we are adding 1 (demonstrate if needed, starting at 1, 1+1=2, 2+1=3, ...). Counting by 2's can also be accomplished by adding 2, and so on and so forth. In this way, multiplication can save us a lot of time. Is it easier to write 3+3+3+3+3 or 3×5?
Continue the conversation and ask students to compare their 3-bar and their 6-bar, what is similar and what is different? The goal of this conversation is to help students see the 6-bar is constructed of two 3-bars and is thus twice the size. If students are not familiar with words like "twice", this is a good time to introduce the terminology. You might ask how many of the 3-bars can fit into one 6-bar. Explain that multiplication has the power to "scale" items or change their size. We love to use a Honey, I Shrunk the Kids or similar example to imagine taking something and drastically increasing its size.
The purpose of this activity is simply to allow students to play with the idea of multiplication. They have already mastered skip counting, now it's time to think about how this power is useful. If time permits and students would benefit from additional exploration, encourage them to be the wizard and cast enlargement spells on items. Students can begin using graph paper to draw an item (like an apple, ant, flower, etc.) and then use their wizardry to enlarge the item. Use the markings on the graph paper to help guide them. For instance, to turn an ant that is 3 squares long 5 times its size we would need to make the length that of five 3-bars (or 15).
Once students have a good feel for how their skip counting skills can be used as repeated addition and scaling, move on to Activity 3.
Activity 3: Emoji Mystery
In this activity, students practice using symbols to convey meaning while also building their multiplication facts. Players are given three emojis, each emoji is a symbol standing in for a number from 1 to 10. They must use the clues to decode the number hiding behind each symbol.
For example, in the instance 😄×😍=30 and 😍×😔=48, students can deduce that both statements contain the symbol 😍. They can "hunt" through the chart to identify a common row or column that contains both 30 and 48 to find both are multiples of 6. From there, they determine what times 6 leads to 30, finding 😄=5 and what times 6 leads to 48 to determine 😔=8.
For graduated fluency, allow students to begin with both "Show Table" and "Show Hints" turned on to use their detective skills with the multiplication grid. As they improve, challenge them to turn each off. They may continue to use skip counting or other strategies. In gaining exposure and playing with the chart, students are continuously building more and more familiarity without learning anything new.
Play
©MathBait created with GeoGebra
Activity 4: Growth Laser
The purpose of this activity is to encourage students to consider multiplication as scaling. Until this point, multiplication has been viewed through the lens of skip counting with a brief introduction to repeated addition and scaling. Now, students have the chance to experiment with multiplying in a new and fun way.
Start by providing students with graphing paper. Have them draw a segment that is 2-3 boxes or units long. Explain they will create a growth laser. This is a machine that can increase the size of something. For younger students, stick to whole numbers, however, for older or more advanced students they will learn this machine can create any size by using rational values. For instance, taking a 3-unit segment and multiplying it by 5/3 can turn it into a segment of length 5. If students are not working with fractions, explain this laser will increase the size of items by making copies. To create a segment twice as long, we must set the dial to 2 and it will multiply the segment by 2.
Allow students to draw their new segment. This might come intuitively to some students and others may have more of a struggle with spacial reasoning. Remind students that to "double" means to make two of. Next, ask students to set their growth laser to 3 and draw the result. Continue upwards to 10 (maximum power) and have students make a table of their results. What do they notice? Help students to see this is a skip counting table, the length of the new segment is exactly how many 2's (or 3's depending on their initial segment) they have counted.
In our digital game, students have a growth laser and must help the Dino grow to save their babies. Level one is direct multiplication, in level two students begin to refine their skills by thinking about the closest multiple.
Play
©MathBait created with GeoGebra
Benefits
In this lesson, students were introduced to the multiplication symbol. This should be an easy transition from their previous knowledge, as in Part 2 students practiced determining facts such as "6 groups of 2 gives us 12". Now we will represent this same idea as 2×6=12. It is much easier to gain student buy-in from the position that we are saving time and making something easier, rather than introducing something new and making things more complicated. By using the perspective of 2×6 is much easier to write than "the number we get by counting 2's six times", the notation is an extension of their existing knowledge that makes things more pleasant for them.
In Emoji Mystery, students continue to use a completed multiplication table to support their growth. This is akin to Hide and Seek from MathBait™ Multiplication Part 2 as they are exploring and gaining additional exposure to the multiplication table without any expectation of memorization. Students build problem solving skills by seeing two multiples of a number and determining what the number is before identifying the missing factor.
Finally, in Growth Laser Rescue, students will use multiplication facts directly. They may continue to use their fingers or count up. For instance, if the Dino is 4ft and the building is 28 ft, students may count up by 4's to determine how to set the laser. We want to continue to expose students to the topic in a fun and non-threatening way. If needed, allow students to continue to use a completed multiplication chart and encourage them to call on it less and less. In level 2 of Growth Laser, students build a higher level of fluency as they consider values close to multiples.
Missing Numbers
A Quick Note
Multiplication BINGO!
Table Mash Up
An Ode
Centipede
Distribution
Conclusion
MathBait™ Multiplication Part 3 is a beast! Designed for students who have completed Parts 1 and 2, or for students in need of additional fluency practice, Part 3 helps encourage students to learn, explore, and play! Throughout MathBait™ Multiplication, each lesson provides novel activities helping students to grow their understanding. Rather than simply memorizing products, they find relationships between values, look for what numbers have in common, and approach multiplication from every angle. This strengthens students' foundations through engaging and meaningful tasks.
What makes MathBait™ Multiplication different from memorization? If you have been following along with the series you might have thought "we are still just practicing the skills, what makes this any different?". In a nutshell, memorization is like steroids. It's a quick fix that helps builds muscle and improve performance. There are also side effects including irreversible damage and stopping steroids causes a withdrawal effect. For math, the memorization steroid is just the same. If students are not constantly practicing, the information isn't connected to anything tangible and is lost, which is why we often forget some of the more tricky products. With MathBait™ Multiplication, we are continuously building in small doses on previous knowledge and providing scaffolding and exposure. Not only does this build muscle and improve performance, it is helping develop relationships and connections that are both stored in long-term memory and more likely to stick because of said connections.
Our games are designed for replay-ability. We recommend students play and play often! With many choices for group and individual games, students can both build fluency and have fun in the process.
We hope you enjoyed Part 3 of our MathBait™ Multiplication series. There is so much to come!
For even more fun learning, make sure to check out our debut novel, Marco the Great and the History of Numberville.
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