MathBait™ Mastering Multiplication Part 1

Welcome to MathBait™ Multiplication Part 1! We are kicking off a week of amazing games, activities, and resources to help your students not only build lasting fluency through deep understanding, but have a blast doing it. Part 1 offers 9 activities and 3 digital games to help your students succeed.

Prerequisites

To get started in part 1, students should be able to count, recognize numerals (1, 2, 3, ...) and preferably write numerals although it is okay if they have not yet perfected their writing skills.

Who is Part 1 For?

Part 1 is great for early learners (as young as 3) as well as older students struggling with multiplication or in need of review. Many of the games and activities provided include more challenging levels and are fun for the whole family!

Goal

In MathBait™ Multiplication Part 1, students will build on their existing knowledge of counting to work with multiples. Throughout our series we will never encourage memorization. Our activities each build on previous understanding allowing students to connect new knowledge to existing schema and promote long term retention. This removes anxiety and helps foster a love and enjoyment of learning.

Ready to make learning math fun and engaging? Pick up your copy of Marco the Great and start your adventure today!

Select a lesson to view details and access our digital games. 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. For the best experience we recommend games are played in full screen mode which is not available on the Safari mobile application.

The Strange Flowers

Almost all math can be thought of as a way to count something. In fact, in A First Course in Abstract Algebra by John Fraleigh (a course generally taken by upper-level college students) the author states to "never underestimate a theorem that counts something". Abstract Algebra, Number Theory, and Analysis are all areas of advanced math with a huge focus on simply counting. Thus, the first step in building students a strong mathematical foundation is to teach them to count.

In this activity, students will be empowered by their existing ability to count as they extend to explore counting in new ways.

Warm Up: A Fairy Tale

Begin by reading this short story aloud to students.

Have you heard of Alice in Wonderland? If not, that's okay. It's the tale of a young girl who followed a rabbit down a hole to find a magical world of talking caterpillars, a grinning cat, and an evil queen. If you get the chance to read it you should. But... you should know one chapter was lost in the sea of Alice's tears. There aren't many of us left who know the true tale. Lucky for you, I'm one of the few! I'll tell it to you too. Although, it might sound a bit crazy if you don't know about counting. You can count right? Wonderful! Well what are we waiting for, let's begin.

On her journey, Alice came across a field of flowers. They were beautiful! There were yellow flowers and blue flowers and purple flowers and red flowers and orange flowers and even colors you've never even heard of or thought about. As she lay down in the field she began to count the dayflowers. 1-2-3... Just then she heard something, no someone, and they were counting too!

She looked around the field but didn't see another soul. Starting again, she counted, "1".

"2" she heard.

"No not two!" Alice called out. "This is the first flower I have counted. I really must ask that you stop, you are going to make me lose my place." Brushing it off, she continued. "2".

"4" the voice sung.

"Now this is really getting to be ridiculous. I have not counted four flowers, I have counted only two! That one there, that is flower number 3."

"6". The number rang through the field. It was no longer one voice but a whole chorus singing out.

Alice had enough. She began frantically looking around to find the voices. Who was calling out these wrong numbers and why? Then she saw it. The dayflower slowly opened its eyes and stared right at her. "8" it said.

"Why won't you let me count?" she asked the dayflower.

"Because you are counting all wrong" the flower said bluntly.

"Wrong? Certainly not! It is you that is wrong! I counted you 3 here, 1-2-3. You stuck your nose in and counted 6. It is you that is wrong!"

Angry, Alice pushed herself up and walked across the field to a new patch of flowers, the beautiful yellow tiger flowers.

"Those dayflowers are mad! I'll count you instead." She pointed to the first flower. "1".

"3!" the flower sung.

"Are you batty too? I have just started! You are not 3 you are 1! And that flower over there, that is number 2!"

"6!" the tiger flower said firmly.

Alice huffed. "I have never met such a horrible flower patch before." And with that she stormed away.

Wonderful right? I mean this was an important part of Alice's journey to be lost forever. You are probably wondering why the flowers counted in such a strange way. Or do you already know? Oh look at that, I'm late! I am so sorry to run off but I really must go, I'm sure you can figure it out yourself... Good Luck!

After reading, ask students why they think the flowers counted in such a strange way. It's okay if they aren't sure. In the next activity, students will have a chance to dive into this idea more.

Activity 1: My Flower Patch

Provide students with paper and pencil and show them the image of the blue dayflower and yellow tiger flower (above). It can be helpful for younger students to also provide a basic sketch.

Ask students to draw 3 or 4 dayflowers on their paper followed by 3 to 4 tiger flowers. When complete generate ideas of other ways we can count. Alice was counting how many full flowers there are, is there something different we can count as well? Help students as needed to see we could instead count the petals.

Count by 1's, adding a number to each petal. The first dayflower should contain 1 and 2, then second 3 and 4, and so on while the tiger flowers should contain 1, 2, and 3, followed by 4, 5, and 6.

Conclude by showing or discussing why the flowers counted in such a strange way. While Alice was counting how many whole flowers there were, the flowers counted by their petals. This meant the dayflowers counted 2, 4, 6, ... and the tiger flowers counted 3, 6, 9, .... Provide students with crayons or colored pencils and invite them to create their own flowers with strange counting. Tell students they are not limited to 2 or 3 petals, they can pick any they want, but make sure each flower has the same number of petals.

A sample worksheet and student response is provided below. If students need support in determining how their flowers would count, encourage them to write numbers in each petal counting by 1's. The largest number in each flower will be the number the flower says.

MathBait_Flower_Patch.pdf

Download PDF • 753KB

Benefits

In this first activity, students are introduced to a new way of counting. They see that there are different ways to count the same thing, in the case of the flowers, they can count the whole flower, or count its petals (or other parts). Students are building on their existing knowledge of counting to lay the foundation of multiples and multiplication. Encourage students to look for similar patterns all around them. What else can be counted in a new way?

The Whisper Game

Now that students have been introduced to skip counting, it is time to practice on their own! While this is one lesson, we recommend starting with 2's and giving students time to become comfortable before moving on to 3's and 5's.

Warm Up: The Whisper Game

In this activity, students count by whispering the in-between numbers and shouting the target numbers we are counting by. Using rhythm can also be beneficial. Have students softly tap their legs on the in-between numbers while clapping and yelling out the others.

Begin with 2's. Students whisper (and tap) the number 1, then loudly call out (and clap) 2. Continue in this manner up to a number they are comfortable with, ultimately trying to get up to at least 50.

Next, increase the difficulty by encouraging students to make their whispers quieter and quieter until they are comfortable counting by 2's without the in-between values.

Continue to play with 3's (whisper 1 and 2, call out 3) and then 5's. Once students have the hang of The Whisper Game, continue to encourage grouping and alternative counting patterns. The goal is to enjoy finding patterns and exploring new abilities within their existing knowledge. When students feel like "I know this already", it is a great confidence booster and fosters a love of learning.

Activity 1: The Maze

In this digital game, students use their skip counting ability to help navigate the friendly kitty through a maze. Start with 2's, when students are comfortable move onto 3's and then 5's. Have students play again and again (each game is a new maze) until they are able to collect all the items.

©MathBait created with GeoGebra

Benefits

The activities in this lesson help students to develop their ability to skip count by 2's, 3's, and 5's. This is not only laying a strong foundation for multiplication, but it is also building an understanding of multiples and the relationship between numbers.

The Multiplication Table

Take time to allow your students to become comfortable skip counting by 2's, 3's, and 5's (no other values needed!). Some additional resources we love include Schoolhouse Rock (Three is a Magic Number and Counting by 5's) and NumberBlocks (available on Netflix and limited availability on YouTube).

We often see classrooms focus on filling out a multiplication table daily. Unfortunately, this does not directly support fluency. As we will see, students can nearly complete a multiplication table knowing only how to skip count by 2's, 3's, and 5's. Students can complete a table yet not have any understanding of multiplication nor be able to quickly or easily recall that 5×6=30. In addition, how the table is presented can cause anxiety and even a dislike of math.

Our goal is to introduce the table without any expectations and in celebration of how much a student already knows from their skip counting alone. Again the goal is not to "learn" or "memorize" the table.

Point to the 1 in the top row and explain the first row is counting by 1's. Have your student fill out the first row. Next point to the 1 in the first column and fill this out too. Continue for 2's, 3's, and 5's. Don't worry about things like 3×5=15 or how to use the table, just work on building confidence and progress. Celebrate how much of the table they can fill out with their knowledge of skip counting.

Skip Counting Table

In need of a table? We got you! Download and print the table below.

MathBait_Skip_Counting_Table.pdf

Download PDF • 103KB

Benefits

We are not huge proponents of the multiplication table. That being said, your students will likely encounter it in their classes. By working on the table early, without any pressure or expectations, we are helping to build a positive view around multiplication. In addition, when your student can skip count by 2's, 3's, and 5's, they will be impressed with how much they can already fill out. This is a win to celebrate! This builds confidence and enjoyment of the subject.

Skip Count Pop!

The purpose of this activity is to help students to recognize patterns in numbers. Just as they graduated from simple counting (1, 2, 3, ...) to skip counting, they will now utilize skip-skip counting to round out their skills.

Warm Up: Sticker Sheets

The goal of this activity is to allow students to discover they already know how to count by 4's, 6's, and 9's.

Materials:

• Paper

• Tape

• Stickers or Stamps

• Envelope (to hold students' counting strips)

Start by cutting strips of paper (about 3" by 1") and handing them out. Each student should have about 20 strips. Have students place two stickers (or two stamps) on each strip.

Once students finish, practice skip counting by 2's by lining up their strips of paper and pointing to each group as they count.

Have students collect a few strips and ask them how many stickers they have collected. Highlight their ability to count by 2's quickly to determine the total quantity. This is an excellent place to begin setting up multiplication by using phrases such as "you found 3 strips of two stickers is 6, or 3 groups of 2 is 6." Encourage students to use similar phrasing to communicate their own results.

Next, have students tape together two strips to make groups of 4 stickers. Ask students how many stickers are in each group now (4). Highlight that 4's are nothing more than two 2's. Since we can count by 2's we can also count by 4's!

Now have students create strips with three stickers (or stamps) and repeat the process. What can we count by when putting together two strips of three? (We can count by 6!).

To conclude, ask students if there are any other values we can count by using 2's and 3's. Students should determine we can count by 6's using 2's as well, or 8's by combining two of the four strips. Students can also use the strips to count by 9's by combining 3 of the three strips.

Repeat one more time with 5's to see that two five strips gives us groups of 10. Students do not need to fluently count by 4, 6, 8, 9, and 10 at this time. The goal is simply to introduce the idea that just as we skip counted by 1's to count by 2's we can skip count our 2's to count by 4's or our 3's to count by 6's.

Activity 1: The Whisper Game

As students are already familiar with The Whisper Game, this is a great time to circle back and practice counting by new values.

Begin by practicing counting by 2's (2, 4, 6, 8, ...). Then count by 4's by whispering the in-between numbers and shouting out the multiples of 4. Students can continue to use their strips as a visual guide to help them organize information.

Give students time to get used to counting by 4's. Allow them to whisper the in-between numbers until they feel more confident. When ready, have students count by 4's and add to their table.

Now introduce skip-skip counting. Still focusing on 2's, skip two numbers (tap, tap, clap) to call out 2, 4, 6, 8, 10, 12, 14, 16, 18, .... Ask students what we are counting by now (6's). Move onto skip counting by 3's (3, 6, 9, 12, 15, 18). What are we counting by now? (Still 6's!). Discuss which method they like better to count by 6's, skip-skip counting 2's or skip counting 3's. There is no right answer. It will likely depend on if the student is more comfortable with 2's or with 3's. Ask students why do both methods work? Use their sticker strips to highlight that we can make a 6 with 3 of the two strips or with 2 of the three strips.

Practice skip counting 5's to count by 10's (although many students pick up on 10's right away, the idea is to highlight how 10's are also constructed from two 5's) as well as skip-skip counting 3's to count by 9's. Ask students to come up with their own strategy for counting by 8's (as 8 is made of 2's, we can skip-skip-skip count to find 8's).

When students are comfortable, they can add the new values to their chart.

Activity 2: Skip Count Pop!

This activity is to help students become more comfortable with skip-skip counting. Numbers will rise on the screen counting by 1's in a random order. Students may continue to use whisper counting as a support, but through more play they will be able to skip count more naturally. Skip Pop levels are easier for higher values (10,9,8) and more challenging for lower values (2 and 3) as students must collect more bubbles in each group.

The design of this game supports students strengthening their skills in skip counting by values such as 4, 6, 8, and 9 and really challenge themselves for skip counting by 2's and 3's. We recommend students begin with 10 and work their way down to 2 as they become more comfortable with the game.

A fun variation is to not worry about the order of the bubbles. This will help students develop the ability to recognize multiples.

©MathBait created with GeoGebra

Benefits

The activities in this lesson focus on students building understanding from existing knowledge. Learning 4's, 6's, 8's, 9's, and 10's isn't new, but simply another iteration of what they have already done. More importantly, students are learning how numbers are related. This is not only building a strong foundation for multiplication, but also for prime factorization, fractions, and more advanced topics. Viewing numbers as able to be manipulated is a great skill and one reason why we do not focus on memorization. Memorizing can make us feel like 4×6=24 and that is it. Instead we want to be able to see 24 as 6×4 or 3×8 or 20+4=2(10)+2(2) or 2×2×2×3 or many other possible ways developing a flexibility in thinking that will be invaluable as students progress.

BUZZ

Our final activity in MathBait™ Multiplication Part 1 is a favorite. It is great for students just mastering skip counting to adults. It's a blast to play in the car, at the dinner table, and in the classroom. Our digital version offers two fun modes, but Buzz can also be played without any technology at all. This game is great as a warm-up or as a full activity.

Begin by selecting a "Buzz Number". At this stage stick with 2, 3, or 5 to start with before graduating to other values. Make sure the number of players is not equal to the Buzz Number (For instance, if a mom and son are playing together, they should pick 3 or 5 as picking 2 with two players will lead to one player having the majority of the forbidden numbers).

Players take turns counting by 1's (1-2-3-4). Here's the twist. On your turn if your number is either a multiple of the Buzz Number or if it contains the Buzz Number, you must instead say "Buzz". In other words, when playing with 2's all the numbers we'd traditionally say when counting by 2's are forbidden as well as numbers that contain a 2 like 23. After a Buzz, the next player must remember the count and continue.

Buzz is both a game of skip counting and multiples and concentration. If a player says a number rather than "buzz" they are out, or if a player forgets the count. However, there are many rule variations you can enact to keep play light and fun.

Example: If playing with a Buzz Number of 3, play would follow the sequence 1, 2, buzz, 4, 5, buzz, 7, 8, buzz, 10, 11, buzz, buzz, 14, buzz, 16, 17, buzz, 19, 20.... Note "buzz" should be said on the multiples (or skip counting numbers) of 3 but also on any number that contains a '3' such as 13 and 23. The 30's are particularly difficult as all numbers are buzz numbers and players must keep track of where they are in the count.

The Digital Game

Digital game play includes two selections: verbal and entry. Verbal is great for the classroom or larger groups working with a shared device. In Verbal mode, players set a "pass time" (in which the device is passed to the next player). Players say the number (or "buzz") aloud and tap on their associated choice (Number or Buzz). The game will then direct what player to pass the device to. If a player taps (and says) the number when they should have said "buzz" (or vice versa) the game will indicate "Game Over".

In Entry Mode, players enter the value or press Buzz. Both methods have a timer that can be set at the start of the game. The digital game also includes Help Mode, which tells players the previous number. Help mode is great for younger players.

©MathBait created with GeoGebra

Benefits

Where skip counting is focusing on a pattern, Buzz helps students begin to recognize and associate certain numbers with their counting number. That is, students will begin to naturally build connections in their brain that associate 3, 6, 9, 12, and so on with 3. We are building on their previous understanding and, again, not introducing anything new but rather looking at what they already know from a different perspective.

Buzz is also traditionally a fast-paced game. This helps students store their understanding in long-term memory making for easier recall. The digital version includes player-set timers, but for younger children, we recommend playing verbally first to get the hang of things.

Conclusion

In MathBait™ Multiplication Part 1, students learned how to leverage their understanding of counting to skip count by 2's, 3's, and 5's. They then skip-skip counted to expand their abilities to 4, 6, 8, 9, and 10.

Allow students time to become comfortable in this phase of their mathematical journey. These games can be played before students are fluently adding and subtracting allowing them time to jump to other skills spiraling back to their skip counting ability. When students are comfortable with addition and subtraction, encourage alternative ways to skip count using patterns (rather than memorization). For instance, to skip count by 9's students can add 10 then subtract 1 (for example from 27 to 36 students can add 10 to 27 to find 37 then take one step back to 36).

Encourage skip counting as much as possible and highlight numbers in our daily lives. Play these counting games any chance you get. Make groups. Allow students to select group sizes. Provide them with lots of things to count creatively.

Remember, we aren't focusing on memorizing, or even being able to know that 4 groups of 6 make 24. We are extending and building on their existing ability to count. Give students time and support to feel confident counting by 2, 3, 4, 5, 6, 8, 9, and 10. (Don't worry about 7's yet!)

Once students develop a strong foundation in counting they are ready to move onto Part 2.

We hope you enjoyed Part 1 of our MathBait™ Multiplication series. There is so much to come!

For hundreds of games, missions, and loads of fun learning math, make sure to check out The Kryptografima by MathBait™.

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