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MathBait™ Multiplication

Create Your Own Bones!

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Napier's Bones are a powerful tool! Playing with the bones helps build fluency and is an excellent introduction to multi-digit multiplication as students develop a deep understanding of place value and what is happening when we use methods such as the standard algorithm. Have your students build their own set of bones with the help of our step-by-step project guide or print out our downloadable set of bones.

Details

Resource Type

Activity

Primary Topic

Napier's Bones

Unit

5

Activity

2

of

5

You can purchase a set of well-crafted Napier's Bones (Creative Crafthouse), or you can play with our digital version (Digital Bones). However, the process of making your own set of Napier's Bones is fun, a great way to introduce rod multiplication, and helps students continue to build fluency with multiples.


In a time crunch? Scroll down to find our printable version. A fun (but more flimsy) way to quickly create a set of bones.


Materials

  • Popsicle Sticks (~30 per set of bones)

  • Markers

  • Ruler

  • Paper

Image of markers, paper, ruler, and popsicle sticks
Materials: Popsicle Sticks, Markers, Ruler, Paper

Step 1: Measure each Popsicle Stick

Once you have collected the Popsicle sticks you will use, start by measuring a stick. This will help to ensure your rods are properly aligned. While the box may provide the measurements, we do not include the rounded edges in our calculations. This helped to avoid a wonky final value.


We used standard sticks from Creatology and measured them to be about 13 cm (excluding the rounded edges).

Popsicle stick with 10 marks
Make 9 equally spaced marks on your first stick

Once you have your measurement, divide it by 10. This will give you the length of each segment. We recommend making about 20 bones per set, two for each digit.


Step 2: Mark Your First Stick

As our stick, not including the rounded ends, measured to be about 13 cm, each segment will be 1.3 cm in height.


Take one stick (this will be your guide stick) and mark off 10 lines based on your measurement. In the image above, we have marked 10 lines each creating a cell of height 1.3 cm.


If working in a larger group or with young students who may have difficulties measuring, we recommend making a few guiding sticks to distribute around the room. Students will be able to complete the remaining steps independently or with minor assistance.


Step 3: Partition Your Sticks

Line up several Popsicle sticks and place the guide stick on the left. Place your ruler flush with the first mark on the guide stick. Finally, use a marker to draw a straight line across each stick.


Ruler atop popsicle sticks
Use a ruler to mark a straight line

Repeat the process for each of the marks on your guide stick.


Popsicle sticks divided into ten equal parts

Step 4: Divide Each Cell Diagonally

Now that your sticks are partitioned, we'll draw a diagonal line through each cell. Line up your ruler to create a diagonal from the top left to the bottom right of each cell.


Popsicle sticks with diagonal line from bottom left to top right of each of the ten sections
Draw a diagonal line through each section

Step 5: Add in the Numbers

Start by adding a digit to the top of each stick (0, 1, 2, 3, ..., 9). We recommend making two of each for a total of 20 sticks.


Next, students will add in the multiples of the digit at the top of the stick. This is a great chance for students to continue to build fluency by working on their skip counting.


In order to create the perfect joints, one multiple will be placed in each cell. The value in the tens place will go above the diagonal while the value in the ones place will go below.


For instance, if making the 3-rod, the first entry will be 0/3 as 3×1=3. We place a 3 in the ones digit, below the diagonal line, and a 0 in the tens digit, above the diagonal line. The remaining entries on this stick will be 0/6, 0/9, 1/2, 1/5, 1/8, 2/1, 2/4, 2/7.


Popsicle sticks with numbers 0, 1, 2, 3, and 4. Each stick contains the multiples of the digit on the top.
Add a digit to the top of each stick and the multiples of that digit below. Place the value in the tens place above the diagonal and the value in the ones place below the diagonal.

Repeat for each stick or "bone". Plain Popsicle sticks and darker colored markers work best for maximum contrast. Colored sticks can be helpful to organize information (for example: 2's are on yellow sticks, 3's on blue, etc.), however they require a very dark marker for contrast and may be more difficult to read.


Step 6: Create Your Lead Bone

The final step is to create a lead bone. This is a single Popsicle stick with the digits 1-9 written to align with each cell.


Set of Napier's Bones
Create a lead bone with the digits 1 to 9

Congratulations! You've made your very own set of Napier's Bones!


Don't have Popsicle sticks? Not to worry! We've included a printable version below with both empty and completed rods.


Napier_Bone_Handout
.pdf
Download PDF • 409KB

Don't forget to check out our digital bones! This allows students to play anywhere and offers step-by-step support and an addition helper for carrying and working with larger values.

The material on this page is copyrighted by MathBait™. Please use and enjoy it! MathBait™ provides a temporary license for Non-Commercial purposes. You are not permitted to copy, distribute, sell, or make derivative work without written permission from MathBait™. 

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