Array Rods (100 pieces total)
Array Rods are a simple manipulative for students to learn about multiplication and division, including the different properties for multiplication. For example, the Distributive Property is illustrated in one of the attached pictures where students can easily manipulate 7x8 into different arrangments (7x1+7x7; 7x2+7x6; 7x3+7x5, etc.). This also helps students learn different ways to meaningfully memorize more difficult facts (i.e., realizing the 7s facts can be broken into 5s and 2s… 7x6 is 5x6 plus 2x6).
Numicons
These number frames are a reimagining of the common “numicons" as all the numbers build upon 5 as a visual benchmark. This set also includes a pegboard for looking at how the numbers add together in reference to 10 (the pegboard is 10 when filled).
They can be used for addition/subtraction and general number sense. Using the pegboard helps students with combinations for 10, but also for understanding regrouping when numbers are over 10 (i.e., seeing that 7+5 is the same as adding 7+3 and then 2 more).
Fraction Squares
Fraction squares can be used for:
- Learning part-whole reasoning
- Comparing fractions
- Fraction addition & subtraction
- Fraction multiplication & division
- Learning about mixed numbers & improper fractions
By creating a smaller version of this popular manipulative, the goal is to allow for printing a large number of these more quickly (and for less cost). It's designed for classroom use in mind so every child can have a set (or two) to use.
Fraction Tiles
Each plate includes 12 individual sets (if you only want ONE set, delete the other 11 sets). This is designed so that class sets can be 3D printed more quickly and efficiently. This manipulative has been used with kids. Also, the “whole” has a hinge so that it can be folded and put into a container more easily. It may be more useful to have more than one set per student (or 3-4 sets per small group) so that students can practice going beyond a whole.
This manipulative is grate for fraction comparisons and arithmetic (add, subtract, multiply, divide). It is a very good tool (when paired with the paper-based number line linked ) to teach children how to place / label fractions on the number line.
Decimal Rods
These Decimal Rods can be used for students to quickly represent decimals with a physical manipulative. The hundredths rods allow for each hundredth to be flipped over (instead of counting out each and every one). The tenths rods can be used with these to compare sizes of each part of a decimal or for using in regrouping with addition/subtraction of decimals. There is also a whole (1) that can be printed and used with whatever problems are being done. There are two plate setups:
- The decimal comparison plate allows for the tenths and hundredths rods to be compared, added, or subtracted while also referencing the whole (1). Students can also use to represent this pictorially, but having these concrete rods as a first step is extremely useful!
- There is an area multiplication setup going up to 3x3 (if you want larger, I suggest moving to use grid paper with students).
These can be printed in whatever colors you wish. If doing two-color printing, I found silver to be a nice background color for the numbers.
Videos on how to use these:
Place Value Rings
These Place Value Rings are inspired by two tools often used for place value (arrow cards & homemade place value expanders such as with styrofoam cups). This set includes the option of including from hundreds to hundredths (whole numbers & decimals), but you may print whatever is most useful.
When using them with students, I would suggest having two sets for them to engage with “place value riddles” such as those below:
- I have 5 tens and 3 ones, what number am I?
- I have 5 tens and 13 ones, what number am I?
- I have 25 tens and 3 ones, what number am I?
- I have 25 tens and 13 ones, what number am I?
Combining and regrouping different place value parts is not naturally intuitive, but these tools can aid students in thinking about place value more robustly (having two sets helps them to see and regroup different digits across place value). It can often be worthwhile doing the first one or two riddles together (repeating this process when doing a new type of riddle with different regrouping).
The print profile should be set up to include supports and brims (supports are necessary for everything but the Ones rings, and the brims are very useful for open air printers like the A1 - if using something like the P1S, you can remove the brim but keep supports).