Guest post by Amanda! Amanda is a mother of two, a special eduction teacher in NYC, and a certified holistic health coach. She writes and shares about motherhood, conscious parenting, and early learning / education in an effort to connect, inspire, and enlighten women and their families all over the world. She'd love for you to join her in her journey by following her on Instagram and Facebook, or you can visit her website here.
The Joquines Grapat brand is one to truly embrace and enjoy. Their nature-inspired wooden pieces come in a wide variety of shapes and shades, and once you get your hands on them you immediately understand why they are such a coveted toy in so many homes.
The mandala pieces and rings and coins can be used to create beautiful designs, but they can also be used to help develop deep number sense and to practice early math concepts. Children often benefit greatly from exposure to tangible resources when exploring early math and these special pieces can aid in kinesthetic learning which often increases both understanding and retention.
Whether you homeschool or are just looking to frontload / reinforce concepts covered in school, here are a few ideas to get you started using your Grapat pieces for mathematical thinking.
1. Number Formation
Providing several different ways to learn how to physically write a number–other than using simply a pencil and paper— is often a helpful practice to commit the shape to kinesthetic memory and to work on fine motor development. Providing children with an outline of a number and modeling how to “cover” the number with loose pieces gives them a different type of experience in number formation. Alternatively, you can use building slats, blocks, or a tracing board to form the numbers and then have the child cover the shape with loose pieces.
2. Represent the Value of a Digit
Children can often recite numbers in order from memory before actually understanding the value of the number (how many it represents). Try presenting a card or coin with a given number on it and then constructing the value of that number with loose parts.
As a scaffold to struggling counters, you can use the rings as an “outline” and ask the child to “fill in” each ring with a mandala piece, thereby making the task slightly more achievable. It is important to note here that Grapat makes a set of coins that have numbers written on them that work really well for this activity.
You can also use a tracing board designed for this and incorporate loose parts as well (shown below). Using different colors for different numbers is typically a good idea to help differentiate between values/numbers.
Rational counting and one to one correspondence is a precursor skill to more advanced skills like skip counting, group counting, base ten understanding, and subitizing. Counting in an organized way is often something children struggle with greatly, causing them to “lose count” and make errors – resulting in frustration and feelings of defeat. Providing them with visually and tangibly pleasing Grapat pieces to manipulate with their hands can help with engagement and organizational skills. Children can touch each piece as they say the number aloud or physically move the pieces to a new spot when counting. Eventually, they can begin to make groups of five or ten to help with more efficient recounting.
4. Classifying/ Making Sets
Inventing systems of ordering and classifying is a really rewarding activity for children to independently (or cooperatively) engage in. Setting up a simple model or suggestion can help them to get started on a variety of sorting activities. Making sets classified by color or number is a great building skill for other concepts such as comparing and understanding parts and wholes.
Which group is bigger? Which is the smallest? Can you make a larger group? Which group has more? Less?
These are different questions that can be worked through when making groups. Subitizing (instantly seeing how many) is another preschool skill that can be developed by frequent comparison work. Working on the meanings of greater than, equal to, and less than at an early age is beneficial to promoting conceptual understanding of a topic that will increase in complexity over time.
Identifying and creating patterns with loose parts is one of my 4-year-old’s favorite activities right now. You can try modeling how to create one by saying what you are doing aloud, “one pink, one purple, one pink, one purple.” Or you can pose questions like, “What do you notice about these pieces here?” and point to a constructed pattern. You can also take it a step further and make patterns in a certain design. Sometimes, we like to make patterns over the colorful lines in one of our area rugs.
7. Spatial Sense /Positional Words
Developing spatial awareness in conjunction with fine and gross motor skill work can be harder for some children than others. Providing ample opportunity to use hands and fingers to organize loose parts in different ways is always a good reinforcement activity.
Working on positional words is one way to do so; you can say something like, “Which color comes before the blue pieces?” or, “Can you put the pink piece after the yellow one?”
Working on above, below, next to, before, after, on top of, underneath, etc. with tangible recourses is great practice.
8. Shape Formation
Similar to forming numbers, shape formation practice can (and should) extend beyond just using paper and pencil. Using an outline or tracing sheet, children can cover lines to practice the straight and curved lines that are required to accurately make a shape. Sometimes, I create shapes with our magnetic tiles and ask my children to trace the outline of the shape with our loose parts. Outlining each side of a shape with different colored pieces also helps to reinforce the number of sides each shape has.
9. Parts and Wholes
Understanding that two or more parts put together make up a whole is a foundational piece of number sense. This concept can be represented in many different ways in drawings and models on paper (number bonds, number sentences, tape diagrams), but once again, tangible manipulatives are helpful tools.
Using a printed diagram or just an open area on the floor or a table, you can practice taking a group of ten and separating it into different groups (2 and 8, 5 and 5, etc.) and start by observing the relationships between these numbers. For more advanced learners, this can be incorporated into more concrete addition and subtraction work.
10. Addition / Subtraction
Using loose parts, children can “act out” or create representations of addition and subtraction sentences or even story problems. Whether or not you actually couple this work with the written representation is up to you. Familiarizing children with “math talk” and appropriate terms while manipulating the pieces is also helpful. Children can either create their own word problems and solve them or can solve ones given to them. For some, mixing colors amongst parts and wholes (rather than choosing one) might be confusing—try to be cognizant of that and use what works best for the child you are working with.
11. Multiplying / Dividing
When learning how to multiply or divide, picture representations are often key in helping children understand the processes involved. Making up stories with younger children that involve making groups and asking guiding questions will help build preliminary foundational understanding.
For example, you can pose a story such as: Addy has 12 cookies and she wants to share them with her 3 friends. How many cookies will each friend get? Representing the cookies with concrete loose parts will allow children the opportunity to work through division without even really knowing it yet.
12. Tens and Ones
When working on place value, a beginning step is typically grouping “ones” into sets of ten. Counting and grouping loose parts can help to kinesthetically reinforce this concept.
Furthermore, using one type of coin or mandala piece and “exchanging” 10 for a new coin or mandala piece will serve as a base for differentiating between tens and ones.
13. Coins and Money
Similar to what was described just above, one way to work on money concept building would be to use Grapat coins in lieu of pennies (giving them a value of 1 cent) and “exchanging” them for a different value (perhaps a nickel or a dime could be represented with a ring.
Practicing counting up to 5 or 10 and making a visual connection between an equal value BUT different “coin” is great foundational practice. Also, just simply having some coins in a wallet or purse is always a fun way to play!
Using loose parts to expose children to the beauties of symmetry can be SO much fun! There are so many inspiring accounts on Instagram that display incredible mandalas that are often symmetrical; search #grapatmandala and let your world be changed forever! Of course, some of these creations can be quite complicated for a youngin’ to replicate, BUT they can sit and observe as you create one and talk about what you are doing.
That said, for more appropriately leveled work for a young child, you can present them with a simple shape and one line of symmetry and model/show how to create symmetrical lines/patterns/designs on the template.
When children first start learning about measurement, they often use objects to determine length, volume, and/or mass before using units such as inches, centimeters, and grams. Using Grapat pieces to explore these concepts provides both tangible and visual opportunities for children.
You can measure household objects or furniture with Grapat's coins and compare lengths in a discussion (or a number sentence). You can fill up different size jars with the same pieces and see which holds more. You can fill up a tied silk with the same number of different pieces and see if there is a difference in weight.
I hope this proves as a helpful resource for all parents and educators reading. Not only are these pieces naturally beautiful and inherently thought-provoking in their own way, they are incredible resourceful and helpful with regard to mathematical understanding. I wish you all the joy and wonder while you explore and learn with these particularly unique and inviting pieces near and dear to my heart.