Step 1. Although it is tempting to have all your math manipulatives set up and ready to go in September, it’s easier to train your students to clean up and learn routines when you put out a few tubs at a time. As children learn to care for each set of materials. then introduce more.
Step 2. When teaching with hands on materials, teach the children the correct names for theme and the categories they belong with. For example, “These are pattern blocks and they are part of the math materials. All the math materials are in blue tubs.”
“The pattern blocks are part of our math materials so we keep them in one of the blue tubs. Look at the pictures on the front of the blue tubs. This one shows the pattern blocks. The words underneath the picture say pattern blocks. This is where you put the pattern blocks after you are finished working with them…”
Step 4. Teach the boundaries for each new set of materials you present. “These blocks are not for throwing or smashing against each other. They stay on the math carpet.”
Remember, you don’t teach all of this in one day! The month of September is training time.
Step 5. When it’s time to clean up after teaching hands on math activities don’t assume that your students are aware of safety issues. Children will throw objects across the carpet into a tub and accidentally hit another child. Many kindergarten children have only played with a few other children at a time and have to learn the dynamics of working within a larger group of people.
Step 6. Always let young children play with the math manipulatives for at least two weeks before using them in a structured activity. This gives children a chance to explore the objects, find out what the manipulatives can and can’t do, and gives them time to learn new vocabulary. At this stage of teaching with manipulatives, add to their vocabulary as they play. For example, “Look, you are balancing the thicker, hexagon block on its side, but the thinner hexagon block falls over… You can roll the cylinders and spheres easily, but not the cubes.”
Step 7. Finally you get to teach with the math manipulatives! Make sure each child has enough space to work. Individual plain plastic table mats or pieces of plain white card spread out in a circle on the carpet work well to define boundaries.
First teach the children new skills using only the math manipulatives (no pictures or symbols). This is the concrete stage.
In the images, the children are learning what the number 4 means. The children build sets of 4 objects many times with various blocks and objects. Give them plenty of time and opportunities to learn, “what does 4 look like” at this stage.
IMPORTANT! Do not move on to the representational or connecting stage until the children appear to successfully understand an idea using math manipulatives only.
Step 8. Representational or Connecting Stage
When a student is able to show you what 4 means with blocks (or another manipulative) introduce the same activity, only this time after you teach with the math manipulatives, draw a pictorial representation of four objects. Let the kids see you working through the process, communicate your thinking as you do it and invite the children to participate. Have the children try the process and guide them to success.
In this image, the children have built sets of 4 with blocks and then traced around the blocks to make pictures that represent their sets. If any children seem ready they can add the symbol, 4, to their pictures.
Step 9. Symbolic stage
Only after a thorough understanding of the connection between math manipulatives and pictures and symbols are children ready to work with symbols alone. Don’t rush things. This stage may or may not be part of your kindergarten government requirements, depending on where you live.
And finally Step 10!!
Surprise… just because a child seems to understand, what the symbol “4” represents at a connecting or symbolic level, don’t assume that they will understand “5”. Start all over at the concrete stage, teaching with math manipulatives only. Do the same thing with any math concept or operation (+-/x).
Teaching children to clean up adds to the their understanding of classifying, ordering and sorting objects and is an opportunity to build their math vocabulary. E.g. “All one inch cubes go in this blue tub.” or “All the math materials are in blue tubs on the math shelf. The science equipment is stored in green tubs under the science display table.” or “Anne, please put the rectangular wooden blocks in this tub with the other geometric solids.”
BONUS! Large printed labels on the tubs are great for teaching letter recognition, beginning and ending sounds, rhyming words and other language arts skills. Each tub has a picture and words to help the children put things away correctly. Use a large easy to read primary font rather than a label maker, which prints too small. During group times, refer to the letters if the tubs.
Check out my favourite math teaching supplies. They are terrific for teaching multiple math concepts.
A note about printing symbols
Children need time to practice printing the digits 0 – 10, in order to be ready to use them when they are ready for connecting level work. . Start early in the year so children will not be struggling to print the numbers when they are ready to record their learning. Children like to paint numbers with their fingers or brushes, to form numbers out of play dough, or to make numbers with a variety of art materials. When they have mastered the formation of numbers, then they can practice printing numbers and symbols smaller.