Open Ended Sorting
Supply the children with a wide variety of object and ask them to sort the objects. When they have finished, ask them why they chose the groups. Help the child identify their criteria for sorting.

Sorting Ideas
Sort by color, size, different items, different animals, animals with fur/feathers, sort animals by type, sort items by use, car/not a car, sort pasta by type, sort by length, height, circumference, shape, etc.

Items to Sort (over the age of 3 for small items)
boxes of scrap materials - cloth, velvet, silk satin, cut into uniform size and shape. Children can sort the material by color or texture.
Many different Bells- cow bells, Christmas bells, children can sort based on color, size, sound.
Buttons- Students can sort them based on the number holes they have, color, shape, size, shiny vs. dull.
Textured Paper cut to uniform size - can be sorted based on texture or color
Other Items: Shells, beads, beans, noodles, seeds, rocks, nature items, nuts, nails, screws, bolts, toys from the room, coins, blocks, stickers, pictures from magazines, books, socks, ribbons, pencils, dolls, stuffed animals, plastic animals, play cars

Comparing items- Have children compare things, which is longer, taller, bigger, smaller, shorter, newer, younger, heavier, louder, colder, faster etc.

Some Comparing Ideas
Length- which is longer, shorter, which is the longest, shortest? compare pencils, string, yarn, ribbon, shoelaces, strips of paper, masking tape lines on the floor, different length rulers, fingers, feet, dolls, toy cars, used crayons
Size- which is bigger, smaller, larger, largest, biggest, smallest? compare toys, buttons, blocks, books, plastic animals, trees, bushes, cups, toy cars, beads, coins, stuffed animals
Height -which is taller, shorter, tallest, shortest? compare children, dolls, trees, plants, toy animals (plastic, stuffed), blocks, block constructions, cups, classify animals as tall or short (giraffe vs a monkey, monkey vs a cat, cat vs a mouse, mouse vs a bug)
Weight - which is heavier, lighter, heaviest, lightest? compare blocks, coffee cans filled with various items (feathers, beads, coins), bags filled with different items, sealed soda bottles filled with items (water, coins, feathers, paper, confetti, pom poms)
Speed - which is fastest, slowest? compare animal speed, children speed, different toy cars on a ramp, different riding toys, shake a parachute fast and slow, jump up and down fast and slow, dance fast and slow, walk fast and slow, talk fast and slow, play two different pieces of music (fast and slow), clap fast and slow
Volume - which is louder, softer? compare voices, music, clapping sounds, singing voices, musical instruments, hit two things together (blocks, toys, stuffed animals), Use a plastic hammer to tap various objects, play music loud and soft, speak/sing loud and soft, clap loud and soft
Temperature - which is colder, warmer, hotter? compare temp of ice vs water, compare temps of water, shade vs in the sun, inside vs outside, body temp coat vs, no coat,
Shade- compare shades of color, lighter vs darker

Seed Sound Jars
Obtain many film or prescription bottles. (Both are great items to get from parents.) Place matching seeds in two containers. I.e. 2 apple seeds, 5 watermelon seeds etc. If using film containers, seal the lids with hot glue or super glue. If using prescription containers, cover the bottles with colored contact paper. This Montessori based activity would normally be introduced to the children in the following manner: without speaking, the teacher picks up one of the containers and shakes it. Then the teacher will pick another bottle and shakes it. Then the teacher shakes the first again. The teacher will shake the bottles and compare them until it is determined if they are a match, if they are not a match, the teacher would shake his/her head "no" and set the second bottle aside, and continue by picking up another bottle and shaking it, comparing it again to the first bottle. When a match is found, the teacher shakes his/her head "yes" and places the two bottles aside, next to each other. Then continues by picking another bottle and try to find its match until all of the matches are found. The child is invited to help when prompted by the teacher, with a shoulder shrug, or by the teacher initiating the child to pick a bottle, etc.

Compare/Contrast
Pick two things. Have the children compare and contrast the two items. Use a Venn diagram to record the answers.

Ordering/Seriation
Placing things in order is a visual part of development in the math category. Children can place things in order according to size, weight, length, height, temperature, or order of events.

Things to order:
Blocks, cars, string, yarn, sticks, nesting cups, plastic or stuffed animals, children (based on height or age), dolls, toys, coins (size, value), measuring spoons or cups, cups, pom poms, feathers, bottles, bowls, stones, cans, theme based shapes (fish, cats, eggs, etc)

Counting at Snack Time
Count out the napkins, the plates, cups, the children. Count out the crackers, (each child gets ____ three, four, five?) cookies, apple slices, banana slices or whatever you are serving.

Shape Snacks
Serve snacks that are in specific shapes, such as circles (crackers, cookies, banana slices), rectangles (ham slices, crackers, cheese slices) etc.

Number Line on the Floor
Create a number line on the floor with masking tape, use contact paper to cover pieces of paper that label the numbers. You can play a ton of games with the number line. Ask the child to hop from one number to the next and say the numbers as they hop. They can skip count by hopping over the odd numbers. You could have one child stand on a number and move forward two or backward x spaces and ask what number they are on now.

Muffin Math Center
Place pieces of paper numbered 1 through 6 in the bottom on a muffin tin. Supply the children with many similar objects to place in the tins. They will place one object in the "1" tin and two in the "2" and so on. The items you use can be theme based or items from your class such as toy animals, beads, blocks, counting chips, dry pasta.

Have the child jump up and down and count the number of times they jump. Count by 2's, 5's and 10's

Have your child take really big steps and count by 1's, 2's, 5's and 10's.

Tap a balloon and try to keep it in the air, count the number of times the children can hit the balloon before it hits the ground.

Count the value of pennies, nickels and dimes.

At a pretend store, price something that $10 or $.10 count how much it will cost for 10 of them. Same thing with something that is $5 or $.05.