Math Games and Activities - teaching 0-10

You can help your child build basic math skills at home without any special materials

Note: this page is a work in progress that we will continue to add to. Last update: July 12, 2020

1) Learning quantities

We start with 1-5. then work on 6-10

• Learn the song "Yellow is the Sun"  to teach quantities 1-10 (start with just singing 1-5 until your child is confident with those)
• Tips for parents: Teaching 1-10 with fingers (sorry the lighting is so poor!)
• Tips for parents: Subitizing 1-5 with color tiles (can use other objects instead!)
• Movement Game: Ordering Finger Cards
• Movement Game: Distance Matching

What's "subitizing"

Subitizing (SOO-bi-tighz-ing) is seeing at a glance how many objects are in a group. (example: if I hold up 4 fingers, you know it is 4 without needing to count each finger) Subitizing gives a better understnading of numbers than just counting.
Math should be mostly UNDERSTANDING concepts, NOT memorization of facts. Subitizing gives this essential foundation for building understanding!

2) Learning numerals

Numerals are the written symbols we use to represent numbers ("5" is the numeral for five, etc.). At this stage, they are learning the NAMES of the numerals; connecting those to the amounts they represent is a separate concept, and comes after they know that the symbol "4" is 'four', etc.

• Tips for caregivers: Teaching Numerals at home 
• Game: What's Missing?

3) Connecting quantity and numeral 1-10

Once your child is confident with identifying both quantities and the numerals, we can put them together - the numeral "3" represents the quantity 

• In the classroom, we first connect quantity and symbol with number rods and number cards. At home, you can use cards/papers that have 1-10 dots on them (grouped in 5s!) for your child to match with cards/papers that have numerals 1-10

Other 1-10 Activities:

• The Zero Game
• Montessori Odds & Evens activity - have numbers 1-10 on papers/cardboard ready & 55 small objects (beans, stones, cheerios, etc.) before starting Note: this is a classic Montessori activity. I have slightly adapted it to incorporate subitizing skills
• Montesori Memory Game of Numbers
• Quantity matching game - with number cards or tally, finger, or dot cards

Summer Enrichment 2: Let's Explore Outdoors!

The Outdoors have limitless opportunities for learning and exploring!

Morning Connection Videos:

Monday - This week we're introducing learning activities to take outdoors - sorting & classifying skills, sink or float experiment, a twist on an active vocab game, and a poem - A house is a house for me

Tuesday - For the months of the year song, ignore my motions and raise your arms for this month! A house is a house for me poem, A beginning sounds game (can also be done with rhyming words, ending, or middle vowel sounds), and making patterns.

Wednesday - Today we introduce "3 words" rhyming game, review finger spelling, and sing the number writing song. Remember that these kinds of language games are one of the best ways you can prepare your child succeed with writing and reading skills.

Thursday - Today we'll sing the seasons song (make sure your child knows it's summer now!!), compare two flowers - dandelion and daffodil, and introduce some sequencing activities. 

What flowers can you find outside now that it is summertime?

Friday - Happy Friday! Today we're singing "Days of the Week" in English and Spanish, and a tossing game with socks that also practices position words ("inside" and "outside") and partitioning 5.

A few outdoor activity ideas:

Sweeping a porch, patio, or sidewalk is fun and great exercise

Sink or Float - Find 6-10 objects outside, make a hypothesis on if they will sink or float, use a bowl of water to find out!

Fun with rocks - collect a few rocks outside, scrub them clean. Draw or paint on one! How many can you stack?

Flowers - How many different kinds of flowers do you see outside? Learn the names of 3. How do they smell?

Paint with Water - Have an old paintbrush? Dip it in a container of water and "paint" outdoors!

Patterns with Nature - collect objects outside (rocks, leaves, sticks, petals, etc) and use them to practice making patterns (how-to video), or try making more elaborate designs (examples)

Outdoor writing - Write with a stick in the dirt, or use sidewalk chalk (or a brick or rock!)

Other math and language resources and ideas on our Montessori at Home page

Sorting & Sequencing Activities for home

You can help your child practice skills of sorting into categories, matching like things, making patterns, and putting items in order without any specialized materials. These activities can be done with items in your house or things you find outside.
You can go for a walk (or likely just step a few feet outside) to gather some sticks, leaves, stones, flowers, etc. for these activities.

Matching and Sorting into categories 

a collection of leaves, ready for pairing

matching leaves

matching leaves to their leaf rubbing (also an art option!)

Sorting objects into groups (also called "classifying") begins with simple tasks for 2-3 years old (ex: spoons vs. forks; cars or stuffed animals, sticks or leaves), and can be made increasingly more challenging as the child grows through their school years.  Objects can be classified (sorted) by: size, shape, color, type, or other characteristics. Some ideas for categories:

- flowers, sticks, and leaves (sorting by type)

- types of coins (give them a handful of change to sort)

- types of beans/grains 

It's great to take the same objects and see if your child can come up with more than one way to sort them. Some items can also be sorted with eyes closed or a blindfold to increase the challenge! 

Comparing and sequencing

Children can compare two objects by different characteristics - which stick is longer? Which leaf is a darker green? Which object is heavier? 

The next level of challenge is to put a group of objects in order. Examples - biggest to smallest, longest to shortest, darkest to lightest shade of a color, heaviest to lightest, roughest to smoothest. Here's some samples: 

Comparing - which is heavier?

Objects sequenced from heaviest to lightest

Objects collected by a child to sequence by length

Sequencing - putting sticks in order from longest to shortest

Patterns

Another form of sequencing is to create patterns. You can do this with anything around the house - legos, hair barrettes, dry beans, cereal, spoons & forks, etc. It also works great with things you find outdoors - different kinds of sticks, leaves, stones, flowers, etc.

A simple alternating pattern

A more complicated pattern

Math Games to practice at home

Beginning Math Activities

"Subitizing" is the ability to see at a glance how many there are (example - if there are 3 oranges sitting on a table, you can tell without counting that there are 3. Here's a short video explaining how to help your child build this skill. Let me know if you have any questions and tell me how it goes!
We practice forming quantities on our fingers along with singing "Yellow is the Sun" (can also be said as a poem)

Quantities 1-10

The first skill children need to master is learning quantities 1-10, beginning with 1-5. 
1. Form numbers on fingers (I made this short video to show how to do it! We recommend learning quantities on fingers first!
2. Form numbers with color tiles (start with 1-5). Explore ways to arrange 4 or 5. Our favorite is the "4 square" & "5 pyramid"

3. Form numbers with tally sticks (5th stick goes straight across other 4)

Other early math activities:

Patterns

Grouping in 5s

Child takes a handful of objects (barrettes, legos, spoons, rocks, etc.) and then puts them in groups of 5 to tell how many there are without counting (start with 10 or fewer):

Sensorial Curriculum - Visual Perception

In the Sensorial curriculum of a Montessori classroom, we develop children's perceptiveness with each of their senses. Our goal is to increase their awareness of what they perceive through their senses and help them develop a mental framework for organizing and understanding these perceptions. The Sensorial curriculum provides a cognitive foundation for math and science.

Within the Sensorial curriculum, we have materials and activities to cultivate each of the senses. This post will only include the Visual perception materials - more to come later!

Size

Cylinder blocks (or knobbed cylinders) - each of the 4 blocks contains 10 cylinders that vary by different dimensions. A child begins working with one block at a time and progresses to being able to do all four blocks (40 cylinders) together.
The cylinder blocks are an example of a self-correcting Montessori material - the child can tell if there is an error because not all the cylinders will fit in!

 Most children are not able to see the small differences between the ten cubes of the Pink Tower when they are first introduced to it. Through repetition and exploration, they gradually become aware and learn to sequence the cubes by size - and feel very proud when they do! The opportunity to develop problem-solving skills is built into all these materials. A child may visually notice that they have a piece out of order, but it is additional challenge to figure out how to fix it. 

The Brown Stair (or Broad Stairs) provides the next level of challenge - the prisms vary in two dimensions instead of all three. After a child can sequence the brown stairs, they enjoy rolling a small wood marble down the steps, hearing the pitch change as it descends.  

The Red Rods come next - 10 rods ranging from 10cm to 1m.

There are additional activities that the children can do with each of these materials, alone or in combination.

A few examples of the many possibilities:

This child has built the Pink Tower with two sides flush,  creating a 1cm ledge on each level. The smallest (1cm) cube can be carefully slid along the step on each cube. 

Color

The first color box has only the three primary colors (red, yellow, blue), with two tablets of each color. Color box II adds secondary colors (orange, green, purple) as well as pink, brown, black, gray, and white.

After matching the color tablets, a child can walk around the room with a basket, looing for an object that is the same color as one of the tablet pairs. They bring the object back to the mat, then go in search of another color. This activity expands their conceptualization of color and exercised their working memory. (The tablets stay on the mat, which adds the challenge of needing to store the color in their mind as they go around the room.)

The Box of 32 pairs provides an increased challenge - matching pairs in four shades of each color. When we introduce the material, we take just one color out of the box at a time and match the four pairs before moving onto the next color. This child has chosen a different approach. She is purposefully engaged so we observe with interest to see what we can learn about her thought process and do not intervene or disrupt her focus.

Color Box 3 has seven shades of each color that can be graded from darkest to lightest

Shape

Children learn the names and forms of geometric shapes with the Geometry Cabinet

Montessori Classroom News March 14, 2018

Spring!!

Spring begins on Tuesday, March 20. We are ready!

We have been watching the trees for signs of spring and observing the daffodils growing in front of the school. We also have a potted daffodil plant that we are watching progress in our classroom.

Counting in “math language”

With good instruction and hard work, every child can understand math!

One of the ways we can help children understand the value and organization of numbers is by teaching them to name numbers in “math language”. Instead of saying thirty-four we will say “3-ten 4.” Similarly the numbers 11 to 19 will be called “ten 1, ten 2, . . . ten 9, and the twenties will be called 2-ten, 2-ten 1, . . . , 2-ten 9.

Saying numbers this way may feel strange to an adult, but it is a huge help to children in learning what each number represents. One of the reasons children in Asian countries tend to have higher math performance is because they use this kind of number naming. We will later teach the traditional number names (i.e. “eleven,” “twenty,” etc.), The children will have a clearer understanding of what values those words mean when they have also learned the number names in “math language.”

Read it Again!

 You have probably noticed that children love repetition! Good books are no exception. Although you may find yourself reciting their favorite books from memory and finding the storyline a little stale, muster up the patience to read that beloved book yet again. Reading the same story many times is great for your child’s development. The repetition allows the child to build off the familiar story, and s/he learns something new each time.

Dr. Seuss books have been favorites in the classroom recently. After reading Green Eggs and Ham a couple times as a group, many of the children will retell the whole story on their own

A house is a house for me

By Mary Anne Hoberman

A hill is a house for an ant, an ant

A hive is a house for a bee

A hole is a house for a mole or a mouse
And a house is a house for me!