Preschool Math (Pre K-2nd Grade) using Math Their Way

 I do this list of activities in this basic order, spiraling around each of these four years. I stop each area when the activities seem to hard for them, because I know I will be getting back to them the following year, or when they seem to have mastered the content of that area.

Weeks 1-5: Free Exploration and Counting
 Introduction
Application and Extension
Counting (Assessment)
Counting On
Learning to Write Numerals


Weeks 6-9 Patterns, part one
 Introduction
 Application and Extension



Weeks 10-13: Sorting and Classifying
Introduction
Application and Extension
Graphing: Introduction


Weeks 14-17: Comparing 
     Introduction
    Application and Extension

Weeks 18-28: Number
(Assessment)
Concept Level
          Introduction
          Application and Extension
Connecting Level
Symbolic Levels

Weeks 29-36: Place Value
(Assessment)
 Introduction: The Counting Game
 Application and Extension


Weeks 37-42: Patterns
Patterns, part two 

source: Math Their Way

Graphing: Introduction (Pre K-2)

Graphing organizes data so patterns and relationships that might otherwise be missed stand out clearly.

You can approach graphing as a in-stages process. 

Begin Graphing with Actual Objects

Groundhog's Day Predictions
An example of this is our Groundhog's Day Predictions graph.Everyone took a guess whether Punxsutawney Phil saw his shadow by putting the cookie the appropriate side up on the graphing chart.

Next Use Picture Graphs

Paper Button Graphing

Picture graphs use a pictorial representation of the actual object on the graph. We used paper buttons rather than actual buttons for one of our graphs. We had sorted actual buttons in many different ways, then they  made their own paper buttons, designing them any way they wanted. Once they were completed, they began graphing them in several ways, using different criteria. They used a piece of posterboard or a dry erase board to make your graph and they placed their buttons on where it is appropriate. First they graphed them according to how many holes they had and then they graphed them according to what shape they were, continuing on for as long as they wanted. 

What are some other things that can be graphed in this way? Any math manipulatives or items from junk boxes can be sorted in this way, with the student making paper representations. If you use the whole family to help with giving data, you can ask such questions as: What would you like for lunch? (If you have four options.) What color Lifesaver is your favorite? What would you like best for a birthday present? What game would you like to play? Use pictures of the different items, from magazine cut-out or student or teacher drawn to fill out the graph.

Graph comparing the number of diesel and steam engines at Railroad Trains, Part 3 Types of Trains

Lastly Symbolic Representation Graphs

Finally, you can now graph just with symbolic representation. For, example, James made a bar graph, comparing the number of diesel and steam engines in use from 1941-1981. You can easily see how the use of diesel engines went up while the use of steam engines went down.

source: Math Their Way, Mary Baratta-Lorton

Sorting and Classifying: Application and Extension (Pre K-2)

Read My Mind

Read My Mind is a silent game in which a designated person sorts an assortment of colored shapes anyway he likes and everyone has to guess how he has sorted them. When one has guessed, he raises his hand. After everyone raises their hand, the first person who raised their hand gets to tell how he thinks they were sorted. If he is wrong, the next person who raised their hand gets to guess.

Quentin, 9/24/08

Sam & James, 2008

Descriptions

Quentin 2008

This game starts by asking your students to gather together a collection of stuffed toys (or any other set of toys that are similar.) One person would pick out one of them, but not tell the rest of us his choice. He then would give a descriptive clue, starting with the most vague clue, and getting more specific as the clues went on, until the choice could be picked out.

Sorting and Classifying Walks

Often when we take walks in the neighborhood, we will go on a math walk, changing the focus of the walk each time. We will decide in advance what we will be looking for, which will be determined by what they are working on in math. One time it might be to look for shapes, colors,  or for types of lines (diagonal, vertical and horizontal, curved, etc.). Another time it might be for things made of metal (or glass or wood or plastic), things that move, things that are rusty, signs, vehicles, textures, delicate things...etc. As you can see, the list goes on almost infinitely. Sometimes we take along with us paper and crayons and he can stop and sketch the various thing he find. He could also take photographs. He can make a book of them. Later walks, we wait until he gets back and he has to sketch the things we found from memory.

Sorting by Senses

You can have things laid out for him to sort according to taste, touch, smell or by sounds. For taste, you can have out examples of sweet, sour, spicy and salty. For touch, you can blindfold him and have him sort things by texture, weight, size or shape. For sounds, they can be loud or soft, near or far. They learn lots of new vocabulary by this type of sorting.

Name Claps

You can have your student clap out the syllables in the names of the people in their family or their friend's names. If they find this difficult, you can write the names on a white board and then write little hills to represent the hops the syllables make. Then clap them out together.

Geoboard Sorting Game
Ask you student to make a geometric shape, such as a triangle.  Have him draw it on Geoboard Dot paper. Can he think of another way of making that same shape? Have him make as many as he can and then sort the dot papers according to the type, size or orientation of the shapes. For example, if he made triangles, have him sort the dot papers so that all the small triangles are in one pile and all the large ones in another, or  have him sort them so that all the right triangles are in one pile and the other triangles in another. How many ways can he sort them?

Geoboard Paths

Put a cube on the bottom right-hand peg of the Geoboard and one at the top left-hand corner. The students trace a path from one cube to the other cube. Once they are satisfied with their paths, they can record them on Geoboard Dot paper. (Since my Geoboard has 6 pegs and the dot paper has 5 pegs, we decided not to use the outer pegs on the top and left-hand side and covered them with bands.) Other students can take one of the papers and copy the patterns.

Geoboard Arrow Game

For this game, you will need to make up a set of direction cards with arrows (see example in photos.) The students then find as many different ways as possible to follow one set of directions. Everyone who finds a different way can copy the pattern onto dot paper and pin the paper on a bulletin board or they can be made up into a book to record the different solutions.

Food Coloring

This is one I remember doing myself when I was small. Provide a package of food coloring and a large quantity of baby food jars or plastic cups. Ask them how many different colors they can make. They can dip a small piece of paper towel or coffee filter in each jar to record the color, if they wish to record their discoveries.

Another great game to play for sorting and classifying is Hullabaloo, which combines sorting with action.

source: Mathematics Their Way, Mary Baratta-Lorton

Learning to Write Numerals (Letters, too!) (Pre K-2nd)

Large Numeral Cards

James, 2008

Make large numerals that cover the whole sheet of paper. The first part of the numeral is drawn in purple and the second part in green. Hang on the wall. Students stand at least ten feet away and trace the shape of the numeral in the air with a finger or two extended. The purple part is traced first and then the green. This helps to eliminate reversals. Once they are confident in tracing it in the air, they can switch to tracing it in the palm of their hand, which is held high enough so that if they raise their eyes slightly, they can still see the large numeral card.

Cooke Dough Numerals

Make a stiff cookie dough by adding an additional 1/2-3/4 cup flour. Have students roll out a snake and fashion a number. You can make up a sheet to help them by writing large numerals on a piece of paper and then cover it with a sheet of waxed paper. The snakes can then be formed into numerals right on top of the waxed paper, using the sheet of numerals as a guide. Transfer to a cookie sheet and bake. 

Numeral Sequence Cards

James, 2008

James and Sam, 2008

Using Numeral Sequence Cards, the student forms the numeral in various materials, such as salt trays, finger paints, pudding, chalkboard or frosting. Numeral Sequence Cards are just cards in which the numerals written on them are written in two parts, with the first part of the numeral written in one color and the second part in a second color. It helps students to see the order in which to make the lines.

Geoboard Numerals

You will need to make numeral pattern cards first. Take a piece of Geoboard Dot Paper and make numerals on them. Students than make the numerals on their geoboards, copying the pattern cards. This is particularly helpful if you have a child who is revearsing their numerals.

Dot-to-dots and plastic number templates can be used as a transition to typical writing worksheets.

source: Mathematics Their Way, Mary Baratta-Lorton

Comparing: Introduction (Pre K-2)

Things in the Room

For this game, you each think of something in the room, such as windows, plants, chairs, pencils, doors, and then the student decides which there is more or less of. When the answer is not obvious, Unifix cubes can be used to count the items that you cannot hold, in a one-on-one correspondence.

Comparing Names

The student writes his name on a sheet of graph paper and then writes the names of his family members or friends in the next rows. Now compare the names. Who has more letters in their name? Who has less? Who has the same? How many more or less letters do each of the names have?

Height Records

Periodically measure everyone in the family's height and compare the measurements to each other's and to their own previous measurements. 

Body Measurements

Using just a length of yarn or string, students measure and compare the length or circumference of various parts of their bodies. They also compare their own measurements with others. The results might surprise you! I was surprised at how many excited exclamations could be heard, such as, "Look, this is how long it is from head to by belly button!"

See-Saw

Comparisons could be made on a See-Saw. Who weighs more? Who weighs less? What two people weight the same as one heavier person? Can you make estimates and check them?

source: Mathematics Their Way, Mary Baratta-Lorton

Sorting and Classifying: Introduction (Pre K-2nd)

Sorting Together

For beginning sorting, you can define the categories by which the students are to sort. You can begin with shapes of various colors and sizes made from colored paper. The students respond to your questions, indication whether or not a particular shape can be placed in a given group. In various turns, you can have them sort by color, size and shape, using appropriate attribute names. Once they are able to sort in this way easily, encourage them to say why a particular shape can or cannot be placed in a particular group.

Junk Box Sorting

Guide your students through exploring and sorting various types of math manipulatives. Ask them questions to help them observe how things are alike and different and sorting various items in different ways. 

source: Mathematics Their Way, Mary Baratta-Lorton

Free Exploration of Math Materials: Application and Extension (Pre K-2)

"Only when children have had time to play and explore new materials in their own way, will they be able to see the materials as learning materials and be able to focus on mathematical concepts rather than on the materials themselves. Without free exploration, children's play interests are unsatisfied and until this need is fulfilled, the children will pursue this priority relentlessly." 

-Mary Baratta-Lorton, Math Their Way

The Jars

For this activity, you will need assorted jars, all different, varying in height, circumference, volume and shape. You will also need a set of measuring cups and spoons. You will also need either water or rice.

Students are left on their own to explore the jars, filling them up with the water or rice. Put a few drops of food coloring and/or extract such as peppermint or lemon as a pleasant change.

Weighing Common Objects

For this activity, you will need a balance scale. If you want, you can make one with two milk or orange juice cartons, washed and cut down to about 1-2 inches. For each one, punch a hole with a hole-punch in each side and thread a piece of string through the holes. Tie the strings at the top and attach to a rubberband. You can attach the rubberband to a  ruler taped to a table. Make two so that comparisons of the weight of objects can be made. Have the students weight two objects such as school supplies or fruit and determine which weighs more or less.

Mirrors 

Many explorations can be made with mirrors. Once explorations with one mirror have been exhausted, two mirrors can be taped together and more discoveries can be made.

Food Coloring

Students fill a cup or jar with water and look at the pattern and colors formed when they drop food coloring in the water.

At another time, put out salt and sugar so that they can compare salt and sugar water patterns.

Reproducing Designs

This beautiful handmade geoboard is from Craftmatter.

On the Geoboard
Have one child make a design on a geoboard and then have him copy the designs on dot paper. Once two have made their designs on dot paper, they can trade their dot papers and reproduce the other child's design on the geoboard.

On Pattern Blocks

With pattern blocks, one can create a design and another student can copy the design... 

or a student can make half a design and have the next student finish the design copying it symmetrically.
You can also use wooden blocks, Unifix cubes or any other math manipulative.

source: Mathematics Their Way, Mary Baratta-Lorton

Place Value: Application and Extension of Place Value (PreK-2)

"There is a fundamental discrepancy between the names of the numbers and the numbers themselves. This causes children great difficulty in trying to make sense out of large numbers." 

-Mary Baratta-Lorton, Math Their Way

 All of the following activities are in base ten. It is critical that both you and your students use the same terminology for base 10 that was used for the other bases. In this way, the earlier grouping games are linked to base ten and students recieve the full benefit from the earlier games. It is fine for students to say "twelve" but reinforce the concepts by saying, "and that means one ten and two." Encourage your students to say this whenever they say or write a numeral. Without this, students rely on their memory and the skill is quickly lost through disuse.

Measuring

Have your student pick out at least 3-5 things around the house to measure with trains of Unifix cubes.

Then have him break the trains into groups of ten.

If he needs to, he can then put them on a place value board.

Have him record the total for each measurement.

Estimating and Checking

Present to your students the task of estimating how many objects are in any empty container you have. You can use any math manipulative for this activity, but I like to use snacks, such as these gummy frogs or goldfish crackers because it interests children. I then ask one student to take the counters out of the container and put one on each small circle of a place value board. A place value board can simply be pieces of cardstock or construcion paper of various colors taped together, each color signifying a different place value. If your student has difficulty with math, is very young or just has difficulty noticing when they have collected ten, you can make the place value columns more clear by putting ten small circles in one section for the ones, ten larger circles for the tens, etc. If you make the circles the same size as the bottom of a bathroom paper cup, you can use those to hold ten of any item you are counting. In the next section have circles large enough for a bowl or coffee can. This container needs to be large enough to hold ten of the bathroom cups, or 100 items per circle.

Once all the circles on the ones section are filled then have your student take them off the ones circles and put them in a bathroom cup and put the cup on the tens side.

For this example, Quentin filled the ones section twice and had three frogs left over. It was easy for them to see that there were 23 in the jar. This is a pleasureable way to learn estimating skills if you do this regularly with different counters and different containers of all sorts of shapes and sizes.

After you have done this several times, you can increase the amount of counters you are usings as well. Initially their estimates will not be so accurate this time, as the numbers you work with are higher. Give your students chances to change their estimates as they go along because the object is for them to get better at estimating, not winning against each other. 

Counting Jars of Objects

Each student counts the number of objects in a jar onto their place value board. When he has finished, he writes the total on a piece of paper and places it in a designated place. We use a bulletin board. Other students check this total by recounting and writing on the previous piece of paper "agree" or "disagree with the  amount that the student that disagrees believes is in the jar. Have the whole family participate, even if the other members of the family are beyond this skill.

Peas in a Pod

Dump a bag of unshelled peas onto a table. First, ask them how many peas on the average are in each pea pod. Record their guesses.

Now open the pea pods and have them count how many peas are on each side, counting one side at a time and recording the numbers as an addition problem. (Number of peas on left side plus number of peas on the right side equals how many peas altogether.) Have them put each pea pod's contents in a cup and have the students place their cups on a graph according to the number of peas inside.

Base Ten Unifix Patterns

We had fun with Base Ten Unifix patterns.

He explored the number six this day.

He just picks a number to explore and adds the cubes to the place value board in groups of that number. Once he reaches ten cubes on the right-hand side, he snaps them together and puts them on the left-hand side.

Here is his cubes once he had added 6 five times.

He makes a record as he works independently, adding one group at a time.

Perimeters

For this activity, you will need records of tile and geoboard designs from exploring numbers at the number stations.

The student places Unifix cubes around the perimeter of the base design, snaps the cubes together into sticks of tens, counts them and records the total. He may repeat this many times for the various designs of six to ten.

Geoboard Design

The student makes a shape on the geoboard using one large band. At first students can cover the pegs inside the one shape with one color of Unifix cubes and the pegs on the outside with a second color Unifix cubes. They then take the Unifix cubes off and record each number and the total number of pegs on their paper.

 (Worksheet for this can be found here.)

After they have become more accomplished with counting, they can just count the pegs and record their numbers as addition problems of their own making.

The Store

We happen to have a little board book that has various shops with prices. It is wonderful additon and subtraction practice. You could use a toy catalogue, a supermarket flyer or make one up yourself. Begin by having students use the place value board at first and then progress to their using this sheet . Have them write the name of the item on the blank and the amount to the right. They can then add the ones and tens columns separately, as the tens are shaded. Be careful to put low numerals in the ones place if you have not covered "carrying" yet.

Recording Number Patterns from Row, Column and Diagonal Patterns with Unifix Cubes

After exploring Row, Column and Diagonal Patterns with Unifix Cubes, you can take the same numbers to explore in a different way. This time the student records these numbers in a stair-step method on graph paper. Set up the graph paper by putting a thick black line down the middle of the paper and have ones on the right side of the line, and tens on the left.

Can you see where he made a mistake, and then tried to erase it?
It is easy to see when you make a mistake when you look at the patterns.

This picture actually shows the patterns found in base 6,
but any base can be done in this way, including base 10.
Can your student predict the continuation of the number sequence?

Recording Number Patterns from Surrounding Patterns

For this activity, you will need your student first to make some Surrounding Pattern pages.

We didn't have enough cubes of any one color, so he had to combine colors to equal  each row. This is fine as long as he doesn't get the colors confused.

Students then put the Unifix cubes back on the graph paper on top of the patterns. They then take the cubes for each row and snap the cubes together and compare the number of cubes with those used in the previous surrounding.

Student breaks the rods into rows of ten and whatever is left over.

source: 

• Mathematics Their Way, Mary Baratta-Lorton