Mathematics


This area of learning includes big ideas about students’ understanding of shapes and spatial relationships, counting and comparison of numbers and objects, and an ability to solve problems using different strategies.  By clicking on any of the progressions below, activities are provided to help you support your child at home.  Should you wish to print these activities for quick reference, click on the printer icon included with each progression.


Big Idea

A kindergarten student will model real world problems by composing 2- and 3- dimensional shapes.

Beginning

Activities

Suggestions for Families
Identifies (points to) 2-dimensional shapes: square, triangle, circle, and rectangle (e.g., point to the circle)
Shape Walk through Books: As you read your child’s favorite book, ask him to point to shapes that might be included in the pictures within the text.

Everyday Shapes: Point to an object (e.g., block, base of a measuring cup, box of cereal, hat made of newspaper, piece of pizza) or shapes within/on objects (e.g., buttons as circles on a cell phone screen; magazines) and ask your child to identify what shape it might be.


Emerging

Activities

Suggestions for Families
Names 2-dimensional shapes: square, triangle, circle, rectangle, and hexagon.
Street Sign Shape Hunt: Take a walk through your neighborhood and help your child find street signs. Have her name squares, circles, rectangles, triangles, and hexagons (six-sided shape) that she sees.
Identifies (points to) 3-dimensional shapes: sphere, cylinder, cube, and cone.
Super Shape Sleuth: Challenge your child to move around your house to identify complex shapes such as a sphere, cylinder, cube, and cone. Talk about the many varied places these shapes could be found (e.g., paper towel tube, soccer ball, balloon, cube of scratch paper, funnel).
Identifies (points to) sides or corners (vertices) when asked.
Parts and Whole: When your child has correctly named a shape, extend the conversation and ask him to point out the sides of a triangle/square or the corners (vertices) of a completed puzzle.


Developing

Activities

Suggestions for Families
Names 3-dimensional shapes: sphere, cylinder, cube, and cone.
Name that Shape: Challenge your child to name items in your home that are made with complex shapes of spheres, cylinders, cubes, and cones (e.g., boxes, soda can, ice cream cone, ball). Extend the activity by asking your child to identify characteristics of these shapes (e.g., round, six sides)
Describes 2- and 3-dimensional shapes using their attributes.
Roll, Slide, Stack: Find some common objects in your home and have your child experiment with the objects to classify them into shapes that roll, slide, or stack. For example, an object that is a sphere can roll over and over but a block cannot.
Classifies, sorts, or identifies shapes as 2- or 3-dimensional.
Create a 2-D and 3-D Museum: Compare and contrast objects that are 2-dimensional and 3-dimensional. Two dimensional shapes have length and width and are described as flat. Three dimensional shapes have length, width, and depth. Create a space for your child to identify some common objects in your house and sort them into “rooms in the museum.” Once your child has established all of the exhibits in the museum, talk about the features of 2-D (length, width, no thickness) and 3-D shapes (faces, edges, vertices or corners).


Demonstrating

Activities

Suggestions for Families
Explains similarities and differences among 2- and 3-dimensional shapes using attributes when classifying, sorting, or identifying.
Be a Shape Detective: Present your child with two objects. Once your child names the shapes of the two objects, ask her to describe how the shapes are similar or different (e.g., corners, base, edges, vertices or corners).
Composes simple shapes to form larger shapes with given attributes (e.g., fills in the outline with shapes).
Pieces and Wholes: Use the front of a cereal box and cut it into four squares. Then cut one of the squares into two right triangles. Cut another square into two right triangles and then cut each triangle into two additional triangles. Ask your child to describe the shapes as he assembles the pieces into the whole puzzle (e.g., these two triangles made a square).
Creates models of real-world figures by composing 2- and 3-dimensional shapes.
Let's Build It: Use household materials (blocks, pipe cleaners, toothpicks, play dough, popsicle sticks, Legos, different types of craft paper) to allow children to build models or collages of figures such as a house, rocket, or other various models of real-world figures.

Self-Correcting Puzzles: Use popsicle sticks to build shapes. On the back side of the popsicles either draw the figure or write the name of the figure once composed (e.g., triangle, square).


Exceeding

Activities

Suggestions for Families
Builds or draws from given defining attributes (e.g., draw a shape with 4 corners and 4 sides and all sides are the same length)
Mystery Shape: Ask your child to draw shapes based on your directions. For example, “draw a shape that has three equal sides.” Once your child has drawn the shape, ask him to name the shape and talk about its attributes.
Uses composite shapes to create additional composite shapes (e.g., adds on to a given or self-created composite shape).
Look What I Built: Give your child pattern blocks or shapes cut from heavy paper and ask her to create a figure. Once the figure is created ask your child to describe the shapes that were used to construct the figure. Then, ask her to add to the figure with additional shapes (e.g., add windows or a chimney [squares] to a figure of a house).
Decomposes rectangles and circles into equal parts by drawing partitions within a given shape.
Equal Shares: Use paper cutouts of rectangles and circles. Ask your child to share the rectangle equally so that you and your child get the same size piece. You can extend this activity with naturally occurring experiences in your home. For example, there might be opportunities to divide a rectangle of brownies for dessert into equal parts.

Big Idea

A kindergarten student will count using multiple strategies. 


Beginning

Activities

Suggestions for Families
Counts to 20.
Fill it Up: Use 20 cupcake paper liners and write one number from 0-20 on the bottom of each. Have your child arrange the cups in order and then add beans, buttons, or pennies to represent the number on the bottom of each cup. Once the cups are filled, dump out the contents and ask your child to count by dropping the objects back into the containers.


Emerging

Activities

Suggestions for Families
Counts to 30.
Calendar Math: Starting with the beginning of each month, have your child circle the date and then count from day one to the present day, touching each number as he counts.

Set the Table: Ask your child to help set the table for dinner. Count out the number of objects that are placed on the table (e.g., plates, cups, napkins, salt and pepper container)

Snack Time: Ask your child to help you distribute the afternoon snack. Count out pretzels, crackers, grapes, or other healthy snacks until your child reaches 30. Extend the activity by asking your child to split the 30 into equal parts to share!


Developing

Activities

Suggestions for Families
Counts to 50 by 1s and 10s.
Bank Teller: Using pennies and dimes, have your child place pennies in a cup until she reaches 50. Show your child how one dime equals 10 pennies. Help her count the dimes by 10 until they reach 50.

What Comes Next?: Count by 10s with your child and periodically stop counting, asking him to supply the next number. (Parent: 10, 20, 30, Child: 40, 50)

Laundry Helper: Ask your child to help sort the laundry and count each item by ones or create piles of 10 pieces until you and your child reach 50.
Counts forward to 30 from a given number within 0-30 (e.g., starting with 15, count up to 30.)
Counting On: As you drive through your neighborhood or community, pick an object to count. Say to your child, I counted three (or another number from 0-30) houses before we turned the block, can you help me count how many more houses you see? You can count other things such as trucks, buses, a specific color of car, stop signs, etc.


Demonstrating

Activities

Suggestions for Families
Counts to 100 by 1s and 10s.
Special Days: Create a calendar with a special event(s) 100 or more days away. Each morning ask your child to add a day and keep track of the number of days that have passed.

Mother May I:
Stand a distance away from your child, tell your child to take a variable number of steps (in groups of 10) to walk toward you. Say to your child, walk to me in two groups of 10 steps; how many steps did you walk?

I Am Thinking of a Number:
Say to your child, I am thinking of a number between 0 and 100 that is a group of 10. Say your tens until you can guess the number I am thinking!
Counts forward to 100 from a given number within 0-100.
You Pick a Number Back and Forth: Ask your child to pick a number from 0-90 and then go back and forth taking turns by saying the next number.


Exceeding

Activities

Suggestions for Families
Counts to 120 by 1s, 5s, and 10s.
Coin Challenge: Collect change throughout the week. Once you have collected a variety of coins, ask your child to help you count the coins by their number and their value.

Beginning

Activities

Suggestions for Families
Counts 10 objects using 1:1 correspondence.
Clean up Time: Ask your child to pick up his or her toys and to count each toy as the toy is placed in its proper storage place.


Emerging

Activities

Suggestions for Families
Counts 1-10 objects presented in a line and tells the number of objects counted. Includes answering questions about “how many.”
Make a Row: Using small toys in your home, line up a number of objects and ask your child to count them. Extend the activity by asking how many more to get to the number 10.
Given a set of up to 10 objects, matches a written numeral to represent the number of objects.
Draw a Card: Using a deck of cards with cards from 1 to 10, ask your child to draw a card and then match the number on the card with the same number of small objects (e.g., Legos, beans, small blocks)


Developing

Activities

Suggestions for Families
When told a number 1-10, count out that many objects (presented in a line).
Show Me How Many: State a number from one to 10 and ask your child to place a number of small objects from your home in a line to represent that number.
Counts 11-20 objects presented in a line using 1:1 correspondence and tells the number of objects counted. Includes answering questions about “how many.”
Make a Row: Using small toys in your home, line up a number of objects and ask your child to count them. Ask your child to count how many and point to each object as he counts.
Given a set of 11-20 objects, matches a written numeral to represent the number of objects.
Treasure Hunt: Move about your house and look for objects where there are 11-20 of something (e.g., books, socks, dishes, toys). Take a number of those objects and place them in a pile. Ask your child to count them and write the numeral that would represent the number of objects (11-20).
Writes numbers 0-10 to represent a quantity.
Write the Number: Using small objects from your home, give your child piles of materials and ask her to write the number that represents the number of objects in the pile.


Demonstrating

Activities

Suggestions for Families
When told a number 0-20, creates a set of objects equal to that number and matches a written numeral to represent the number of objects.
First Person Wins: Ask your child to name a number between 0-20. Create a set of objects to represent that number. See who is the first to do so. Ask your child to write down the numeral to represent that number.
Counts up to 20 objects when presented in a rectangular array or circle. Includes answering questions about “how many.”
How Many: Arrange up to 20 beans or other small objects in a circle or in a rectangular array (beans in lines with the same number in each line). Ask your child to count the number of objects present.
Counts objects up to 10 in a scattered array. Includes answering questions about “how many.”
Gathering Leaves: Walk through your yard and ask your child to count the number of leaves they see as they count from 1-10. Vary the activity by asking your child to count only specific colors of leaves.
Answers questions about “one larger” in a set up of up to 10 objects using the number names.
The Helper: Ask your child to sort kitchen utensils after they have been washed. Count the number of forks as your child places them in their storage location. Ask how many would we have if we had one more? Two more?
Writes numbers 11-20 to represent a quantity.
It’s All in a Number: Take a tour through your house and find objects that have 11-20 in number. Ask your child to count the objects (e.g., towels, books, shoes, toys, chairs) and then write the number down on a piece of paper to represent the number counted.


Exceeding

Activities

Suggestions for Families
Counts more than 20 objects, presented in a variety of ways (e.g., scattered, lines, rectangular array, circles).
More than 20?: In a variety of settings, ask your child to count more than 20 objects. For example, in a walk through the neighborhood your child might be able to count the number of houses on all sides of a block. Ask your child to count the number of minute markers on a face clock. Count the number of days on the calendar for a particular month.
Given a set of more than 20 objects, matches a written numeral to represent the number of objects.
Treasure Hunt: Move about your house and look for objects where there are more than 20 of something (e.g., books, socks, dishes, toys). Take a number of those objects and place them in a pile. Ask your child to count them and write the numeral that would represent the number of objects (20+).
Writes numbers greater than 20.
Spill the Beans: Place more than 20 beans in a cup. Ask your child to “spill the beans,” count them, and write the numeral that represents the number of beans.


B
ig Idea

A kindergarten student will compare objects and numbers represented in different ways to solve real world problems.

Beginning

Activities

Suggestions for Families
Identifies/matches equal sets of objects using 1:1 correspondence.
Make a Match: Using small objects from your home, set out a number of objects and ask your child to match the same number of objects by placing his or her object one by one next to the objects you have set out.


Emerging

Activities

Suggestions for Families
Given two sets of objects, identifies whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group (0-10 per set).
Same, More, or Less: Look for naturally occurring opportunities to compare and contrast sets of objects from 0-10. Children can compare piles of books, numbers of Legos, piles of toys, etc.


Developing

Activities

Suggestions for Families
Explains and/or shows whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group between 0-10 per set using counting or matching strategies (e.g., “this group is larger because it has 2 more objects than the other group”).
Number Crunchers: Set up two sets of objects with the number of objects ranging from 0-10. Ask your child to count the objects in each set and describe which set is greater than (has more), less than (has fewer), or if the sets are equal to one another.
Compares two numbers between 1-5 presented as written numerals (e.g., holds up the written numbers, points to or circles the number).
Number Match: Have your child write numbers one through five on two sets of note cards. Your child can also draw the number of items on the card to help facilitate the numeral with the objects. Shuffle the cards and place them face down. Have your child pick up two cards and state whether the cards match with one another. If not, return the cards face down and draw again.


Demonstrating

Activities

Suggestions for Families
Solves real world problems involving comparison of numbers of objects—greater than, less than, equal (e.g., use counting, etc.).
Household Helper: Ask your child to solve simple problems that use comparison. For example, if your family needs to set four places at the dinner table, set out two. Have your child determine whether or not you have less than the number required for everyone to have a place to eat. Ask your child about the number of pencils she has in her book bag and whether or not there are fewer pencils in the book bag than needed.
Compares two numbers between 1-10 presented as written numerals, with at least one number being between 6 and 10 (e.g., hold up the written numbers, points to or circles the number).
Same Numeral?: Using two sets of cards (one set from 1-10 and one set from 6-10), have your child draw one card from each stack and compare the two numbers. Ask your child to describe the relationship between the two numbers.


Exceeding

Activities

Suggestions for Families
Solves real world problems by comparing two written numbers greater than 10, records the result with >, <, or =.
Everyday Math: Ask your child to solve real world problems, comparing solutions. For example, perhaps when packing toys in a book bag set out a number of toys and ask your child to predict how many toys might fit in the bag. Compare the prediction with the actual result.

Big Idea

A kindergarten student will apply multiple strategies to solve real world problems using addition and subtraction.

Beginning

Activities

Suggestions for Families
Uses objects or fingers to represent a real-world addition or subtraction problem within 5, when read aloud.
Making Five: Ask your child simple questions and model how many more to make five or how many less from five to solve problems  For example, say we have five cookies and there are three children. How many cookies would we have left over?


Emerging

Activities

Suggestions for Families
Draws pictures to represent a real-world addition or subtraction problem within 5, when read aloud.
Let’s Draw It: As your child begins to understand adding and subtracting, model those processes using pictures to display the results.


Developing

Activities

Suggestions for Families
Uses counting strategies (e.g., ten frames, counting on, counting back, mental images, number lines, acting out) to solve addition and subtraction problems within 10.
How Many More? How Many Less?: When you and your child solve a problem, use phrases like "let’s count on" or "count back" to come to the solution.
Finds the missing number to make 5 (e.g., using ten frames, number lines).
Let’s Solve It: Use objects to help your child solve mathematics problems to five. For example, say we have three books to read, how many more books until we have five?
Decomposing numbers into pairs in more than one way, using objects or drawings within 10.
What is the Number Pair?: Use cards numbered one to ten and ask your child to draw two cards. Use small objects or drawings to help your child add or subtract the two numbers.


Demonstrating

Activities

Suggestions for Families
Solves real-world problems by adding and subtracting within 10 and explains the strategy used. The strategy can include the equation.
Can You Help Me Solve This Problem?: Ask your child to help you solve simple but needed real-world problems. For example, say tell me how many more spoons we need to set the table.  Ask your child how he came up with the answer.
Responds immediately and accurately (verbally) to addition and subtraction within 5.
To Add or Subtract?: Write the numbers 1-5 on three sets of cards. Have your child draw two cards. Ask your child what the two numbers added together or subtracted from one another equal.
Finds the missing number to make 10 (e.g., using ten frames, number lines).
Let’s Solve It: Use objects to help your child solve mathematics problems to ten. For example, say we have six books to read, how many more books until we have ten?
Composes and decomposes numbers from 11 to 19 into ten ones and some further ones by using objects or drawings. Records compositions or decompositions by a drawing or an equation.
What is the Number Pair?: Use cards numbered 1-19 and ask your child to draw two cards. Use small objects or drawings to help your child add or subtract the two numbers.


Exceeding

Activities

Suggestions for Families
Solves real-world problems by adding and subtracting within 11-19 and explains the strategy used. The strategy can include the equation.
Can You Help Me Solve This Problem?: Ask your child to help you solve simple but needed real-world problems. For example, say tell me how many more envelopes we need to send invitations to the party.  Ask your child how she came up with the answer.
Responds immediately and accurately, verbally or in writing, to addition and subtraction problems within 10.
To Add or Subtract?: Write the numbers 1-10 on three sets of cards. Have your child draw two cards. Ask your child what the two numbers added together or subtracted from one another equal.
Composes and decomposes numbers more than 20 into ten ones and some further ones by using objects or drawings. Records compositions or decompositions by a drawing or equation.
What is the Number Pair?: Use cards numbered 1-30 and ask your child to draw two cards. Use small objects or drawings to help your child add or subtract the two numbers.