Elementary Mathematics K- 1st Grade

Our website is designed to provide New Milford families with valuable information and resources in support of children's mathematics learning. 

Beginning in school year 2014-15, New Milford is implementing Investigations in Number, Data, and Space in Kindergarten through Grade 5.  Check out the "For Families" page on their website!  This essay describes the Role of Games in Investigations

For each grade level K-5, there are activities and online games by topic to support student learning.


Counting & Cardinality

What Your Child Will Learn

- Count to 100 by ones and by tens. (K.CC.1)

- Count forward starting with any number (instead of having to begin at 1). (K.CC.2)

- Write numbers from 0 to 20. (K.CC.3)

-When counting objects, say the number names in order, pairing each object with one and only one number name and each number name with one and only one object. (K.CC.4)

- Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. (K.CC.4)

- Understand that each successive number name refers to a quantity that is one larger. (K.CC.4)

- Count to answer “how many?” (K.CC.5)

- Identify whether one group of objects is greater than, less than, or equal to the number of objects in another group (K.CC.6)

- Compare two numbers between 1 and 10 presented as written numerals. (K.CC.7)


- One-to-one Correspondence: Students assign one number to each object as they count

- Greater Than: A number that has a higher value than another number

- Equal: Having the same value

- Count On: Starting at a given number and counting forward from that number

- Less Than: A number that has a lower value than another number

Activities at Home

- Play the license plate game with numbers as you walk through your neighborhood. Have them look for a 1 on a license plate. Then find a 2, then a 3, and so on.

- Write your name and a family member’s name. How many letters are in your name? How many are in your family member’s name? Which name has more?

- Look through a store ad. Cut out numbers 0-20. Put the numbers in order from least to greatest.

- Grab a handful of an item, cereal, beans, etc. Estimate how many pieces you grabbed. Now count them. Was your estimate close?

- Estimate how many spoonfuls it take to finish a bowl of cereal. Count each spoonful as you eat.

- Walk around your home. Count how items are plugged into the wall.

- Show the number 5 in as many ways as you can. Use pictures and numbers.

Kindergarten Operations & Algebraic Thinking

What Your Child Will Learn

- Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (K.OA.1)

- Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem (K.OA.2)

- Break apart (decompose) numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1)  (K.OA.3) (Note: It is a Grade 1 expectation that students understand and write equations.)

- Find the number that makes 10 when added to a given number, e.g., by using objects or drawings, and record the answer with a drawing or equation For example, if you have 6, what number is needed to make 10? (K.OA.4) 

- Fluently add and subtract within 5. (K.OA.5)


- Add: To join together two or more numbers

- Subtract: To take one quantity away from another

- Compose: To put decomposed numbers back together. 10 and 5 is  15.

- Decompose: To break a number into smaller parts to simplify computation. Example: 15 is 10 and 5

Activities at Home

- Use cereal pieces to solve the following problem: Mason has 10 pieces of cereal. He eats 4 pieces. How many pieces are left?

- How old are you now? Subtract one from that number and record it. Add 3 to that number and record it.

- Count backwards from 100. Skip count to 100 by 10s. Which took longer? Write your answer.

- Go outside and find two clovers. Write an equation to show how many leaves are on both clovers.

- Use some fruit to solve the following problem: Ken has 5 bananas in a bunch.
He eats some. There are 3 left. How many bananas did he eat?

- Ben had 4 chairs at his kitchen table in the morning. After school there was only
1 chair at the kitchen table. How many chairs are missing?

Kindergarten Number & Operations in Base Ten

What Your Child Will Learn

Make (compose) or break apart (decompose) numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 is 10 and 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.  (K.NBT.1) (Note that using and understanding the equal sign and equations in a Grade 1 standard.)


- Place Value: The value of the place of the digit in the number
(For example: in 27, 2 is in the 10's place and is worth 20)

- Compose: Putting numbers together to make a new number
(For example: 5 and 10 make 15)

- Decompose: Breaking a number apart
(For example: 15 is 8 and 7)

- Ten: A group of ten ones

- Add: To join two or more numbers

- Subtract: To take one quantity away from

Activities at Home

- Use a stick of spaghetti to represent 10 and marshmallows to represent ones.
Represent the numbers 12, 13, and 16 with the spaghetti and marshmallows.

- Use a popsicle stick to represent a ten and beans to represent ones.

- Using a deck of cards, give your child a 10 card, and draw another number card,
then add the numbers together and show the number with sticks and beans.

- Walk from one end of the kitchen to the other and count how many steps,
then show how many steps were taken with sticks and beans.

Measurement & Data

What Your Child Will Learn

- Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. (K.MD.1)

- Compare two objects with common measurable attribute, to see which object has “more of”/“less of” the attribute.
For example, directly compare the heights of two children and describe one child as taller/shorter. (K.MD.2)

- Sort objects into categories; count the numbers of objects in each category and sort the categories by count. (K.MD.3)


- Attribute: A characteristic of an object that students use to define the object.
Example:Thin, thick, small, large, 3 sides, 4 sides, etc.

- Weight: A measure of how heavy something is

- Non-Standard Units of measurement: Any real item that can be used to measure.
Examples include paperclips, cookies, pennies, or yarn

- Length: The distance between two points or objects

- Sorting: Grouping objects based on similar attributes

Activities at Home

- Trace your foot with chalk outside. Trace a friend’s or family member’s foot too.
Which foot is longer?

- Sort a bag of skittles or other candy by color. Count each color.
What color has the most? What color has the least?

- Get three different cups. Put them in order from shortest to tallest.

- Sort the mail by name.
Who has the least amount of mail? Who has the most amount of mail?

- Find 3 objects in the home that are longer than your shoe.


What Your Child Will Learn

- Describe objects in the environment using names of shapes, and tell positions of these objects
using terms such as above, below, beside, in front of, behind, and next to. (K.G.1)

- Correctly name shapes regardless of their size or orientation. (K.G.2)
Identify shapes as two-dimensional (lying in a plane, “flat”) or three- dimensional (“solid”). (K.G.3)

- Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length.) (K.G.4)

- Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. (K.G.5)

- Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle? (K.G.6)


- Two-Dimensional (flat): The outline of a shapesuch as a triangle, square, or rectangle

- Three-Dimensional (solid): A shape having length, width, and height

- Face: The flat surface of a solid figure

- Side: Line-segments of shapes

- Square: A four-sided shape with equal sides
and square corners

- Rectangle: A four-sided shape with two sets of sides that are equal and parallel, and four right (square) angles

- Circle: A flat shape with no sides or corners

- Triangle: A three-sided figure

- Hexagon: A shape with six sides

- Sphere: A solid shape similar to a basketball

- Cylinder: A 3-D shape with two circular faces

- Cube: A 3-D shape with six square faces

- Cone: A 3-D shape with a curved surface
and one circular face

Activities at Home

- Look around your home for solid shapes. Name at least 3 solid shapes.

- Look around your home for flat shapes. Draw at least three of the shapes.

- Look around your home for circles. Count them and record how many you found.

- Use bendy straw, toothpicks, or pipe cleaners to many shapes as you can.
Record the names of your shapes.

- Make a picture using 2 circles, 3 triangles, & 1 rectangle. Describe to a friend how you made it.

- Explore Position words. Use toys to model before, after, above, below, and beside.
Describe using attributes. Ex. The blue car is behind the red car.

First Grade

Operations & Algebraic Thinking

What Your Child Will Learn

- Add and subtract within 20 to solve word problems. (1.OA.1)

- Add three whole numbers to solve word problems. (1.OA.2)

- Use properties of operations to add and subtract. (1.OA.3)

- Understand subtraction as an unknown-addend problem. (1.OA.4)

- Relate counting on or back to addition and subtraction. (1.OA.5)

- Add and subtract within 20 and fluently within 10. Use strategies to add and subtract. (1.OA.6)

- Understand the meaning of the equal sign and determine if equations are true. (1.OA.7)

- Find the missing number in an addition or subtraction equation. (1.OA.8)


- Addition: To join two or more groups.
2 + 3 =

- Subtraction: To find the difference when two groups are compared or to find out how many are left when items are taken away from a group.

- Equation: a mathematical statement containing an equal sign, to show that two expressions are equal

- Addend: Any numbers being added together
(Example: 3 + 4 = 7, 3 and 4 are the addends)
Count On: start from any given number and count forward

- Count Back: start from any given number and count backwards

- Equal sign (=): A symbol used to show that two amounts have the same value. 384 = 384

- Sum:The answer to an addition problem.
In 2 + 3 = 5, 5 it is the sum.

- Difference: The answer to a subtraction problem.
In 8 – 3 = 5, 5 is the difference.

- Number Sentence: A sentence that includes numbers, operation symbols ( +,- ), and a greater than or less than symbol ( >,< ) or equal sign. 5 + 3 = 8 25 < 32

Activities At Home

- Roll single digit numbers and add them together.

- Roll 2-digit or 3-digit numbers and add them together.

- Add all the digits of your house number together.

- Make a train with Legos or colored blocks. Write a number sentence for the different colors in the train.

- Add the price of two items at a store.

- Compare gas prices to find the lowest amount.

- Start with 20 counters (beans, pennies, etc.) and roll two dice to make a 2-digit number.
Subtract counters until you get to 0.

- Give your student an addition or subtraction number sentence
and ask them to make up a story problem to go with the number sentence.

- Make a physical array with counters and record on paper using symbols

Number & Operations Base Ten

What Your Child Will Learn

- Count to 120 starting at any number. Read and write numbers. (1.NBT.1)

- Understand that the two-digits in a two-digit number represent tens and ones. (1.NBT.2)

- Compare two-digit numbers using >, =, and

- Add within 100. (1.NBT.4.)

- Given a two-digit number, mentally find 10 more or less without counting. (1.NBT.5)

- Subtract 10 from multiples of 10 (10-90). (1.NBT.6)


- Place Value: the value of the place of the digit in a number

- Digit: A symbol used to show a number

- Greater Than: (>) a symbol used to compare two numbers,
with the greater number listed first. Example: 8 > 6

- Less Than: (<) a symbol used to compare two numbers, with the lesser number given first. Example: 6 < 9

- Equal to: (=) having the same value

- Add: To join together sets to find the total or sum

- Subtract: to find the difference when two groups are compared or to find out how many are left when items are taken away from a group

Activities At Home

- Count objects such as jellybeans in a bowl, pennies in a jar, cheerios in a baggie, etc.

- Find numbers in newspapers, magazines, or on items around the house.

- Practice counting with your student while doing various activities-driving in the car, jumping rope, waiting in line at a store, etc.

- Divide a deck of cards evenly between players. Each player flips over a card, the player with the highest card wins the cards. Continue until one player has all cards in the deck.

- Put different items into groups and talk about which group has more or less items using the terms greater than and less than.

- Roll dice and create numbers. Say what is 10 more or 10 less than that number.


What Your Child Will Learn

- Distinguish between defining and non-defining attributes. (1.G.1)

- Compose two or three-dimensional shapes to create a composite shape. (1.G.2)

-Partition circles and rectangles into two and four equal shares. (1.G.3)


- Face: the flat surface of a solid figure

- Side: a line segment joining two corners of a figure

- Attributes: a characteristic such as shape or size

- Angle: two rays that share an endpoint

-Two-Dimensional: the outline of a shape such as a triangle, square, or rectangle

- Three-Dimensional: a solid figure

- Composite: made up of several different things

- Half: 2 equal parts

- Quarter: 4 equal parts

- Circle: a closed round figure

- Rectangle: a shape with four sides and four square corners

- Square: a rectangle that has four equal sides

- Triangle: a shape with three sides and three corners

- Trapezoid: a four-sided shape with only two opposite sides that are parallel *

- Cube: a solid with 6 faces all the same size

- Rectangular Prism: a solid with two identical rectangular bases

- Cone: a solid with one curved surface, one flat surface that comes to a point

- Cylinder: a solid with one curved surface and two identical circle bases

- Whole: all, everything, total amount

* Students do not need to know the definition of a trapezoid. They should be able to identify it and compare it with a rectangle. Rectangles have 4 square corners and trapezoids do not.

Activities At Home

- Go on a shape hunt outside, ask your student to name the shapes of doors, windows,
bicycle wheels, etc.

- Ask your student to identify the shapes of various road signs while traveling in the car.

- Talk with your student about the various shapes of items packaged in the grocery store.

- Build with blocks. Discuss what shapes were used to create the structure.