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.

Below  are online-games and activities that support Grade 2- 3 mathematics.

#### Operations & Algebraic Thinking

What will your student will learn?

- Add and subtract within 100 to solve one- and two-step word problems. (2.OA.1)

- Fluently add and subtract within 20 using mental strategies.

- By the end of Grade 2, know all sums of two one-digit numbers. (2.OA.2)

- Determine odd or even numbers and write an equation to express an even number. (2.OA.3)

- Use addition to find the total number of objects in rows and columns. (2.OA.4)

Vocabulary

- Addition: To join two or more groups.
2 + 3 = 5

- 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.

In 2 + 3 = 5, 2 and 3 are addends.

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

In 2 + 3 = 5, 5 it is the sum.

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

- 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

- Regroup: To exchange amounts of equal value to rename a number.

- Array: An arrangement that shows objects in rows and columns.

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

- Compose: To put decomposed numbers back together. 10 + 5 = 15.

Activities At Home

- Roll single digit numbers and add them together.

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

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

- Represent two digit numbers with popsicle sticks – make bundles of ten for the tens and use single sticks for the ones. Add the piles together.

- Use small items (counters, beans, small toys) to represent number sentences. Use index cards to make +, -, <, >, and = symbols. Show a number sentence with a missing element: 7 + ___ = 12. Have your student find the missing addend.

- Add the price of two items at a store.

- Compare gas prices to find the lowest amount.

- Roll a 2-digt number and subtract it from 99 or 100.

- Start with 100 counters (beans, pennies, etc.) and roll two dice to make a 2-digit number. Subtract counters until you get to 0.

up a story problem to go with the number sentence.

- Look for items that are in repeated sets or groups – panes in a window, pickets on a fence, sodas in a six-pack, wheels on cars or bicycles.

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

#### Number & Operations in Base Ten

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

- Count within 1000; skip-count by 5s, 10s, and 100s. (2.NBT.2)

- Read and write numbers to 1000 with numerals, number names, and expanded form (2.NBT.3)

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

- Fluently add and subtract within 100. (2.NBT.5)

- Add up to four two-digit numbers. (2.NBT.6)

- Add and subtract within 1000. (2.NBT.7)

- Mentally add or subtract 10 or 100 to a number 100-900. (2.NBT.8)

- Explain why addition and subtraction strategies work. (2.NBT.9)

Vocabulary

- Skip Count: to count in equal increments by 2s, 3s, 4s, 5s, or 10s

- Numeral: a symbol used to represent a number

- Expanded Form: a way of writing numbers to show place value (346=300+40+6)

Activities At Home

- Skip count when counting groups of nickels and dimes.

- Count in a pattern while doing a rhythmic or repeated task – stirring pancake batter, brushing hair, putting away groceries, walking.

- Roll two dice to make a two digit number. Subtract it from 99 or 100.

- Represent two digit numbers with popsicle sticks - make bundles of ten for the tens and use single sticks for the ones.

- Roll dice to make two or three digit numbers with a partner. See who can make the larger number.

- Compare prices of various items (gas, toys, etc) to find the lowest amount.

- Make numbers or find numbers on labels and compare them.

- Find or roll numbers and write them in expanded form.

- Find or roll numbers and tell which place value each digit represents

#### Measurement and Data

What will your student will learn?

- Measure the length of an object by selecting and using appropriate tools (2.MD.1)

- Measure the length of an object twice, using length units of different lengths (2.MD.2)

- Estimate lengths using inches, feet, centimeters, and meters. (2.MD.3)

- Measure to compare two objects. (2.MD.4)

- Use addition and subtraction to solve word problems with lengths. (2.MD.5)

- Show whole numbers, sums, and differences on a number line. (2.MD.6)

- Tell and write time to the nearest five minutes. (2.MD.7)

- Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies. (2.MD.8)

- Gather measurement data and show it on a line plot. (2.MD.9)

- Draw a picture graph and a bar graph to show data with up to four categories. (2.MD.9)

Vocabulary

- Inch: a customary unit of length

- Yard: a customary unit of length equal to 36 inches or 3 feet

- Foot: a customary unit of length
equal to 12 inches

- Centimeter: a metric unit of length, about the width of your finger

- Meter: a metric unit of length
equal to 100 centimeters

- Estimate: a number close to an exact amount

- Length: the distance from one
point to another

- Equation: a number sentence with an equal sign,
the amount on one side of the equal sign has the
same value as the amount on the other side

- Number Line: a diagram that
represents numbers as points on a line

- Analog Clock: a clock with numbers 1 to 12
around the face and rotating hands to show
the hour, minutes, and seconds

- Digital Clock: a clock that uses
numerals only to show the time

- Minute: a unit of time equal to 60 seconds

- Hour: a unit of time equal to
60 minutes

- Quarter Hour: a unit of time that measures
fifteen minutes

- Half Hour: a unit of time that
measures thirty minutes

- Half Past: thirty minutes past the hour

- Penny: a coin worth 1 cent

- Nickel: a coin worth 5 cents

- Dime: a coin worth 10 cents

- Quarter: a coin worth 25 cents

- Data: Information that has numbers

- Line Plot: a graph showing frequency of
data on a number line

- Table: an organized way to list data

- Bar Graph: a graph that uses the height or
length  of rectangles to compare data

- Picture Graph: a graph that uses pictures to show data

Activities At Home

- Look at a TV guide and locate the time a favorite show starts.
Have your child find that time on an analog clock.

- Look through an ad in the paper to locate an item your child would want (less than &10.00).
Have your child count out that much money, then ask them to make change from a \$10.00 bill.

- Have your child pick out two or three items in an ad, then add the amounts together
to see how much the items would cost altogether.

- Estimate the lengths of various objects around the house, such as a table, a book,
a toothbrush, etc. Next, Measure the same objects using a ruler with inches and
centimeters to compare the estimate to the actual length.

- Measure the four sides of a square or rectangular table using inches, and then
add the four sides together to find out how long the table is around.

- Measure two different book lengths using centimeters. Compare the two lengths and
determine how much longer one book is than the other.

- Give your child various amounts of money to count, using dollars, quarters, dimes,
nickels, and pennies.

- Survey various family members about their favorite sport, color, ice cream flavor, or
pizza topping. Create a bar graph to show the data.

#### Geometry

What will your student will learn?

- Recognize and draw shapes with specified attributes such as number of sides, angles, or faces. (2.G.1)

- Partition a rectangle into rows and columns and count to find the total. (2.G.2)

- Partition circles and rectangles into two, three, or four equal shares. (2.G.3)

Vocabulary

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

- Closed Figure: a plane figure that completely
surrounds an area

- Edge: the line segment where two
faces of a solid figure meet

- Face: a flat surface on a solid figure

- Figure: a shape in 2 or 3 dimensions

- Half: 2 equal parts

- Hexagon: a figure with 6 sides

- Partition: to divide into parts

- Pentagon: a figure with 5 sides

- Open Figure: a plane figure that does not
completely enclose an area

- Thirds: three equal parts

- Triangle: a figure with 3 sides

- Whole: all of the parts

- Vertex: where two line segments,
lines or rays meet to form an angle

Activities At Home

- Look for 2-D and 3-D shapes around your house and community.

- Compare 2-D and 3-D shapes. Look for the 2-D shapes that make up the 3-D shapes.

- Talk about the shapes of foods that are eaten. For example, oranges are spheres.

- Talk about the shapes of containers in stores. For example, cans are cylinders and boxes are rectangular prisms or cubes.

#### Operations & Algebraic Thinking

- Understand the meaning of multiplication (3.OA.1)

- Understand the meaning of division (3.OA.2)
Solve word problems using multiplication and division (3.OA.3)

- Determine the unknown whole number in a multiplication or division problem (? X 8 = 24) (3.OA.4)

- Understand the properties of multiplication (3.OA.5)

- Understand division as an unknown factor problem (3.OA.6)

- Fluently multiply and divide within 100 (3.OA.7)

- Solve word problems using addition, subtraction, multiplication and/or division (3.OA.8)

- Identify and explain arithmetic patterns (3.OA.9)

Vocabulary

- Division: to make equal groups

- Dividend: a number that is divided by another number

- Array: an arrangement that shows objects in columns and rows

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

- Estimation: a number close to an exact amount

- Product: the result of multiplication

- Grouping: dividing things into equal groups (sets)

- Quotient: the number, not including the remainder, that results from dividing

- Partition: to divide into parts

- Multiplication: an operation on two numbers to find their product. It can be thought of as repeated addition.

- Multiple: a product of two whole numbers

- Remainder: the amount left over when a whole number cannot be divided into equal whole numbers

- Factor: a number that is multiplied by another number to get a product

- 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.

- Addition: To join two or more groups. 2 + 3 = 5

- Addend: A number that is added to another in an addition problem. In 2 + 3 = 5, 2 and 3 are addends.

- 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.

- Mental Computation: the calculation of something
mentally

Activities at Home

- Make arrays out of household items (e.g., pennies, beans, blocks)

-  Select multiplication or division facts to illustrate or write a word problem.

- Hunt for multiple sets of objects in the home. Use repeated addition and multiplication
to find the totals.

- Sort coins according to type, count the number of coins and then multiply to find the
total value of pennies (x 1), nickels (x 5), dimes (x 10) and quarters (x 25).

- Roll 2 number cubes. Find the products of the factors.

- Count quantities of items by 2’s, 3’s, 5’s, and 10’s.

- Roll 2 number cubes to determine the factors. Make an array to find the product.

- Use a calculator to solve word problems using multiplication and division. For example, Callie wants to buy 20 apples that cost \$ .19 each. What is the total cost of her purchase? Michael has 332 quarters. He wants to put them into groups of 4. How many groups will he make?

- Act out division problems with counters. For example, Brad has 12 rabbits. He puts the
same number of rabbits into each of 4 cages. How many rabbits does Brad put in each cage?
Roll 2 number cubes and write the fact families.
For example, for rolls of 4 and 6, write: 4 X 6 = 24, 6 X 4 = 24, 24 ¸ 6 = 4, 24 ¸ 4 = 6.

- Ask your student to find the missing factor. For example, 5 X what number? = 75?

#### Number and Operations in Base Ten

- Round whole numbers to the nearest 10 or 100 (3.NBT.1)

- Add and subtract within 1000 (3.NBT.2)

- Multiply one digit numbers by multiples of 10. (3.NBT.3)

Vocabulary

- Place value: The location of a digit in a number

- Value: The value of a digit based on its place value

- Product: the result of multiplication

- Factor: a number that is multiplied by another number to get a product

- Multiple: a product of two whole numbers

- Addition: To join two or more groups. 2 + 3 = 5

an addition problem. In 2 + 3 = 5, 2 and 3 are addends.

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

- 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.

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

Activities at Home

- Roll 2 number cubes. Find the products of the factors.

- Locate numbers in catalogs or newspapers, then practice rounding them
to the nearest tens and hundreds.

- Roll a number cube and practice multiplying that number by ten.
After mastery, try with two number cubes.

- Practice adding and subtracting three-digit numbers.

- Show your child various numbers of dimes and have your child practice
counting the amount of money (4 dimes x 10 cents = 40 cents).

#### Number & Operations Fractions

- Understand the meaning of a fraction. (3.NF.1)

- Place a fraction on a number line (3.NF.2)

- Understand equivalent fractions (3.NF.3)

Vocabulary

- Denominator: the bottom number in a fraction. It tells how many equal parts the set or whole has
been divided into

- Equivalent Fractions: two or more fractions that name the same amount

- Fraction: a number that names part of a
whole or part of a group

- Greatest: the largest in a group

- Least: the smallest in a group

- Number Line: a line with equally spaced tick marks named by numbers

- Numerator: the top number in a fraction.
It tells how many of the equal parts of the whole
or group are being considered

- Order: arrangement according to size, amount, or value

Activities at Home

- Go on a fraction hunt! Look for household items that are divided into equal parts
(fractions of a whole and fractions of a set). Record the fractions.

- Roll number cubes to make fractions. Draw pictures of the fractions you make.
Place the fractions you've made in order on a number line.

- Identify fractions at meal times. For example, you ate 1/2 of an apple, 3/4 stalk of celery,
1 whole tuna sandwich, and 2/3 of a glass of milk.

- Practice making equivalent fractions.

- Plot fractions on a number line.

#### Measurement and Data

- Tell and write time to the nearest minute and understand elapsed time (3.MD.1)

- Measure and estimate liquid volumes (3.MD.2)
Create picture graphs and bar graphs to represent data (3.MD.3)

- Measure with a ruler to the nearest ¼ inch (3.MD.4)

- Understand area. (3.MD.5)

- Measure the area by counting unit squares. (3.MD.6)

- Use multiplication to find area of rectangles. (3.MD.7)

- Solve problems that use perimeter. (3.MD.8)

Vocabulary

- Analog Clock: A clock that shows time by moving hands around a circle for hours,minutes, and sometimes seconds

- Area: The number of square units needed to cover a surface

- Digital Clock: A clock that shows time to the minute using digits

- Distance: The amount of space between two given points

- Elapsed Time: A measurement of the amount of time from one event to another

- Estimate: A guess or rough calculation of worth, quantity, or size

- Mass: A measure of how much matter is in an object.

- Measure: Use of standard units to find out size or quantity in regard to length, height, area, mass, volume, time, perimeter

- Perimeter: The distance around a figure

- Scaled Bar Graph: A graph that uses bars to show data

- Scaled Pictograph: A graph that uses pictures to show data

- Standard Unit: A traditional unit of measurement from the metric or customary system. Examples include inches, meters, pounds, etc.

- Time: Seconds, minutes, hours, days, months, years, and so on. Time is shown on a clock or calendar.

- Volume: The amount of space occupied by an object

Activities at Home

- Share and discuss tables and graphs found in newspapers and magazines.

- Conduct a survey among family members or friends and construct a bar graph or pictograph.

- Make a physical pictograph using real objects (e.g., fruits, vegetables, cereal,
kitchen tools). Record the graph on paper. Change the scale to create a new pictograph.

- Make records of important times of the day (wake-up, dinner, going to school,
getting home from school, etc.) and practice telling how long between activities.

- Calculate elapsed time by finding out how long it takes to complete daily activities
(soccer practice, homework, take a shower, etc.)

- Measure the perimeter and area of the rooms in your home to determine
which rooms are the smallest and largest.

- Use grid paper to make rectangles with the same perimeters.
Determine the area of each rectangle.

- Fill a small box with blocks (e.g., sugar cubes) to determine its volume.
Brainstorm multiple strategies to determine the volume.

#### Geometry

- Understand the attributes of quadrilaterals. (3.G.1)

- Divide shapes into parts with equal areas. (3.G.2)

Vocabulary

- Congruent: Shapes that have the same size and shape

- Parallelogram: A quadrilateral with two pairs of parallel sides and two pairs of equal sides

- Polygon: A closed, 2-D figure with straight lines

- Quadrilateral: A polygon with four sides

- Rectangle: A 2-D figure with 4 sides and 4 right angles, opposite sides are parallel

- Rhombus: A 2-D figure with 4 equal sides and 4 angles (not necessarily equal),
opposite sides are parallel

- Square: A 2-D figure with 4 equal sides and 4 right angles

- Fraction: A number that names part of a whole

- Trapezoid: A 2-D figure that has 4 sides and 4 angles, one pair of sides is parallel

- Right angle: An angle that forms a square corner

Activities at Home

- Use grid paper to create congruent shapes.

- Identify, describe, and classify different household objects as solid figures.

- Identify angles that are less than, equal to and greater than right angles.

- Use tangrams to make plane figures.

- Cut pieces of yarn to make line segments. Measure each segment in inches
(to the nearest quarter inch) and centimeters.

- Go stargazing and make imaginary line segments by connecting the stars (points).
Create geometric shapes.

- Go on a shape hunt! Look for geometric shapes in your home and community. Create a chart to show your findings.