# Elementary Mathematics 4th-5th 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.

## 4th Grade

#### Operations & Algebraic Thinking

**What Your Child Will Learn**

- Interpret multiplication as comparison, for example, 35 is 5 times as many as 7. (4.OA.1)

- Multiply or divide to solve word problems (4.OA.2)

Solve multi-step word problems using the four operations.

- Problems will include interpreting a remainder and/or using equations with a letter standing for the unknown. (4.OA.3)

- Find factor pairs for numbers to 100 and tell if numbers are prime or composite. (4.OA.4)

Understand Patterns with numbers or shapes. (4.OA.5)

**Vocabulary**

- Factor: A number that is multiplied by another

(factor x factor = product)

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

- Expanded Form: a graph that shows the frequency of data along a number line

- Multiple: The product of a given whole number and another whole number

- Compare: Tell how a number is related to another number

using >, <, =, or different

- Array: An arrangement of objects in rows and columns

- Identity Property: (Any number times 1 is that number

- Commutative Property: 5 x 7 is the same as 7 x 5

- Associative Property: (2 x 3) x 4 = 2 x (3 x 4)

- Zero Property: Any number times 0 is 0

- Product: The answer to a multiplication problem

- Remainder: The amount left over when a number cannot be divided equally

- Divisor: The number that divides the dividend

- Dividend: A number being divided

- Quotient: the result of a division

- Estimate: To find a number close to an exact amount

**Activities At Home**

• Draw shapes and divide into different fractions

• Create numbers to use in fractions

• Use measuring cups when baking or cooking

• Pick numbers to create fractions-Practice simplifying them

• Make up numbers, roll numbers with dice, or find numbers (on labels) and compare them

• Find numbers and write them in expanded form

• Make numbers and tell which place value (and/or value) each digit represents

• Place large numbers on a number line

• Collect objects (i.e. Cheerios) and estimate how many

• Draw pictures and make models of numbers

• Practice addition and subtraction facts

#### Number & Operations in Base Ten

**What Your Child Will Learn**

- Understand multi-digit place value to 1,000,000. (4.NBT.1)

- Read, write, and represent multi-digit whole numbers in standard and expanded form. (4.NBT.2)

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

Round multi-digit whole numbers. (4.NBT.3)

- Fluently add and subtract multi-digit numbers. (4.NBT.4)

- Multiply multi-digit numbers and explain the calculations by using equations,

rectangular arrays, and/or area models. (4.NBT.5)

- Divide multi-digit dividends with one-digit divisors, including interpreting the remainders. (4.NBT.6)

* Grade 4 students work with whole numbers less than or equal to 1,000,000.

**Vocabulary**

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

- Digit: A symbol used to show a number

- Estimate: An approximate calculation that is close to the exact number based on rounding

- Compare: Tell how a number is related to another number using >, <, =, or different

- Rounding: to find the nearest ten, hundred, or thousand (and so on).

For example, 391 rounds up to 400 and 331 rounds up to 300.

- Expanded Form: Writing a number as the sum of the values in each digit

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

**Activities At Home**

• Make up numbers, roll numbers with dice, or find numbers (on labels) and compare them

• Find numbers and write them in expanded form

• Make numbers and tell which place value (and/or value) each digit represents

• Place large numbers on a number line • Collect objects (i.e. Cheerios) and estimate how many

• Draw pictures and make models of numbers • Practice addition and subtraction facts

#### Number & Operations Fractions

**What Your Child Will Learn**

- Understand equivalent fractions. (4.NF.1)

- Compare fractions with symbols >,<, or =. (4.NF.2)

- Add and subtract fractions, including mixed numbers with like denominators. (4.NF.3)

- Decompose a fraction into a sum of fractions with the same denominator in more than one way.

Ex: 3/8=1/8+1/8+1/8; 3/8= 1/8+2/8; 2 1/8= 1+1+1/8= 8/8+8/8+1/8. (4.NF.3)

- Add and subtract fractions to solve word problems. (4.NF.3)

- Multiply a fraction by a whole number. Ex: 3 x 2/5= 2/5+2/5+2/5. (4.NF.4)

- Understand a fraction is a multiple of a unit fraction. Ex: 5/4 as the product of 5 x (1/4). (4.NF.4)

- Multiply a fraction by a whole number to solve word problems. (4.NF.4)

- Express and add fractions with denominators 10 and 100. (4.NF.5)

- Read, write, and represent decimal notation for fractions with denominators 10 or 100. (4.NF.6)

- Compare two decimals to hundredths using symbols >, <, or = and justify the conclusions. (4.NF.7)

**Vocabulary**

- Denominator: The number below the bar in a fraction that tells how many equal parts are in the whole

- Compare: Tell how a number is related to another number using <, >, or =.

- Numerator: The number above the bar in a fraction that tells how many pares of the whole

- Unit Fraction: one piece of the whole represented as 1/a.

- Equivalent: (=) having the same value

- Decimal: A number system (based on 10) with one or more digits to the right of the decimal point.

- Mixed Number: A number that is made up of a whole number and a fraction

- Decimal Point: A symbol that seperates dollars and cents in money, and the ones place from the tenths place in decimal numbers.

**Activities At Home**

- Draw different shapes. Divide them into different fractions.

- Create numbers to use in fractions. Draw these fractions as parts of a whole or set.

- Use measuring cups when baking or cooking.

- Use centimeter paper to draw decimals.

- Relate dimes to tenths and pennies to hundredths and make up decimals using dimes and pennies.

- Use a menu to compare money.

- Roll dice to make decimal numbers and compare them.

- Write decimal numbers in expanded form.

- Write decimal numbers in word form.

- Identify decimals in a newspaper.

- Practice multiplication and division facts.

#### Measurement & Data

**What Your Child Will Learn**

- Convert equivalent measurements in the same measurement system. Ex. 12 in=1 ft. (4.MD.1)

- Solve measurement word problems with distance, time, liquid volumes, masses of objects, and money. (4.MD.2)

- Apply the area and perimeter formulas for rectangles. (4.MD.3)

- Add and subtract fractions on a line plot. (4.MD.4)

- Understand and measure angles. (4.MD.5)

- Measure and draw angles using a protractor. (4.MD.6)

- Break apart an angle into 2 smaller angles and know that the larger angle is the sum of the two smaller angles (4.MD.7)

**Vocabulary**

- Perimeter: The distance around and object.

- Capacity: The greatest amount a container can hold.

- Area: The measure, in square units, of the inside of a plane figure.

- Line Plot: A graph that shows the frequency of data along a number line.

- Volume: The number of cubic units that fits inside a solid figure.

- Angles: The figure formed when two rays or line segments share the same endpoint.

- Elapsed Time: The amount of time that passes between two times.

- Protractor: A tool used to measure angles.

**Activities At Home**

- Use measurement tools when baking or cooking.

- Compare items by length or weight.

- Practice scheduling events to determine elapsed time.

- Use string to measure wrist, neck, and waist and make comparisons.

- Read an analog clock throughout the day.

- Use a stopwatch to keep track on how much T.V is watched throughout the week and how much .time is spent on homework, and compare the two amounts of time.

- Take an object and estimate the weight then use a scale to determine the exact weight, and compare the two amounts.

- Use a ruler to measure objects around the house in inches or centimeters.

- Explore the area and volume of a cereal box.

- Identify real world angles as acute, right, or obtuse.

- Draw shapes. Identify their angles as obtuse, acute, and right angles.

- Draw pictures with intersecting lines, perpendicular lines, and parallel lines.

- Use a ruler to find a perimeter of plane figures.

- Practice multiplication and division facts.

#### Geometry

**What Your Child Will Learn**

- Identify and draw points, lines, line segments, rays, angles (right, acute, obtuse),

and perpendicular and parallel lines in 2-dimensional figures (4.G.1)

- Classify two-dimensional figures. (4.G.2)

- Understand line of symmetry for a two-dimensional figure. (4.G.3)

**Vocabulary**

- Point: An exact position or location.

- Angles: The figure formed when two rays or line segments share the same endpoint.

- Line: A straight path extending in both directions

with no endpoints.

- Perpendicular Lines: Lines that intersect to form right angles.

- Line Segments: A part of a line that includes

two points, called endpoints, and all the points

between them.

- Parallel Lines: Lines in a plane that never intersect.

- Ray: A part of a line, with one endpoint,

that continues without end in one direction.

- Two-Dimensional Figure: A closed plane figure with length and width.

- Symmetry: When one half of a figure looks like the mirror image of the other half.

**Activities At Home**

- Name two-dimensional figures and find examples at home.

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

- Identify real world angles as acute, right, or obtuse.

- Draw shapes. Identify their angles as obtuse, acute, and right angles.

- Draw pictures with intersecting lines, perpendicular lines, and parallel lines.

- Use tangrams to make two-dimensional figures.

- Practice multiplication and division facts.