Third Grade Overview - Carroll County Public School District

In third grade your children will focus in 4 critical areas:

Your children will develop an understanding of whole number multiplication and division. Activities will focus on problem involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. In equal-sized group problems, division can require finding the unknown number of groups or the unknown group size. The children will use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties solving problems with single digit factors. They will compare strategies to learn the relationship between multiplication and division.

Critical Area 2

Your children will develop an understanding of fractions, beginning with unit fractions. They will view fractions as being built out of unit fractions and use fractions along with visual models to represent parts of a whole. Children will also understand that the size of a fractional part is relative to the size of the whole. They will be able to use fractions to represent numbers equal to, less than, and greater than one. They will also be able to compare fractions using visual models and strategies noticing equal numerators or denominators.

Critical Area 3

Your child will recognize area as an attribute of a 2-dimensional shape. They measure the area of a shape by finding the total number of same size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. The children will understand the rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, children will connect area to multiplication, and justify using multiplication to determine the area of a rectangle

Critical Area 4

Unit 1

Third Grade Mathematics
Unit 1
Foundations of Multiplication, Division, and Area
Printable Parent Letter

Your child will be learning about multiplication, division, and area over the course of several units. During this unit, your child will develop an understanding of the multiple meanings of multiplication and division of whole numbers through activities and problems involving equal –sized groups, arrays, and area sized models. An understanding of the commutative property will also be developed as arrays are built to solve problems.

Your child will also solve problems to develop an understanding of the connection between multiplication and the measurement of area. He/she will recognize area as an attribute of two dimensional regions, and will measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps (a square with sides of unit length being the standard unit for measuring area). Finally, your child will understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students will connect area to multiplication.

Students Need To

Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. Describe a context in which a total number of objects can be expressed as 5 x 7.
Identify arithmetic patterns (including patterns in the addition and multiplication table) and explain them using properties of operations.
Apply properties of operations as strategies to multiply and divide. If 6 x 4 is known, then 4 x 6 = 24 is also known. (commutative property of multiplication)
Interpret whole-number quotients of whole numbers. For example, interpret 56 / 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned equally into equal shares of 8 objects each. Describe a context in which a number of shares or a number of groups can be expressed as 56/8
Use multiplication and division within 100 to solve word problems in situations involving equal groups, and arrays. Use drawings and equations with a symbol for the unknown number to represent the problem.
Recognize area as an attribute of plane figures and understand concepts of area and measurement.
- a) A square with length 1 unit, called ‘a unit square", is said to have "one square unit" of area, and can be used to measure area.
- b) A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
Measure areas by counting unit squares (square cm, square m, square in, square ft., and improvised units).
Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths
Tell and write time to the nearest minute.

Ways Parents Can Help

Point out objects around you, in and outside of your home, that are arranged in equal groups and arrays (rows and columns). Ask your child to use this arrangement to determine the actual or estimated total number of objects.
When solving basic facts, ask your child to describe patterns he/she notices. After your child communicates potential patterns, have him/her use a calculator to see if the pattern continues when multiplied by factors greater than 10.
Use a set of flash cards to play Commutative Property Memory. 1. Create a set that includes pairs of facts like- 2x5 and 5x2, 4 x 1 and 1x4, etc. 2. Lay the cards face down. 3. The first player flips over a card and says the product. 4. If correct he or she flips over another card, hoping it has the same factors in a different order. 5. If it is a pair, player one will say the product, take the pair, and go again. If it is not a match, both cards are placed face down and player two takes his turn. 6. Repeat until there are no more cards on the table. 7. The player with the most pairs wins.
When solving word problems, have objects available for your child to help him "make sense" of the problem, and see the mathematics. Create a basket with baggies of small objects like pennies, Legos, and M and M’s that can be used to create equal groups and arrays. If your child has these materials at his fingertips, he will be more likely to pull them out and use them.
Draw large shapes on the sidewalk or a poster board. Choose a square unit that can be used to cover the shape (ie: Cheez-its, Golden Grahams). Before tiling the area, make an estimate about how many it might take to cover the shape. Determine the area of the shape.

Key Vocabulary

Key Vocabulary to Know

array: an arrangement of objects in equal columns and rows

area: the number of square units needed to cover a surface

Commutative Property of Multiplication: a property of multiplication in which the product stays the same when the order of the factors is changed (i.e., a x b = b x a)

dividend: the number being divided

divisor: the number by which a dividend is being divided

factor: the numbers or terms multiplied in an expression. (a factor times a factor equals the product)

multiple: the product when numbers are multiplied together

partition: a division into or distribution in portions or shares

product: the result of multiplying one factor times another factor
8 x 8 = 64

square unit: a unit for measuring area such as square inch, square centimeter, or square mile

quotient: the result of division 24 / 3 = 8

Unit 2

Third Grade Mathematics
Unit 2
Addition, Subtraction, and Measurement
Printable Parent Letter

During Unit 2, your children will add and subtract within 1000 by applying their understanding of models for addition and subtraction. They will develop, discuss, and use efficient, accurate, and generalizable methods to compute the sums and differences of whole numbers in base ten notations, using their understanding of place value and the properties of the operations (they will need not use formal terms for these properties). Your children will work to develop written methods for recording sums and differences. They will be introduced to the concept of rounding, which provides them with another strategy to judge the reasonableness of their answers in addition and subtraction situations. Perimeter provides a context in which students can practice both rounding and addition and subtraction (e.g. estimating the perimeter of a polygon). They will also develop a conceptual understanding of measuring mass, liquid volume and intervals of time. Measurement word problems will be used as a context for the development of fluency in addition and subtraction.

Students Need To

Add and subtract within 1000 using strategies and algorithms based on the following: place value, properties of operations and the relationship between addition and subtraction
Use place value understanding to round whole numbers to the nearest 10 or 100
Solve two-step word problems. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length.
Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).
Add or subtract to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with measurement scale) to represent the problem.

Ways Parents Can Help

Help your child use addition or subtraction to solve real world problems (e.g. adding a bill, calculating change from a purchase…)
Practice reading an analog clock.
Help your child determine an end time given the start time and the duration of the event (e.g. you put something in the oven at 5:15 p.m. and it needs 32 minutes to cook, what time should you take it out of the oven).
Look at real world examples showing liquid volumes and masses (e.g. packaged food such as a cereal box). Play a game to see how close your child can get to estimating these measurements.

Key Vocabulary

Key Vocabulary to Know

Addend - the numbers in a addition problem to be added together

Addition - the action of joining numbers together

Associative Property - regrouping addends or factors will not impact to total.

Commutative Property - changing the order of addends or factors does not change the total.

Difference - the answer to a subtraction problem

Digit - a numeric symbol that is used to represent numbers

Estimate - an approximate total

Equal - having the same value or being the same size

Identity Property - the value of a factor does not change when multiplied by 1, nor does an addend when zero is added.

Inverse operation - the opposite

Minuend - the number in which another number is subtracted from

More - a greater value or larger size

Multiples of 10 and 100 - when a number is multiplied by 10 or 100

Number line - a line in which the numbers mark intervals

Operation - addition, subtraction, multiplication, and division

Place value - the value of a digit based on it's position in a number

Standard algorithm - the traditional method of computing numbers

Subtraction - the action of taking the value of one number away from another

Subtrahend - the number to be subracted in a problem

Sum - the answer to an addition problem

Capacity - the amount of liquid an object and hold

Gram - metric unit of mass (weight)

Elapsed time - the amount of time that has passed.

Height - the quality of being tall

Kilogram - a metric unit of mass (weight) 1,ooo grams

Liter - metric unit of capacity (volume)

Mass - weight

Measure - a standard unit used to express the size, amount, or degree of something.

Milliliter - metric unit of capacity (volume) 1/1000 of a liter

Minutes - measurement of time 60 seconds

Perimeter - the distance around the outside of an object

Scale - the intervals in which a bar graph is labeled or the value of the image on a pictograph.

Standard unit - an established common unit (ie: foot, inch, cm)

Unit 3

Third Grade Mathematics
Unit 3
Equal Partitioning and Naming Fractions
Printable Parent Letter

During Unit 3, your children will develop an understanding of fractions, beginning with unit fractions. They will view fractions as being built out of unit fractions, and use fractions along with visual fraction models to represent parts of a whole. Your children will understand a fraction as a number on a number line and represent fractions on a number line.

Students Need To

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Partition shapes into parts with equal area. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ of the area of the shape.
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

Ways Parents Can Help

Involve your child in cooking activities. Have them select the appropriate measuring spoons and cups for the recipe. If ingredients need to be doubled or halved, ask them to figure out what the new quantity would be for the recipe.
When food items need to be cut or shared equally by your family or a group of people, have your child consider how many parts there will be and what fractional part each person will get.
Divide a large pile of objects (cereal, plastic animals, blocks, etc.) equally into 4 piles to illustrate one-fourth. Recombine the group to divide into other fractions.
Fold a piece of paper into halves, and then into halves again with your child. Open it up to show the division of fourths. Fold the paper again into fourths then make another fold to show eighths.
Count the rooms in your house and make up some fraction facts about them. One-half of the rooms have windows; one-third of them have pillows; etc.
While in the car, mark the passing of time with fractions. "We are one-third of the way there." "It will take us 20 minutes to get to the library." "In how many minutes will we be half-way there?"

Key Vocabulary

Key Vocabulary to Know

Fraction: A number that represents one or more equal parts of a whole

Unit fraction: A fraction in which its numerator is 1 and its denominator is a whole number

Numerator: The number of parts one selects from the whole

Denominator: The number of parts the "whole" is partitioned into

Halves: either of two equal parts into which a whole can be partitioned

Fourths: one or more of four equal parts into which a whole can be partitioned

Sixths: one or more of six equal parts into which a whole can be partitioned

Eighths: one or more of eight equal parts into which a whole can be partitioned

Tenths: one or more of ten equal parts into which a whole can be partitioned

Thirds: one or more of three equal parts into which a whole can be partitioned

Unit interval: on a number line, it is the whole that is the interval from 0 to 1, as measured by length

Unit 4

Third Grade Mathematics
Unit 4
Multiplication and Division
Printable Parent Letter

Your child will be learning about multiplication and division over the course of several units. During this unit, your child will continue to develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal –sized groups, arrays, and area sized models. He/she will come to understand multiplication as finding an unknown product and division as finding an unknown factor. A variety of equal-sized group situations will be presented to develop the understanding that division can require finding the unknown number of groups or the unknown group size. Strategic practice in order to become fluent with multiplication and division facts will continue throughout this unit. By the end of Unit 4, students will be expected to be able to solve two-step word problems and choose the equation that represents the situation with a letter standing for the unknown quantity. In Unit 5, students will be expected to solve two-step word problems and write the equation that represents the situation with a letter standing for the unknown quantity.

Students Need To

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. Use drawings and equations with a symbol for the unknown number to represent the problem.
Identify arithmetic patterns (including patterns in the addition and multiplication table) and explain them using properties of operations.
Interpret whole-number quotients of whole numbers. For example, interpret 56 / 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned equally into equal shares of 8 objects each. Describe a context in which a number of shares or a number of groups can be expressed as 56/8
Solve two-step word problems using the four operations. Represent these problems using equations with a letter for the unknown quantity. Assess reasonableness of answers using mental computation and estimation strategies including rounding.
Understand division as an unknown-factor problem. For example, find 32/8 by finding the number that makes 32 when multiplied by 8.
Multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g. knowing that 8 x 5 = 40, one knows 40/8=5) or properties of operations.

Ways Parents Can Help

Refer to the ideas described in the Unit One Parent Letter. They apply to this Unit as well.
Play Multiplication War. This game is played quite similarly to traditional "war". Arrange the deck by taking out all of the face cards, 9, 8 and 7. This will ensure the facts created will only be those in Set One and Set Two. 1. Shuffle the deck and deal all cards out to the two players. 2. The players each turn over two cards. 3. Each player multiplies the two cards, and says aloud the entire equation- "9 times 2 is 18" instead of just "18". 4. The player with the greater product takes all of the cards. 5. If there is a tie in naming the product, "war" begins. Each player places 3 cards face down, then they turn over two to multiply together. The player with the greater product takes all of the cards on the table. 6. Play ends when either player has all the cards or after an allotted time. The winner is the player with the most cards.
Play Hit the Target. Remove the face cards from a deck of playing cards. 1. Have one player close his or her eyes and choose one card from the deck. The number on that card is your target. 2. Place the remaining cards face up on the playing surface. 3. All players take turns looking for two cards that you can add, subtract, multiply or divide to get the number on the target card. 4. When a combination is correctly found/stated the player takes the set of cards. 5. If the player is incorrect, he loses a turn. 6. If a player cannot find a combination he passes and is out of the game for that round. Play continues with the next player. 7. Keep playing until no more combinations can be found that equal the target number. 8. Each player receives one point for each pair earned. 9. Repeat the game with a different target number. 10. The winner is the first person to earn ____ points.

Key Vocabulary

Key Vocabulary to Know

array: an arrangement of objects in equal columns and rows

area: the number of square units needed to cover a surface

Commutative Property of Multiplication: a property of multiplication in which the product stays the same when the order of the factors is changed (i.e., a x b = b x a)

dividend: the number being divided

divisor: the number by which a dividend is being divided

factor: the numbers or terms multiplied in an expression. (a factor times a factor equals the product)

multiple: the product when numbers are multiplied together

partition: a division into or distribution in portions or shares

product: the result of multiplying one factor times another factor
8 x 8 = 64

square unit: a unit for measuring area such as square inch, square centimeter, or square mile

quotient: the result of division 24 /3 = 8

Unit 5

Third Grade Mathematics
Unit 5
Equivalence and Comparing Fractions
Printable Parent Letter

During Unit 5, your children will build the understanding that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Your children will use fractions to represent numbers equal to, less than, and greater than one. They will solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators. Your children will apply their knowledge of fractions by using rulers to measure to the nearest fourth of an inch. They will organize their measurement data on a line plot.

Students Have To

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
Recognize and generate simple equivalent fractions, e.g., ½=2/4, 4/6=2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >,=, or <, and justify the conclusions, e.g., by using a visual fraction model.
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.
Show the data by making a line plot, where the horizontal scale is marked off inappropriate units- whole numbers, halves, or quarters. (X’s or dots can be used to plot the data.)

Ways Parents Can Help

When cooking, explore the concept of equivalent fractions when measuring ingredients. For example, use two one-fourth measurements to equal a one-half measurement or three one-third measurements to equal one whole measurement.
Explore the concept of equivalent fractions when measuring length with a ruler. For example, two-eighths of an inch is equivalent to one-fourth of an inch.
Compare fractional amounts when they have the same numerator or the same denominator. For example, one-fourth of an inch is less than three-fourths of an inch; one-half of a cup is greater than one-third of a cup.
Use chalk on the driveway to create the “key” on a basketball court or hopscotch board with specific measurements. Simply draw some lines on the driveway for your child to measure to the nearest ½ inch.
Take weekly measurements of the plants/flowers that are beginning to grow in your garden. Record the measurements in a chart.
Ask your child to grab a handful of string beans, potatoes, or carrots. Have him/her measure to the nearest ¼ inch and record the data on a line plot.

Key Vocabulary

Key Vocabulary to Know

Fraction: A number that represents one or more equal parts of a whole

Unit fraction: A fraction in which its numerator is 1 and its denominator is a whole number

Numerator: The number of parts one selects from the whole

Denominator: The number of parts the “whole” is partitioned into

Halves: either of two equal parts into which a whole can be partitioned

Fourths: one or more of four equal parts into which a whole can be partitioned

Sixths: one or more of six equal parts into which a whole can be partitioned

Eighths: one or more of eight equal parts into which a whole can be partitioned

Tenths: one or more of ten equal parts into which a whole can be partitioned

Thirds: one or more of three equal parts into which a whole can be partitioned

Equivalent: having the same value or amount

Compare: to examine in order to note similarities and differences

Unit interval: on a number line, it is the whole that is the interval from 0 to 1, as measured by length

Interval: distance between two points

Inch: customary unit for measuring length

Length: the measure of the greatest dimension of anything measured from end to end

Line Plot: A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line.

Unit 6

Third Grade Mathematics
Unit 6
Multiplication, Division, and Area
Printable Parent Letter

During this unit, your child will develop a conceptual understanding of decomposing multiplication problems through the use of the distributive property and the concept of area. Your child will not be required to use the properties explicitly, but will be expected to discuss the concepts and use area diagrams to support their reasoning. In addition, your child will use area as a context to further develop multiplicative thinking. This includes solving problems involving rectangular areas by multiplying side lengths and solving for and unknown number in related multiplication and division equations.

Students Need To

Apply properties of operations as strategies to multiply and divide.
- If 3 x 5 x 2 can be found b 3 x 5 = 15, then 15 x 2= 30 , or by 5 x 2 = 10, then 3 x 10 = 30. (associative property of multiplication)
- Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5+2) = (8 x 5 ) = ( 8 x 2 ) – 40 + 16 = 56. (distributive property)
Identify arithmetic patterns (including patterns in the addition and multiplication table) and explain them using properties of operations.
Determine the unknown whole number in a multiplication or division equation relating three whole numbers . For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = __ / 3, 6 x 6 = ?.
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division. By the end of Grade 3, know from memory all products of two one-digit numbers.
Use place value understanding to round whole numbers to the nearest 10 or 100.
Multiply one-digit whole numbers by multiples of 10 in the range 10 – 90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Area
Relate area to the operations of multiplication and addition.
- Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b +c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning.
- Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non –overlapping rectangles, applying this technique to solve real world problems
- Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
Multiply one-digit whole numbers by multiples of 10 in the range 10 – 90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Ways Parents Can Help

Refer to the ideas described in the Unit One and Two Parent Letters. They apply to this Unit as well.
Use grid paper to make a "floor plan" of a room in your house. Be sure to include large objects that cover a portion of the floor (ie: furniture, rugs). Determine the area of each object included in your plan.
Measure the area of the rooms in your home to determine which rooms have the most/least area.
Look for real world examples of area of shapes which are rectilinear (made of non-overlapping rectangles) such as a tiled floor. Help your child to see that they can find the area for each rectangle and then add the areas to get a total area of the shape.

Key Vocabulary

Key Vocabulary to Know

array: an arrangement of objects in equal columns and rows

area: the number of square units needed to cover a surface

Associative Property of Multiplication: 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2= 30 or by 5 x 2 = 10, then 3 x 10 = 30

Commutative Property of Multiplication: a property of multiplication in which the product stays the same when the order of the factors is changed (i.e., a x b = b x a)

Distributive Property of Multiplication: multiplying a number is the same as multiplying its addends by the number then adding the products

dividend: the number being divided

divisor: the number by which a dividend is being divided

factor: the numbers or terms multiplied in an expression. (a factor times a factor equals the product)

multiple: the product when numbers are multiplied together

partition: a division into or distribution in portions or shares

product: the result of multiplying one factor times another factor 8 x 8 = 64

square unit: a unit for measuring area such as square inch, square centimeter, or square mile

quotient: the result of division 24/3 = 8

Unit 7

Third Grade Mathematics
Unit 7
Geometry and Measurement
Printable Parent Letter

During this unit, students will be describing, analyzing, and comparing quadrilaterals. They will classify the quadrilaterals by their sides and angles, and connect these attributes with definitions of them. Students will also recognize area and perimeter as an attribute of two dimensional regions and apply prior work with these concepts to solve problems.

Students Need To

Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Ways Parents Can Help

Find examples of quadrilaterals around your home. Have your child describe the attributes of the quadrilaterals found. Challenge your child to use the terms congruent, parallel sides, and square corners in his/her description.
Find the perimeter of a room, table, or countertop in your home by: 1. Sketching the object(s). 2. Measuring the sides to the nearest inch. 3. Recording the measurements. 4. Finding the sum of the measurements.
Find three different sized books. Measure and record the length and width of each book. Record the measurements and use multiplication to calculate the area.
Play “20 Questions” with quadrilaterals. Sit back-to-back with your child. Have your child draw a quadrilateral on a piece of paper. You ask questions regarding the shape while your child answers “yes” or “no” until you are able to name the shape. (Ex. Does the shape have 4 square corners? Does the shape have 1 set of parallel sides?). You can then switch roles and have your child ask questions about a shape you draw.
Have your child use Legos, blocks, post-its, etc. to build a floor plan for a house. Measure the length and width of each room. How much carpet would be needed for each room? How much trim would be needed for each room?

Key Vocabulary

Unit 8

Third Grade Mathematics
Unit 8
Demonstrate Computational Fluency
Printable Parent Letter

During this unit, students will focus on problem solving in order to demonstrate fluency with addition and subtraction to 1000 and demonstrate fluency for multiplication and division within 100. Students will solve problems involving measurement and estimation of liquid volumes, and masses of objects. In addition, students will represent data using picture graphs and bar graphs and interpret the data to solve problems. In Grade 3 students draw picture graphs in which each picture represents more than one object, and they draw bar graphs in which the height of a given bar in tick marks must be multiplied by the scale factor in order to yield the number of objects in the given category.

Students Need To

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with measurement scale) to represent the problem. (This unit extends students work in Unit 2 to include multiplication and division to solve problems involving measurement quantities). Note: Students are NOT responsible for doing conversions. However, the comparison between ml and l / g and kg may help students “reason” about volumes and masses.
Fluently add and subtract within 1000 using strategies and algorithms based on the following: place value, properties of operations or the relationship between addition and subtraction. Note: A range of algorithms may be used.
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 x 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Solve two-step problems involving the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Ways Parents Can Help

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. Ask questions to interpret the data in the graph.
Create and help your child solve real world 2 step word problems (add or subtract and multiply or divide). For example, we baked 2 trays of 15 cookies. We want to share them equally between 5 bags. How many cookies should we place into each bag?
Give your child the grocery ads in the newspaper to make a shopping list. Assign a budget. Have your child use mental math to estimate the total cost of the items and then figure out the change. Then ask your child to calculate the actual sum and difference.
Create and help your child solve some real world measurement problems involving liquid volumes and masses of objects. For example, a 1 liter soda bottle has a liquid volume of 1,000 milliliters. How many milliliters would be in a serving if you shared it among two people, four people, 5 people, 10 people (etc.)?
Give your child an addition or subtraction problem and have them explain how they solved it.