Subjects › Grade 3 Math
Grade 3 Math: multiplication, fractions, area, and more, explained step by step
This course covers the full Grade 3 Common Core math curriculum: multiplication and division within 100, place value and addition/subtraction within 1000, unit fractions and equivalent fractions on the number line, time, liquid volume and mass, scaled graphs and line plots, area and perimeter, and classifying two-dimensional shapes. It builds on Grade 2 skills like addition and subtraction within 100, skip counting, and recognizing halves and fourths of shapes, and it stops before Grade 4 topics like multi-digit multiplication and fraction operations.
A lesson starts from something the student can already do and moves one question at a time. If a student says 5 x 7 is 30, the tutor doesn't just correct it; it asks the student to draw or describe 5 groups of 7 and count, so the mistake gets found and fixed by the student. The tutor keeps track of which ideas a student can explain and which ones they can actually do, and checks back on earlier topics, like multiplication facts, when they come up again in later work like area of rectangles.
Who it is for
- Third graders learning multiplication and division for the first time
- Students who know addition and subtraction within 100 but haven't started multiplication
- Parents who want to see exactly what their child is working on and why
- Teachers looking for extra practice aligned to Common Core Grade 3 standards
- Students who need more time on fractions or area before moving to Grade 4
What you will be able to do
- Multiply and divide fluently within 100 and explain what multiplication and division mean
- Add and subtract three-digit numbers with regrouping and round to the nearest 10 or 100
- Solve one- and two-step word problems with all four operations, checking if the answer makes sense
- Place, name, and compare fractions on a number line, including equivalent fractions
- Tell time to the minute, solve time-interval problems, and work with liters, grams, and kilograms
- Find the area and perimeter of rectangles and other shapes, and classify shapes by their attributes
A taste of a lesson on Area of rectangles by tiling and multiplying side lengths
The tutor asks, you answer, and it works from what you actually said. No videos to sit through.
The 28 topics in Grade 3 Math
Each topic builds on the ones before it. The tutor checks what you already know and starts there.
Meaning of multiplication as equal groups and arrays
Multiplication as total objects in equal groups (5 groups of 7 is 5 x 7). Represent products with equal-group drawings, arrays, and repeated addition. Understand the vocabulary of factors and products and that multiplication is commutative in arrays (rotating an array gives the same count). Students should be able to write an equation for a picture and draw a picture for an equation.
Meaning of division as equal sharing and equal grouping
Division as partitioning a total into equal shares (56 shared among 8 people gives 7 each) and as finding how many equal groups fit (56 into groups of 8 gives 7 groups). Relate division to multiplication by seeing that a total split into equal groups is a multiplication with a missing factor. Students should explain both meanings with objects or drawings and recognize division situations in word problems.
Builds on Meaning of multiplication as equal groups and arrays
Properties of operations for multiplication
Commutative property (3 x 4 = 4 x 3), associative property for grouping three factors, and the distributive property shown with area models (7 x 8 = 7 x 5 + 7 x 3). Use these properties as strategies to derive harder facts from easier ones, such as 6 x 7 from 5 x 7 + 7. Students should justify why each strategy works.
Builds on Meaning of multiplication as equal groups and arrays
Multiplication facts for 0, 1, 2, 5, 10 and the related division facts
Recall products involving 0, 1, 2, 5, and 10 and explain the zero and one properties (any number times 1 is itself; any number times 0 is 0). Use doubling and skip counting to find 2s, 5s, and 10s, and connect each multiplication fact to a division fact (8 x 5 = 40 so 40 / 5 = 8).
Builds on Meaning of division as equal sharing and equal grouping, Properties of operations for multiplication
Multiplication and division facts for 3, 4, 6, 7, 8, 9 within 100
Fluently recall all products of one-digit numbers within 100, using strategies such as breaking apart a factor (6 x 7 = 5 x 7 + 7), doubling (4 x 6 = 2 x 6 doubled), and known facts (9 x 6 = 10 x 6 - 6). Use the inverse relationship to recall division facts quickly. Fluency means answering in a few seconds without counting by ones.
Builds on Multiplication facts for 0, 1, 2, 5, 10 and the related division facts
Unknown factor and unknown quantity equations
Division as an unknown-factor problem: 32 / 8 is the number that makes 32 when multiplied by 8. Determine unknown whole numbers in equations relating three numbers, such as 8 x ? = 48, 5 = box / 3, and 6 x 6 = ?. Use a letter or box to represent the unknown and check the answer by substitution.
Builds on Meaning of division as equal sharing and equal grouping, Multiplication and division facts for 3, 4, 6, 7, 8, 9 within 100
Patterns in addition and multiplication tables
Identify patterns in multiplication tables, such as products of 9 whose digits sum to 9, products of 4 always being even, and the pattern of counting by a number in a column. Explain each pattern using properties of operations, for example why 4 times any number is even because it is 2 times 2 times the number.
Builds on Properties of operations for multiplication, Multiplication and division facts for 3, 4, 6, 7, 8, 9 within 100
One-step multiplication and division word problems
Solve one-step word problems involving equal groups, arrays, and measurement quantities (for example, a box holds 6 pencils and there are 7 boxes), using drawings and equations with a symbol for the unknown. Decide whether a problem is multiplication or division and whether the unknown is the product, the group size, or the number of groups.
Builds on Unknown factor and unknown quantity equations
Place value and rounding to the nearest 10 or 100
Understand three-digit numbers as hundreds, tens, and ones. Round whole numbers to the nearest 10 or 100 by looking at the digit to the right of the rounding place and using a number line to justify the choice. Points exactly halfway (such as 150) round up by convention.
Fluent addition and subtraction within 1000
Add and subtract three-digit numbers using place value strategies, decomposition into hundreds, tens, and ones, and the standard algorithm with regrouping (carrying and borrowing across zeros). Check results using the inverse operation. Fluency means accurate, efficient computation with reasons for each step.
Builds on Place value and rounding to the nearest 10 or 100
Two-step word problems with four operations and estimation
Solve two-step word problems using addition, subtraction, multiplication, and division, writing an equation with a letter for the unknown. Check whether answers are reasonable using mental math and estimation, for example recognizing that 4 boxes of 19 is about 80 so an answer of 800 is wrong.
Builds on One-step multiplication and division word problems, Fluent addition and subtraction within 1000
Multiplying one-digit numbers by multiples of 10
Compute products such as 9 x 80 and 5 x 60 by thinking of the multiple of 10 as a number of tens (9 x 80 = 9 x 8 tens = 72 tens = 720). Use place value and the associative property to justify the strategy.
Builds on Multiplication and division facts for 3, 4, 6, 7, 8, 9 within 100, Place value and rounding to the nearest 10 or 100
Unit fractions as equal parts of a whole
Understand a fraction 1/b as one part when a whole is partitioned into b equal parts, and a/b as a parts of size 1/b. Name and draw fractions of shapes and sets, and recognize that the parts must be equal in size for the fraction name to apply.
Fractions as numbers on the number line
Represent 1/b on a number line by partitioning the interval from 0 to 1 into b equal parts, and represent a/b by marking off a lengths of 1/b from 0. The endpoint of each interval is the fraction's location. Include fractions greater than or equal to 1 on the number line and recognize whole numbers as fractions.
Builds on Unit fractions as equal parts of a whole
Equivalent fractions and expressing whole numbers as fractions
Understand two fractions as equivalent when they are the same size or the same point on a number line. Generate simple equivalent fractions such as 1/2 = 2/4 and 4/6 = 2/3 and justify them with visual models. Express whole numbers as fractions (3 = 3/1 = 6/2) and recognize fractions equal to 1 or other whole numbers.
Builds on Multiplication and division facts for 3, 4, 6, 7, 8, 9 within 100, Fractions as numbers on the number line
Comparing fractions
Compare two fractions with the same numerator or the same denominator by reasoning about size (for example, 1/4 is less than 1/3 because fourths are smaller pieces; 2/5 is greater than 1/5). Recognize that comparisons only make sense when both fractions refer to the same whole. Record results with the symbols >, <, and =.
Builds on Equivalent fractions and expressing whole numbers as fractions
Telling and writing time to the nearest minute
Read analog clocks to the nearest minute and write times in digital form, including a.m. and p.m. Understand that there are 60 minutes in an hour, use skip counting by 5s to read the minute hand, and use place value to read clock times as hours and minutes (for example, 3:45 is 3 hours and 45 minutes). Measure time intervals in minutes by counting along a clock or number line.
Builds on Multiplication facts for 0, 1, 2, 5, 10 and the related division facts, Fluent addition and subtraction within 1000
Time interval word problems in minutes
Solve word problems involving adding and subtracting time intervals in minutes, such as a movie starts at 2:45 and lasts 58 minutes, using a number line diagram to show the elapsed time and crossing the hour.
Builds on Telling and writing time to the nearest minute
Measuring liquid volume and mass in metric units
Measure and estimate liquid volumes in liters (l) and milliliters and masses in grams (g) and kilograms (kg), knowing that 1 kg = 1000 g and that these units suit objects of different sizes. Solve one-step word problems involving addition, subtraction, multiplication, or division of masses or volumes given in the same units, such as 4 bottles of 2 liters each.
Builds on One-step multiplication and division word problems, Fluent addition and subtraction within 1000
Scaled picture graphs and bar graphs
Draw scaled picture graphs where each symbol represents several units and scaled bar graphs with labeled axes and a scale such as 2, 5, or 10. Solve one- and two-step how-many-more and how-many-less problems using information in these graphs.
Builds on Two-step word problems with four operations and estimation
Measuring to halves and fourths of an inch and making line plots
Measure lengths of objects to the nearest half inch and quarter inch using rulers with those markings. Record the measurements and display them as a line plot whose horizontal scale is marked in whole numbers, halves, or quarters, and answer questions about the data set.
Builds on Fractions as numbers on the number line, Equivalent fractions and expressing whole numbers as fractions
Area as an attribute of plane figures and unit squares
Recognize area as the amount of surface a plane figure covers. A unit square with side 1 unit has one square unit of area. A figure covered without gaps or overlaps by n unit squares has area n square units. Measure area by counting unit squares, including square centimeters, inches, feet, meters and improvised units.
Builds on Unit fractions as equal parts of a whole
Area of rectangles by tiling and multiplying side lengths
Find the area of a rectangle with whole-number side lengths by tiling it with unit squares, and show that the count equals the product of the side lengths (a rows of b squares gives a x b). Use the formula area = length x width to solve real-world and mathematical problems and represent whole-number products as rectangular areas.
Builds on Meaning of multiplication as equal groups and arrays, Multiplication and division facts for 3, 4, 6, 7, 8, 9 within 100, Area as an attribute of plane figures and unit squares
Distributive property with area models
Show with tiling that a rectangle of width a and length b + c has area equal to a x b + a x c. Use area models to represent the distributive property, such as 6 x 7 as 6 x 5 + 6 x 2, and use this to reason about unknown products.
Builds on Properties of operations for multiplication, Multiplication and division facts for 3, 4, 6, 7, 8, 9 within 100, Area of rectangles by tiling and multiplying side lengths
Area of rectilinear figures by decomposition
Recognize area as additive. Find the area of a rectilinear figure (an L-shape or other figure made of right angles) by decomposing it into non-overlapping rectangles, finding each area, and adding. Apply the technique to real-world problems such as the area of a floor plan or garden.
Builds on Distributive property with area models
Perimeter of polygons and rectangles with equal perimeters
Find the perimeter of polygons given side lengths by adding all sides, find an unknown side length when the perimeter and other sides are known, and show that rectangles can have the same perimeter but different areas (or the same area with different widths and lengths). Solve real-world perimeter problems.
Builds on Multiplication and division facts for 3, 4, 6, 7, 8, 9 within 100, Fluent addition and subtraction within 1000, Area of rectangles by tiling and multiplying side lengths
Partitioning shapes into equal areas with unit fractions
Partition a shape into parts with equal area, such as splitting a rectangle into 4 parts of equal area, and express each part's area as a unit fraction of the whole (1/4 of the area). Understand that equal-area parts need not have the same shape.
Builds on Unit fractions as equal parts of a whole, Area as an attribute of plane figures and unit squares
Shape categories and attributes including rhombuses
Recognize that shapes in different categories may share attributes such as four sides, and that shared attributes define a larger category, such as quadrilaterals. Identify rhombuses (four equal sides, opposite sides parallel) and distinguish them from rectangles, squares, and trapezoids, and classify shapes by their sides and angles.
Practice questions in Grade 3 Math
A few of the kinds of questions you will work through, with answers.
What is 7 x 8?
See the answer
56
7 groups of 8 is 56; one way to find it is 7 x 5 = 35 plus 7 x 3 = 21, and 35 + 21 = 56.
What is 503 minus 268?
See the answer
235
Regrouping across the zero: 503 becomes 4 hundreds, 9 tens, 13 ones, then subtract 268 to get 235.
Which is greater, 3/8 or 3/5?
See the answer
3/5
Both have the same numerator, but fifths are larger pieces than eighths, so 3/5 is greater.
A movie starts at 2:45 and lasts 58 minutes. What time does it end?
See the answer
3:43
From 2:45 to 3:45 is 60 minutes; going back 2 minutes from 3:45 gives 3:43.
An L-shaped room is made of a 6-by-4 rectangle and a 3-by-2 rectangle attached to it. What is the total area?
See the answer
30 square units
6 x 4 = 24 and 3 x 2 = 6, and the areas add because they don't overlap: 24 + 6 = 30.
A store has 8 boxes of 6 markers each. 15 markers are sold. How many markers are left?
See the answer
33
8 x 6 = 48 markers total, then 48 - 15 = 33 remain.
Questions about this subject
My child hasn't learned multiplication at all yet. Is this too advanced?
No. The course starts with what multiplication means, using equal groups and arrays, before any facts or fluency work, so no prior multiplication knowledge is assumed.
Does this cover fraction addition or multi-digit multiplication?
No. This course stays within Grade 3 standards: unit and equivalent fractions on the number line, and multiplication within 100. Fraction operations and multi-digit multiplication are Grade 4 topics.
How does the tutor handle a student who gets stuck on multiplication facts?
It falls back to strategies like skip counting, doubling, or breaking a fact into known pieces (6 x 7 as 5 x 7 plus 7), rather than just supplying the answer.
Can this be used alongside a classroom curriculum?
Yes, the topics follow the standard Grade 3 Common Core order, so a student can use it to practice or catch up on whatever their class is currently covering.
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