Subjects › Grade 5 Math
Grade 5 Math: build fraction, decimal, and volume skills by talking them through
This course covers the full Grade 5 Common Core math curriculum: writing and evaluating numerical expressions, extending patterns to ordered pairs, place value through thousandths, multi-digit whole number and decimal operations, adding, multiplying, and dividing fractions, converting measurement units, reading line plots with fractional data, graphing points in the first quadrant, finding volume of rectangular prisms, and classifying two-dimensional figures by their properties.
A lesson starts from what the student can already do and moves forward one question at a time. If a student says 2/3 + 1/2 = 3/5, the tutor doesn't just mark it wrong - it asks what a common denominator for 3 and 2 could be, then has the student redo the addition with that denominator. The tutor checks both whether the student can explain an idea, like why multiplying by a fraction less than 1 gives a smaller result, and whether they can actually do it, like carrying out 7/8 divided by 1/4.
Who it is for
- Fifth graders working through Common Core math, in school or at home
- Students who are solid on Grade 4 fractions and decimals but new to operations on them
- Parents who want a clear, step-by-step way to support homework on fractions and volume
- Teachers looking for extra one-on-one practice between lessons
- Students reviewing over a summer before starting middle school math
What you will be able to do
- Evaluate numerical expressions with parentheses, brackets, and braces in the right order
- Add, subtract, multiply, and divide decimals to the hundredths place
- Add, subtract, multiply, and divide fractions and mixed numbers, including in word problems
- Convert measurement units within the customary or metric system and solve multi-step problems
- Find the volume of a rectangular prism and explain why length x width x height works
- Graph points in the first quadrant and classify two-dimensional figures by their properties
A taste of a lesson on Multiplying fractions by whole numbers and fractions
The tutor asks, you answer, and it works from what you actually said. No videos to sit through.
The 23 topics in Grade 5 Math
Each topic builds on the ones before it. The tutor checks what you already know and starts there.
Numerical expressions and order of operations
Use parentheses, brackets, and braces in numerical expressions and evaluate them using the order of operations (multiply and divide before add and subtract, work inside grouping symbols first). Write simple expressions that record calculations in words (e.g., 'add 8 and 7, then multiply by 2' is 2 x (8 + 7)) and interpret an expression without evaluating it, such as recognizing that 3 x (18932 + 921) is 3 times as large as 18932 + 921. Students should be able to explain why grouping symbols change the result.
Numerical patterns and ordered pairs
Generate two numerical patterns from two given rules (e.g., add 3 starting at 0; add 6 starting at 0). Identify the relationship between corresponding terms (the second sequence is always twice the first), form ordered pairs from corresponding terms, and explain why the pairs graph as a straight line pattern. Students should see that the pattern of terms, not just the list, reveals the rule.
Builds on Numerical expressions and order of operations
Place value patterns in base ten
Recognize that in a multi-digit number a digit represents 10 times what it represents in the place to its right and one tenth of what it represents in the place to its left (e.g., in 555, each 5 is ten times the 5 to its right). Use whole-number exponents to denote powers of 10 (10^3 = 1000) and explain how multiplying or dividing by powers of 10 shifts digits and the decimal point, including how the number of zeros in a product by a power of 10 relates to the exponent.
Reading, writing, and expanded form of decimals
Read and write decimals to thousandths using base-ten numerals, number names (e.g., 347.392 is three hundred forty-seven and three hundred ninety-two thousandths), and expanded form (3 x 100 + 4 x 10 + 7 x 1 + 3 x 1/10 + 9 x 1/100 + 2 x 1/1000). Students should connect tenths, hundredths, and thousandths to fractions with denominators 10, 100, and 1000.
Builds on Place value patterns in base ten
Comparing and rounding decimals
Compare two decimals to thousandths using the meaning of digits in each place, recording results with >, =, and <. Round decimals to any place (tenths, hundredths, thousandths, ones, tens) by looking at the digit to the right of the rounding place and using a number line to justify the result. Students should explain why 0.8 equals 0.800 and why 0.45 is greater than 0.405.
Builds on Reading, writing, and expanded form of decimals
Multi-digit whole number multiplication
Multiply multi-digit whole numbers fluently using the standard algorithm, and explain why it works using place value and the distributive property (e.g., 36 x 24 = 36 x 20 + 36 x 4). Students should estimate products to check reasonableness and solve multiplication word problems with multi-digit factors.
Builds on Numerical expressions and order of operations, Place value patterns in base ten
Whole number division with two-digit divisors
Find whole-number quotients of whole numbers with dividends up to four digits and divisors up to two digits, using strategies based on place value, the distributive property, and the relationship between multiplication and division. Illustrate and explain the calculation with equations, arrays, or area models, and interpret remainders in context.
Builds on Multi-digit whole number multiplication
Adding and subtracting decimals to hundredths
Add and subtract decimals to hundredths using concrete models (base-ten blocks, money), drawings, and place value strategies, lining up decimal points and regrouping across places. Relate each strategy to a written method and explain why decimal points must align.
Builds on Comparing and rounding decimals
Multiplying and dividing decimals to hundredths
Multiply and divide decimals to hundredths using concrete models or drawings, place value, and the relationship to whole-number operations (e.g., 0.4 x 0.6 as 4 x 6 = 24 with the product scaled to 0.24 using a 10 by 10 grid). Explain decimal placement, multiply decimals by powers of 10 by shifting the decimal point, and relate each strategy to a written method.
Builds on Place value patterns in base ten, Multi-digit whole number multiplication, Whole number division with two-digit divisors, Adding and subtracting decimals to hundredths
Adding and subtracting fractions with unlike denominators
Add and subtract fractions and mixed numbers with unlike denominators by replacing fractions with equivalent fractions that share a common denominator (e.g., 2/3 + 5/6 = 4/6 + 5/6 = 9/6 = 1 1/2). Students should use the idea that equivalent fractions name the same amount, and check that answers are reasonable against benchmark fractions such as 0, 1/2, and 1.
Fraction addition and subtraction word problems
Solve word problems involving addition and subtraction of fractions that refer to the same whole, including unlike denominators, by representing the problem with visual fraction models (bar models, area models) or equations. Use benchmark fractions to estimate and judge whether answers are reasonable.
Builds on Adding and subtracting fractions with unlike denominators
Fractions as division
Interpret a fraction a/b as the division a divided by b, so that 3/4 means 3 divided by 4 and equals three fourths of one whole. Solve word problems where whole numbers are shared equally and the answer is a fraction or mixed number (e.g., 5 sandwiches shared among 4 people is 5/4 = 1 1/4 sandwiches each), representing each with a visual model.
Builds on Whole number division with two-digit divisors
Multiplying fractions by whole numbers and fractions
Interpret the product (a/b) x q as a parts of a partition of q into b equal parts, equivalently as a x q divided by b; use visual fraction models to show that 2/3 of 4 is 8/3. Multiply a fraction or whole number by a fraction, and find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction size, showing the area equals the product of the side lengths.
Builds on Adding and subtracting fractions with unlike denominators, Fractions as division
Multiplication as scaling
Interpret multiplication as scaling (resizing). Without performing the multiplication, compare the size of a product to the size of one factor based on the size of the other factor (e.g., 8 x 1/2 is smaller than 8 and 8 x 3/2 is larger than 8). Explain why multiplying a number by a fraction greater than 1 gives a product larger than the original number, and why multiplying by a fraction less than 1 gives a smaller product.
Builds on Multiplying fractions by whole numbers and fractions
Multiplying fractions and mixed numbers in word problems
Solve real world problems involving multiplication of fractions and mixed numbers, such as finding part of a recipe or distance, using visual fraction models or equations to represent the situation. Students should multiply mixed numbers by converting to improper fractions and check that the answer is reasonable.
Builds on Multiplying fractions by whole numbers and fractions, Multiplication as scaling
Dividing unit fractions and whole numbers by unit fractions
Interpret division of a unit fraction by a nonzero whole number (1/3 divided by 4 is 1/12, shown with a visual model and a story context) and division of a whole number by a unit fraction (4 divided by 1/5 is 20, because there are 5 fifths in each whole). Explain the relationship between multiplication and division that makes these quotients work, and compute such quotients.
Builds on Fractions as division, Multiplying fractions by whole numbers and fractions
Division of unit fractions in word problems
Solve real world problems involving division of unit fractions by nonzero whole numbers and whole numbers by unit fractions, using visual fraction models and equations. Example: how much chocolate does each person get if 1/5 pound is shared among 4 people, or how many 1/3-cup servings are in 6 cups.
Builds on Dividing unit fractions and whole numbers by unit fractions
Converting measurement units and multi-step measurement problems
Convert among different-sized standard units within one measurement system (customary: inches, feet, yards, ounces, pounds, cups, quarts, gallons; metric: mm, cm, m, km, g, kg, mL, L), e.g., 5 cm = 0.05 m, and use these conversions in multi-step real world problems. Students should understand that smaller units give larger counts and use decimals or fractions appropriately.
Builds on Reading, writing, and expanded form of decimals, Multiplying and dividing decimals to hundredths
Line plots with fractional measurements
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8), with the horizontal scale marked in those fractions. Use operations on fractions (addition, subtraction, and sharing) to solve problems about the information on the line plot, such as finding the total amount or the difference between the largest and smallest values.
Builds on Fraction addition and subtraction word problems, Fractions as division
The coordinate plane and graphing in the first quadrant
Use two perpendicular number lines (axes) meeting at the origin, where both 0s coincide, to define a coordinate system and locate a point in the plane by its ordered pair (x, y). Graph points in the first quadrant to represent real world and mathematical problems, and interpret the coordinate values in the context of the situation (e.g., time and distance).
Builds on Numerical patterns and ordered pairs
Volume as packed unit cubes
Recognize volume as an attribute of solid figures. A cube with side length 1 unit is a unit cube with one cubic unit of volume; a solid that can be packed without gaps or overlaps by n unit cubes has volume n cubic units. Measure volumes by counting unit cubes using cubic cm, cubic inches, cubic feet, and improvised units.
Volume of rectangular prisms and additivity
Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, showing the count equals length x width x height and also base area x height. Apply V = l x w x h and V = b x h to real world and math problems, and use additivity: decompose a solid made of two non-overlapping right rectangular prisms, add their volumes, and solve composite-figure problems.
Builds on Multi-digit whole number multiplication, Volume as packed unit cubes
Classifying two-dimensional figures in a hierarchy
Classify two-dimensional figures (triangles by angles and sides, quadrilaterals such as parallelograms, rhombuses, rectangles, squares, trapezoids) into a hierarchy based on properties. Understand that attributes belonging to a category also belong to all its subcategories: all rectangles have four right angles, and since squares are rectangles, all squares have four right angles. Students should justify classifications with properties.
Practice questions in Grade 5 Math
A few of the kinds of questions you will work through, with answers.
Evaluate: 3 + (8 - 2) x 4
See the answer
27
First do the parentheses: 8 - 2 = 6, then multiply 6 x 4 = 24, then add 3 to get 27.
Round 4.567 to the nearest hundredth.
See the answer
4.57
Look at the thousandths digit, 7, which rounds the hundredths digit up from 6 to 7.
What is 0.4 x 0.6?
See the answer
0.24
4 x 6 = 24, and since both factors have one decimal place each, the product has two decimal places: 0.24.
What is 2/3 + 5/6?
See the answer
1 1/2
Rewrite 2/3 as 4/6, then 4/6 + 5/6 = 9/6, which simplifies to 1 1/2.
How many 1/4-cup servings are in 3 cups of flour?
See the answer
12
Dividing 3 by 1/4 means asking how many fourths fit into 3 wholes: 3 divided by 1/4 = 3 x 4 = 12.
A box is 5 units long, 3 units wide, and 2 units tall. What is its volume?
See the answer
30 cubic units
Volume equals length x width x height, so 5 x 3 x 2 = 30 cubic units.
Questions about this subject
Does this course cover ratios or percents?
No. Those topics start in Grade 6. This course stays within the Grade 5 Common Core scope: expressions, place value through thousandths, fraction and decimal operations, measurement, volume, and 2D figure classification.
What math does my child need to know before starting?
Grade 4 skills: multi-digit whole number operations, recognizing equivalent fractions and comparing them, basic decimal notation for tenths and hundredths, and finding area and perimeter of rectangles.
How does the tutor handle a student who gets a fraction problem wrong?
It asks a question that targets the likely misstep, such as checking the common denominator before redoing an addition, rather than just giving the correct answer right away.
Does the course include word problems or just computation?
Both. Most topics pair a computation skill, like multiplying fractions, with word problems that use it, like finding part of a recipe or a distance.
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