Grade 5 · secular · Common Core-aligned
This is a full year of fifth-grade math built around three ideas: how our number system extends into decimals, how fractions behave when you combine or split them, and how measurement and space help you model real things like boxes and graphs. Every new skill gets a picture first — blocks, an area drawing, a number line, a fraction bar — before your child ever sees the shortcut version. By June, they should be able to add, subtract, multiply, and divide decimals and fractions without hesitating, and plot and read points on a graph. That's the runway sixth grade assumes they already have.
The whole year, in plain English. Tap any unit to see every skill inside, nothing is hidden.
This unit takes the decimal and whole-number place-value understanding your child built in fourth grade and stretches it further — down to thousandths and up through powers of ten. The one idea underneath everything here is that a digit's value depends entirely on where it sits, not on the digit itself.
Given a multi-digit whole number or decimal, state the value represented by a specified digit, and explain why the digit to its left is worth 10 times as much.
Build a physical or drawn base-ten block model of a decimal to thousandths and match it to its digit form.
Explain the pattern in the number of zeros in a product when a whole number is multiplied by 10, 100, or 1,000.
Predict where the decimal point lands when a decimal is multiplied or divided by a power of ten, using exponent notation to name the power.
Write a decimal to the thousandths in word form, standard form, and expanded form, and convert among the three.
Compare two decimals to the thousandths place using place value reasoning, and justify the comparison by referring to the value of a specific digit rather than digit count.
Round a decimal to a specified place (tenths, hundredths, or thousandths) using a number line or place value reasoning, and justify why the digit changed or stayed the same.
Given an unfamiliar real-world measurement context (e.g., a runner's split times to the thousandth of a second), determine which of several decimals represents the closest finish and explain the ranking using place value.
Now that place value is solid, this unit stretches addition, subtraction, multiplication, and division to work on decimals. Every operation starts as a picture — a grid for adding, an area model for multiplying, hops on a number line for dividing — before the standard written steps show up.
Add and subtract decimals to the hundredths using a base-ten grid model, aligning place value.
Explain why decimal points, not digits, must be aligned when adding or subtracting decimals.
Multiply a decimal by a whole number using an area model, then connect the model to the standard algorithm.
Predict whether a product will be larger or smaller than the starting factor when multiplying by a decimal less than one, before computing.
Use estimation by rounding factors to check whether a decimal product's placement of the decimal point is reasonable.
Divide a decimal by a whole number using place-value reasoning and a number-line model of equal groups.
Compare two decimal quotient problems with different-sized divisors and explain which produces the larger quotient and why.
Solve a multi-step word problem combining decimal addition, subtraction, multiplication, and division in an unfamiliar money-and-measurement context.
Classify a set of decimal computation errors by which place-value step broke down (alignment, decimal placement, or grouping).
This unit stretches long division to two-digit divisors. The core idea: dividing by a bigger number is the same operation as before, just done with an estimate you check and adjust as you go, using an area model to make the process visible.
Estimate a two-digit-divisor quotient by rounding both numbers to place-value-friendly amounts before dividing.
Represent a multi-digit division problem as an area model with an unknown side length.
Explain why the partial quotients in an area model sum to the total quotient.
Execute the standard long division algorithm with a two-digit divisor and a whole-number quotient.
Adjust an initial quotient estimate when the first trial digit is too high or too low.
Classify a division word problem by which remainder-handling rule applies: round up, round down, or express as a fraction.
Justify in one written sentence why a remainder was rounded up, rounded down, or expressed as a fraction in a specific problem.
Evaluate a numerical expression containing division and grouping symbols, applying order of operations.
Write a numerical expression, using grouping symbols, that records the two-step calculation described in a word problem.
Estimate whether a computed quotient is reasonable by comparing it to a place-value-friendly estimate.
This unit teaches adding and subtracting fractions and mixed numbers with different-sized denominators. The idea repeated all unit long: pieces of different sizes can't be combined until they're renamed into the same size — fraction bars first, shortcut second.
Given two fraction bars with different denominators, the student explains why the pieces cannot be combined without renaming.
The student finds a common denominator for two given fractions using an equivalence model (fraction bars or a number line).
The student adds and subtracts two fractions with unlike denominators, showing the renaming step and the final answer.
The student adds and subtracts mixed numbers with unlike denominators, regrouping a whole into fraction pieces when needed.
The student classifies a fraction as closer to 0, 1/2, or 1 by comparing it to benchmark fractions on a number line.
The student estimates the sum of two unlike-denominator fractions using benchmark reasoning before computing an exact answer.
The student solves a one-step word problem requiring addition or subtraction of unlike-denominator fractions, selecting the correct operation from context.
Given a real-world context never used in instruction (e.g., combining leftover paint amounts measured in different fraction units across three containers), the student determines whether the situation requires addition, subtraction, or is unsolvable with given information.
Here fractions get multiplied instead of added, which means the pieces themselves change size rather than staying the same size and combining. The core idea: multiplying by a fraction less than one means taking a part of a part, and an area model shows exactly why the result shrinks.
Given a picture of a whole cut into fourths with 3 parts shaded, and 4 copies of that shape, find the total shaded amount as 4 x 3/4.
Shade a rectangle to show 2/3 of 3/4, using rows for one fraction and columns for the other, and name the overlap fraction.
Given a fraction-times-fraction area model with rows and columns already shaded, write the matching equation as numerator-times-numerator over denominator-times-denominator.
State whether a product will be greater than, less than, or equal to a given factor, without multiplying, based on whether the other factor is greater than, less than, or equal to 1.
Multiply two proper fractions by multiplying numerators and multiplying denominators, and simplify the result.
Convert a mixed number to an improper fraction and multiply it by another fraction or mixed number.
Explain, using an area model or a size-reasoning sentence, why a fraction-times-fraction product is smaller than both factors.
Solve a word problem asking for a fractional part of a fractional part of a real quantity (e.g. area of a garden plot), using a labeled area model.
Solve a scaling word problem set in a context never used in instruction (e.g. map distance shrinking by a fraction), deciding without being told whether the answer should be bigger or smaller than the start.
Compare a fraction-times-fraction area model to a fraction addition bar model for the same two fractions, and state what changes between the two operations.
Students learn to divide a whole number by a unit fraction (like 6 ÷ 1/3) and a unit fraction by a whole number (like 1/5 ÷ 4). Both get built from fraction bars and number lines before any shortcut — the unit is built to confront head-on the idea that division always makes numbers smaller.
Given a whole number and a unit fraction, draw a fraction bar or number line model showing how many unit-fraction pieces fit inside the whole number.
Given a completed picture of a whole number split into unit-fraction pieces, count the pieces and state the total.
Given a completed fraction bar model for whole number ÷ unit fraction, write the matching division expression and quotient.
Given a unit fraction and a whole number, draw a fraction bar model showing the unit fraction split into that many equal smaller pieces.
Explain why 6 ÷ 1/3 produces a larger number than 6, using the fraction bar model as evidence.
Compare a whole ÷ unit fraction model and a unit fraction ÷ whole model side by side and identify what is different about which quantity gets split.
Given a real-world story problem, decide whether it requires whole ÷ unit fraction or unit fraction ÷ whole number, and justify the choice.
Given a mixed set of Unit 5 multiplication and Unit 6 division fraction word problems, identify which operation each story requires and solve it.
Solve a novel measurement story involving a non-foot, non-familiar unit of measure requiring whole ÷ unit fraction, with no operation cue given.
This unit takes flat-shape area thinking into three dimensions. Kids pack rectangular prisms with unit cubes and count them, then discover that multiplying the three edge lengths gives the exact same number — two methods that always agree.
Count unit cubes packed into a rectangular prism shown in a layered picture to find its volume.
Explain why the number of unit cubes packed into a prism equals length times width times height.
Calculate the volume of a rectangular prism given its three edge lengths using the formula V = l x w x h.
Given a partially-packed prism picture missing some cubes, find the number of cubes needed to finish one layer.
Apply the volume formula to a real-world context, such as a shipping box or fish tank, to find how much it holds.
Decompose a composite figure made of two rectangular prisms into two separate prisms to find total volume.
Solve for a missing edge length of a rectangular prism given its volume and its other two edge lengths.
Distinguish which of three volume problem types (single prism, composite figure, missing edge) a given word problem requires.
Find the volume of a composite figure never seen in class, built from two prisms in an unfamiliar arrangement, using both counting and multiplying, and reconcile the two answers.
The year's closing unit. Two number lines from Unit 1, set perpendicular to each other, become a coordinate plane. Kids plot and read points in the first quadrant, then generate number patterns using fraction and decimal operations from earlier units and graph them to compare.
Label the x-axis, y-axis, and origin on a first-quadrant coordinate grid.
Plot an ordered pair on a first-quadrant grid by moving right along the x-axis then up parallel to the y-axis.
Explain why the order of the two numbers in an ordered pair changes which point is named.
Interpret the coordinates of a point plotted in a real-world context, such as distance traveled over time.
Generate a numerical pattern by applying a given whole-number rule repeatedly to produce a sequence of terms.
Generate two numerical patterns from two related rules using fraction or decimal operations from Units 4-6, and form ordered pairs from corresponding terms.
Compare two numerical sequences generated from related rules by graphing their corresponding ordered pairs and describing the relationship between the sequences.
Infer the rule relating two corresponding sequences when given only their graphed points, in a context and number pairing not used during instruction.
Distinguish between a point's location in the context of the real-world situation it represents and its bare coordinate values.
From the parent guide
This is a full year of fifth-grade math built around three ideas: how our number system extends into decimals, how fractions behave when you combine or split them, and how measurement and space help you model real things like boxes and graphs. Every new skill gets a picture first — blocks, an area drawing, a number line, a fraction bar — before your child ever sees the shortcut version. By June, they should be able to add, subtract, multiply, and divide decimals and fractions without hesitating, and plot and read points on a graph. That's the runway sixth grade assumes they already have.
Unit 1 · what to expect
This unit takes the decimal and whole-number place-value understanding your child built in fourth grade and stretches it further — down to thousandths and up through powers of ten. The one idea underneath everything here is that a digit's value depends entirely on where it sits, not on the digit itself.
The full guide covers all 8 units: where kids get stuck, what to say, and how to tell it's working. Included with the course.
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