Grade 4 · secular · Common Core-aligned
This is the year your child moves from "school arithmetic" into "real math." They'll learn to name numbers up to a million, add and subtract big numbers reliably, multiply and divide multi-digit numbers using a picture-based method that actually explains why the standard steps work, and then take that same understanding into fractions and decimals. It ends with converting units, measuring angles, and sorting shapes by their properties instead of by "what they look like." Every new skill starts as a drawing — boxes, bars, a number line — before it turns into digits on a page, so your child always has something to point at when they get confused.
The whole year, in plain English. Tap any unit to see every skill inside, nothing is hidden.
Your child learns to read, write, compare, and round numbers up to a million, always with a place value chart or number line next to the numbers so digits never float free of meaning. This is the same grouping idea from grade 3 (tens, hundreds, ones), just stretched further, with the added idea of "periods" — the comma-separated groups of three digits.
Identify the value of a digit in a multi-digit number based on its position, up to the millions place.
Write a multi-digit number up to 1,000,000 in standard, expanded, and word form.
Explain why grouping digits into periods of three helps read and write large numbers.
Compare two multi-digit numbers up to 1,000,000 using >, <, or =, based on place value.
Determine whether a number with more digits is always greater, by comparing counterexamples.
Round a multi-digit number to a specified place using a number line model.
Justify a rounding choice by identifying the number's position between two benchmark values on a number line.
Apply place value, comparison, and rounding together to solve a problem involving an unfamiliar large-number context, such as ranking distances or budgets never used in instruction.
Your child moves from naming place value to using it — regrouping ("carrying" and "borrowing," though we don't call it that) when adding and subtracting large numbers. It starts with blocks so regrouping is seen as trading ten of one place for one of the next, and only turns into the standard written steps once your child can explain a trade out loud.
Given a two-digit plus two-digit addition problem shown with base-ten blocks, state which place must be regrouped and why.
Add two multi-digit whole numbers using the standard algorithm, regrouping across two or more places.
Subtract multi-digit whole numbers using the standard algorithm, including across a zero in the minuend.
Explain what happens to the value of a digit when ten of one place are traded for one of the next place during a subtraction regrouping.
Estimate a sum or difference by rounding both numbers to the nearest ten, hundred, or thousand before computing.
Judge whether an exact answer to a multi-digit addition or subtraction problem is reasonable by comparing it to an estimate.
Solve a two-step word problem requiring both addition and subtraction of multi-digit numbers, choosing which operation applies at each step.
Solve an unfamiliar multi-step problem involving quantities given in a new context (e.g., a data table not used in instruction), including a check using estimation.
Compare two solution strategies for the same subtraction problem — standard algorithm versus a mental or compensation strategy — and identify which is more efficient for that specific problem.
This unit teaches your child to tell apart two kinds of "comparing": additive ("how much more") and multiplicative ("how many times as many"). They build a bar model first, before writing any equation — the picture decides which operation is right, not a keyword.
Given a comparison sentence like '3 times as many apples as pears,' student draws a bar model showing the smaller quantity's bar copied 3 times.
Student sorts eight word problems into 'additive comparison' and 'multiplicative comparison' bins based on sentence structure, not keywords.
Given a multiplicative comparison word problem, student writes an equation using a letter for the unknown and solves it.
Student explains why two problems with the same two numbers but different wording require different equations.
Given a three-number multi-step word problem, student identifies what the first computed quantity represents before using it in a second step.
Student solves a multi-step word problem combining addition or subtraction with multiplicative comparison, showing both steps.
Given an unfamiliar real-world scenario never discussed in class (e.g. comparing recipe scaling amounts), student decides whether it calls for additive or multiplicative comparison and justifies the choice.
Student recalls the meaning of 'times as many' when given an isolated comparison phrase without a full word problem.
Your child extends the grade 3 idea of area-as-covering into a full method for multiplying big numbers: break each factor into place-value pieces, multiply the pieces, add them up. This is called the area model, and it's taught for a while before the standard algorithm ever appears — the algorithm is introduced explicitly as a shortcut for boxes your child has already drawn many times.
Given a 2-digit number, decompose it into tens and ones and write both parts in expanded form.
Draw an area model for a 1-digit by multi-digit multiplication problem, labeling each box with the place-value parts multiplied.
Given a completed area model with its boxes and values already labeled, write the matching list of partial products and add them to find the total.
Calculate the product of a 1-digit number and a 4-digit number using partial products, and connect each partial product to its area model box.
Draw an area model for a 2-digit by 2-digit multiplication problem, showing all four boxes and their place values.
Explain why decomposing both factors of a multiplication problem by place value and adding the partial products gives the same exact product as multiplying the whole numbers.
Execute the standard algorithm for 2-digit by 2-digit multiplication, and identify which area-model box each written partial product represents.
Estimate the product of two multi-digit numbers by rounding each factor before multiplying, and judge whether the estimate is reasonable.
Solve a multi-step word problem requiring multiplication, choosing whether to compute exactly or estimate, and state why the question's demand requires that precision.
Given a novel real-world scenario never used in this unit's instruction, decide whether a bigger area model necessarily requires more total work than a smaller one, and justify the decision using actual computed values.
This unit runs Unit 4 backwards. Your child already knows: side length times side length gives area. Now they're given the area and one side, and have to find the missing side — that missing side is the quotient. Long division gets built as a written record of this same box-based reasoning, not as a new set of arbitrary steps to memorize.
Given a rectangle's area and one side length, find the missing side length using an area model with partial quotients.
Explain why the long division algorithm produces the same quotient as the area-model partial-quotients method for the same problem.
Divide a 2-, 3-, or 4-digit dividend by a 1-digit divisor using the standard long division algorithm, with and without a remainder.
Check a division answer by multiplying the quotient by the divisor and adding any remainder, to verify it equals the dividend.
Given a word problem with a remainder, decide whether the situation requires dropping the remainder, rounding the quotient up, or expressing the remainder as a fraction.
Solve a multistep word problem that combines multiplicative comparison and division with a remainder, in a context never used during instruction.
Estimate a division quotient using rounding and compatible numbers before computing, to judge whether a computed answer is reasonable.
Compare two division word problems that use the same numbers but different remainder-handling requirements, and identify what makes them different.
A short, focused unit. Your child learns to test whether one number is a factor of another using "division with no remainder" from Unit 5, builds factor pairs and lists of multiples using arrays and number-line hops, sorts numbers into prime and composite by counting factor pairs, and spots patterns on a hundred chart.
Given a whole number up to 100, list all of its factor pairs by testing division with no remainder.
Explain why a number and 1 are always a factor pair of that number, using an array picture.
List the first ten multiples of a given one- or two-digit number using repeated multiplication.
Sort a given task into 'asks for factors' or 'asks for multiples' by matching it to the taught tell for each.
Classify a whole number from 2 to 100 as prime or composite by checking its factor pairs.
Given a 1-100 number chart with multiples of a number shaded, identify the resulting visual and numerical pattern.
Explain in words why a given number pattern happens, referring to the operation that generates it.
Determine whether a large unfamiliar number (e.g. 89 or 71) is prime or composite when no factor pair is immediately obvious.
The biggest unit of the year at 32 days. Your child learns that a fraction is a shaded amount, not just two numbers stacked up. It moves from equivalence (same amount, different-looking fraction) to comparing fractions with unlike denominators, to adding and subtracting like-denominator fractions, to whole-number-times-fraction, and finally to decimals — introduced as fractions with denominator 10 or 100, shown on a grid, before any decimal point shows up.
Given a fraction bar shaded to show a fraction, partition it into smaller equal pieces and name the new equivalent fraction.
Explain why two fractions with different numerators and denominators can represent the same shaded amount.
Compare two fractions with unlike denominators using a benchmark fraction such as 1/2.
Find a common denominator for two fractions using multiples, and use it to compare them.
Add and subtract fractions with the same denominator using a fraction bar model.
Decide whether an unfamiliar fraction addition or subtraction problem needs a common denominator before adding, given fractions with unlike denominators embedded in a word problem the class has not seen before.
Multiply a whole number by a fraction by modeling repeated addition of the fraction on a number line.
Identify and correct a fraction-multiplication error that applies the addition rule instead of repeated addition.
Represent a fraction with denominator 10 or 100 on a hundredths grid and write its decimal notation.
Compare two decimals to hundredths using a grid model rather than digit count.
Given a real-world measurement context using an unfamiliar unit split into tenths, decide how to represent and compare the amounts using decimal grids without being told to do so.
The longest unit of the year at 36 days, braiding three strands: converting units, measuring angles, and classifying shapes. Unit conversion is multiplicative comparison (Unit 3) applied to units instead of quantities. Angle measurement takes Unit 7's "fraction of a whole" picture and wraps it around a circle. Shape classification asks your child to use precise angle and line vocabulary instead of judging shapes by eye.
Given a table of within-system unit relationships (e.g. 1 ft = 12 in), state the relationship for km/m, kg/g, lb/oz, l/ml, and hr/min/sec from memory.
Convert a measurement from a larger unit to a smaller unit (e.g. 3 ft to inches) by multiplying by the number of small units per large unit.
Explain why converting to a smaller unit means multiplying, connecting it to 'times as many' comparison language.
Solve a multi-step word problem that requires converting units and then adding, subtracting, multiplying, or dividing the converted values.
Apply the area and perimeter formulas for a rectangle to find an unknown side length given the other side and the area or perimeter.
Measure a given angle with a protractor to the nearest whole degree and sketch an angle of a specified measure.
Explain an angle's measure as the fraction of a full circular arc it takes up, connecting it to the fraction-bar model of a whole.
Find an unknown angle in a diagram by adding or subtracting known adjacent angle measures.
Classify a two-dimensional figure by the presence of parallel or perpendicular lines and by the types of angles it contains.
Given an unfamiliar irregular polygon with unlabeled angles, decide which quadrilateral categories it could and could not belong to, and justify the decision using at least two properties.
Identify lines of symmetry in a two-dimensional figure, including figures with more than one line of symmetry.
Compare an additive ('how much more') and a multiplicative ('how many times as many') solution path for the same unit-conversion word problem and decide which the problem actually asks for.
From the parent guide
This is the year your child moves from "school arithmetic" into "real math." They'll learn to name numbers up to a million, add and subtract big numbers reliably, multiply and divide multi-digit numbers using a picture-based method that actually explains why the standard steps work, and then take that same understanding into fractions and decimals. It ends with converting units, measuring angles, and sorting shapes by their properties instead of by "what they look like." Every new skill starts as a drawing — boxes, bars, a number line — before it turns into digits on a page, so your child always has something to point at when they get confused.
Unit 1 · what to expect
Your child learns to read, write, compare, and round numbers up to a million, always with a place value chart or number line next to the numbers so digits never float free of meaning. This is the same grouping idea from grade 3 (tens, hundreds, ones), just stretched further, with the added idea of "periods" — the comma-separated groups of three digits.
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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