Grade 2 · secular · Common Core-aligned
A full second-grade math year built for one adult and one child at a kitchen table. Your child moves from understanding what the digits in a number like 347 mean, to adding and subtracting two-digit numbers with regrouping, to meeting multiplication before it has a name in the form of equal rows and columns. Then it goes outward: measuring with a ruler, telling time to five minutes, counting coins, naming shapes by their sides and corners, splitting a pizza fairly into thirds. Every idea arrives first as something they can hold, blocks or coins or paper shapes or a ruler, before it becomes a written number sentence. By June your child can read an unlabelled word problem and work out for themselves which kind of math it is asking for.
The whole year, in plain English. Tap any unit to see every skill inside, nothing is hidden.
This unit teaches that any number is just groups of ten, bundled up. Your child moves from tens-and-ones with two-digit numbers into bundling ten tens into a hundred, then reading, writing, and comparing three-digit numbers. Whatever blocks or drawings you use here become the mental picture for every number they write for the rest of the year.
Given a pile of up to 9 loose ones, bundle them into a group of ten when possible and state how many tens and ones remain.
Given ten bundled tens shown as blocks, name the group as one hundred and state how many ones it equals.
Given a 3-digit number built from blocks, read it aloud and write it using hundreds, tens, and ones digits in the correct places.
Given the same quantity built two different ways (e.g., 3 hundreds 2 tens vs. 2 hundreds 12 tens), explain why both represent the same number.
Given two 3-digit numbers with the same hundreds digit, compare them using greater than, less than, or equal to based on the tens or ones place.
Given a start number, skip-count forward by 5s, 10s, or 100s to a stated stopping point.
Given a 3-digit number never used in instruction, build it with blocks in a way the teacher did not model and justify the digit values.
Given a real classroom-counting context never modeled in the unit (e.g., counting the total pencils in the whole school building using boxes of 100, packs of 10, and loose pencils, with no blocks or place-value mat present), state how many hundreds, tens, and ones the total has and justify the answer without being told which representation to use.
Your child takes the bundling idea from Unit 1 and uses it to add and subtract two-digit numbers — physically breaking a ten into ten ones, or bundling ten ones into a ten, with the same blocks. It moves from fully-modeled block work toward doing it on paper alone, then into word problems. Facts within 20 (like 8+7) get practiced daily but aren't retaught — they should already be fast.
Given a pile of ones blocks totaling more than 10, the student bundles 10 ones into 1 ten and states the new count.
The student adds two two-digit numbers within 100 that require regrouping ones into a ten, using blocks then a written record.
The student subtracts two-digit numbers within 100 that require breaking a ten into ten ones, using blocks then a written record.
The student explains why adding the subtracted number back to the difference recreates the starting number, using a part-whole block diagram.
The student adds up to four two-digit numbers within 100, tracking regrouped tens across more than one column.
The student solves a one-step addition or subtraction word problem within 100 by matching the story to a number sentence.
The student solves a two-step word problem within 100, identifying the hidden middle quantity before finding the final answer.
The student recalls addition and subtraction facts within 20 automatically, without counting on fingers.
Given an unfamiliar context (splitting a mixed bag of two different bundled items into totals), the student applies regrouping to find a combined total without being told which operation to use.
Given a two-step story set at a birthday party (a context never used for teaching, with numbers to 100 and no operation words), the student finds the hidden middle amount and the final answer using only a picture of party items to count.
Your child takes 'equal groups' from Unit 2 and renames them as arrays — objects lined up in rows and columns. They find totals by repeated addition, sort counts into two equal piles to decide even or odd, and ask which counts can form a neat rectangle at all.
Child builds an array with a given number of rows and a given number in each row, using counters.
Child counts the total number of objects in an array by counting each row and adding the rows together.
Child writes (by tapping number and plus-sign tiles) the repeated-addition sentence that matches a shown array.
Child determines whether a set of objects counted by rows gives the same total when counted by columns instead.
Child sorts a set of counters into two equal groups by pairing, and names the count as even or odd based on whether any counter is left over.
Given a number of objects, child predicts before building whether that number will form a perfect rectangle (array with no leftovers), then tests the prediction with counters.
Child explains, using a specific count of objects the child has never arranged before, whether it can form a rectangle and why, without being told the count in advance.
Child recalls, when shown a completed array picture with rows and columns already drawn, the correct repeated-addition sentence matching it.
Child decides whether a real-world object set the class has never discussed (e.g. a photo of a tiled floor with an irregular border, or a bag of buttons the teacher pours out unannounced) can be arranged into a rectangle with no leftovers, using only the pairing/building method, with no array, muffin-tin, or egg-carton example having been used for that specific object type during instruction.
Your child learns to measure length with a ruler in inches and centimeters, and to read a clock to the nearest five minutes with a.m./p.m. The core idea underneath both: fair comparison needs a fixed-size unit — a ruler's inch never changes, unlike a hand span or a stride.
Measure the length of a real object to the nearest whole inch using a ruler placed with one end at the 0 mark.
Measure the same object once in inches and once in centimeters and state which unit gives the bigger number.
Estimate the length of an object in inches before measuring it, then measure to check the estimate.
Find the difference in length between two objects by lining up their ends and counting the leftover units.
Represent an addition or subtraction of lengths on a ruler-based number line, starting the count at 0.
Solve a one-step word problem involving lengths in the same unit, choosing addition or subtraction based on the story.
Read and state the time shown on an analog clock to the nearest five minutes, including a.m. or p.m. given a context clue.
Read and state whole-hour times shown on an analog clock, naming the hour pointed to by the short hand when the long hand points to 12.
Determine an unknown end time given a start time and an elapsed number of hours, in a context the child has not measured before (e.g., a trip length stated in a new story).
Compare two written or shown times and identify which comes first in the school day, using a.m./p.m. labels.
Decide whether counting more small blocks or fewer big blocks gives a longer measured line, when shown a brand-new pair of same-length lines measured in two unnamed, never-before-seen unit shapes (not inches or centimeters).
Your child learns that coins are unequal-sized groups — a dime is one small object worth ten, a penny is one small object worth one. That's a genuinely new idea after four units where 'how many objects' and 'how much value' were the same number. It leans hard on skip-counting (Unit 3) and the bundling idea that ten small units make one bigger unit (Unit 1).
Name the value of a penny, nickel, dime, and quarter when shown the coin.
Skip-count a group of same-value coins (all nickels, or all dimes) to find the total value.
Order coins from smallest to largest value before counting a mixed group.
Find the total value of a mixed group of pennies, nickels, dimes, and quarters by combining skip-counting and counting on.
Explain why a dime is worth more than a nickel even though the dime is physically smaller.
Compare two different coin groups to determine which has greater total value, or that they are equal.
Write a total money amount using dollar and cent notation ($ and ¢) for amounts under one dollar and for whole dollar amounts.
Solve a one-step word problem involving buying an item with exact coin or bill amounts.
Determine the coins needed to make change from a purchase using simple amounts (e.g., pay a quarter for a 15-cent item).
Decide whether a mixed coin group is enough to buy two items together, when no one has stated their combined price.
Compare the value of a dollar bill to an equivalent group of coins (100 pennies, or mixed coins totaling $1).
Your child learns that a shape's name comes from countable features — number of sides, corners, whether sides are equal — not from how it looks at a glance. This moves them past Grade 1's 'name-by-sight' approach into naming by side count, spotting vertices, and comparing side lengths.
Child names a shape as a triangle, quadrilateral, pentagon, or hexagon by counting its sides.
Child touches each side of a shape one at a time to count the total number of sides.
Child points to the vertex (corner) of a shape where two sides meet.
Child compares two sides of the same shape to decide if they are equal or unequal in length.
Child sorts a mixed pile of shapes into groups by shared side count, ignoring color, size, and orientation.
Child explains why two very different-looking shapes share the same name.
Child builds or draws a shape that matches a spoken set of attribute clues (e.g., '4 sides, all equal').
Given a brand-new shape never shown in class with an unusual number of sides, child predicts what it should be called by extending the side-count naming pattern.
Shown a real object never discussed in this unit (a stop sign, a picture frame, a slice of pizza box), child taps whether it has equal sides by visually comparing, with no adult touch-counting model and no string provided.
Your child learns to split circles and rectangles into halves, thirds, and fourths. The one idea repeated every day: equal shares means equal SIZE, not equal COUNT of pieces. A shape cut into three unequal pieces is not thirds, no matter how confidently it looks like three pieces.
Recall the words 'half,' 'third,' and 'fourth' when shown a shape split into 2, 3, or 4 equal parts.
Recognize a picture of a circle or rectangle correctly split into two equal shares as showing halves.
Execute the teacher-modeled fold-in-half routine on a new paper rectangle: fold so the two edges line up exactly, open it, and point to the fold line as the cut between two equal shares.
Classify a shape split into a given number of pieces as an equal partition or an unequal partition by comparing piece sizes.
Explain why two pieces of a partitioned shape are or are not equal shares by pointing to a size comparison (overlay or matching edges), not just the piece count.
Compare two correctly-cut halves of the same-sized whole that have different outline shapes (e.g. straight cut vs. diagonal cut) and confirm both are equal shares.
Partition a paper circle or rectangle into two, three, or four equal shares by folding or cutting, when asked for a specific share name.
Infer, when shown two same-size wholes each split into a different number of equal shares (e.g. one into halves, one into fourths), which single piece is bigger.
Judge whether a half of one whole and a half of a different-sized whole can both correctly be called 'a half,' given only that each piece matches its own whole's other half.
Given a real classroom object never used in instruction (e.g. a shared bag of pretzels, a lunch tray, a garden plot photo), judge whether a proposed split into pieces gives each of 3 people equal shares, with no fold, cut-line, or picture-overlay cue provided.
No new skills get taught here. This is where every routine from the year — place value, adding/subtracting, arrays, measuring, money, shapes, fractions — gets mixed together unlabeled, because real problems never come with a unit number attached. It starts by checking each skill still works alone, then mixes two topics, then three, then all seven.
Given an unlabeled word problem naming objects being joined or separated, the child selects addition or subtraction within 100 and solves it.
Given a two-digit number, the child represents it as tens and ones using base-ten blocks or a drawing.
Given a picture of an array, the child states the repeated addition sentence it shows.
Given a mixed set of unlabeled word problems (money, measurement, arrays, place value), the child sorts each by the action described (joining, separating, comparing, sharing) before solving.
Given a real object and a ruler, the child measures its length in inches and checks the number against an estimate made by eye.
Given two differently-sized pieces from a partitioned shape, the child determines whether they show equal shares.
Given a shape divided into parts of visibly different sizes, the child explains why it is not divided into equal fourths even though it has four parts.
Given a multi-step performance task combining a coin total, a measured length, and a fraction of a shared object, the child solves each part in sequence and states the final answer.
Given a brand-new context never used in any prior unit (splitting a stack of stickers three ways, some by count and some by leftover fraction), the child decides which of this year's ideas applies and solves it.
Given a story about a farm animal that gets fed scoops of feed at feeding time and then some scoops spill and are lost, told with no numbers pictured in the familiar coin/ruler/array/shape formats this unit used, the child decides on their own whether this needs joining, separating, comparing, or sharing math, and solves it.
From the parent guide
A full second-grade math year built for one adult and one child at a kitchen table. Your child moves from understanding what the digits in a number like 347 mean, to adding and subtracting two-digit numbers with regrouping, to meeting multiplication before it has a name in the form of equal rows and columns. Then it goes outward: measuring with a ruler, telling time to five minutes, counting coins, naming shapes by their sides and corners, splitting a pizza fairly into thirds. Every idea arrives first as something they can hold, blocks or coins or paper shapes or a ruler, before it becomes a written number sentence. By June your child can read an unlabelled word problem and work out for themselves which kind of math it is asking for.
Unit 1 · what to expect
This unit teaches that any number is just groups of ten, bundled up. Your child moves from tens-and-ones with two-digit numbers into bundling ten tens into a hundred, then reading, writing, and comparing three-digit numbers. Whatever blocks or drawings you use here become the mental picture for every number they write for the rest of the year.
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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