Grade 1 · Christian · NGSS/CCSS-aligned
A full year of first-grade math in short daily sessions, run by you rather than by a textbook. You get a script to read and your child answers by tapping, so no teaching background is needed. Your child starts by counting objects and comparing groups, learns what the equals sign actually means, gets quick at adding and subtracting within 10 and then within 20 using a make-a-ten trick, comes to see two-digit numbers as bundles of tens and ones, compares and adds them, measures things, reads clocks, and finishes by sorting data and cutting shapes into equal pieces. Every new idea begins with objects your child can touch, counters and straws and bundles, before a single number or symbol shows up on paper.
The whole year, in plain English. Tap any unit to see every skill inside, nothing is hidden.
This is the on-ramp for the whole year. Your child stretches counting from small sets up to 120, learns to count on from any number instead of always starting at 1, and meets the number line as a picture of counting they already know how to do. It also builds the words 'more, fewer, same' and the idea of a group of ten as a bundle — both come back constantly for the rest of the year.
Child counts a set of up to 20 pictured objects by touching or tapping each one exactly once and states the total.
Child extends one-to-one counting to sets of up to 120 objects arranged in bundled groups of ten plus extra ones.
Child explains that counting the same set in a different order or arrangement gives the same total.
Child counts on from a stated number between 1 and 20 to find a total, without restarting the count at 1.
Child compares two pictured groups of objects and taps which has more, fewer, or the same amount, after counting both.
Child locates a stated number on a number line by hopping forward one mark at a time from zero or another known point.
Child uses a number line to count on from a two-digit starting number in a context never used during instruction, such as counting on from a page number or a scoreboard number.
Child recalls the count sequence in order from 1 to 20 without skipping or repeating a number.
This unit teaches the equals sign as 'the two sides show the same amount' — not 'now write the answer.' Every equation starts as objects: two matching groups, a join story, a split story. Number sentences come after, as the record of what already happened with real things.
Child taps 'same' for a pictured equation like 4 objects = 4 objects and 'not same' for 4 objects = 5 objects.
Child sorts a mixed set of true and false number sentences (3=3, 4+1=5, 5=2+3, 4+1=6) into 'same' and 'not same' piles by counting both sides.
Child explains, using objects, why 5 = 2 + 3 is true even though the sum is on the left.
Child finds the missing number of objects needed so that 3 + __ = 5 using counters.
Child identifies the missing-number card that makes a pictured equation true when the blank appears in different positions (start, middle, end).
Given two new pictured groups never seen in the unit (10 buttons vs. two groups of 5 buttons), child judges whether a proposed equation is true or false.
Child recalls that the equals sign is read aloud as 'is the same as,' not 'makes' or 'equals the answer.'
Child compares a bare-match equation (6=6) with a false addition equation (6=7) and states which is true using object counts as evidence.
This is where addition and subtraction within 10 go from 'act it out with objects' to 'know it fast.' The big idea is the fact family: three numbers like 3, 4, and 7 make one part-part-whole story, and knowing one fact unlocks three related ones.
Given an object picture showing two groups joining (e.g. 3 ducks and 4 ducks), the student taps the numeral card showing the total.
Given an object picture showing a group with some taken away, the student taps the numeral card showing how many are left.
Given a completed part-part-whole picture (e.g. 3 red counters and 4 blue counters make 7 counters), the student explains why the same three numbers can make an addition fact and a related subtraction fact.
Given one addition fact within 10, the student generates the matching subtraction fact using the same three numbers.
The student sorts a mixed set of within-10 addition and subtraction fact cards into 'joining' and 'separating' piles by the story action, not the numbers shown.
The student counts on from the larger number to solve an addition fact within 10, using fingers or a number line, without recounting from one.
Given a new within-10 object picture never seen in class, the student decides whether it shows a joining or a separating story and picks the matching number sentence.
The student recalls the sum or difference for within-10 facts quickly (within about 3 seconds) without counting all objects one by one.
Children learn to regroup numbers past 10 into one ten plus extra ones, using ten-frames as the visual model. This covers make-a-ten addition, take-apart-a-ten subtraction, and then applying both in problems with three numbers or two steps.
Recall the ten-partner (addend pair summing to 10) for any number 1-9, shown with objects.
Recognize a full ten-frame picture as the quantity ten without recounting each unit.
Explain why moving counters to fill a ten-frame does not change the total number of objects in a make-a-ten addition problem.
Execute the make-a-ten strategy to solve an addition fact within 20 using a ten-frame and loose counters.
Execute the take-apart-a-ten strategy to solve a subtraction fact within 20 by removing loose ones before the ten.
Identify which of two pictured ten-frame regroupings correctly represents a given make-a-ten addition or subtraction.
Compare two different orders of adding the same three numbers and determine both totals are the same.
Select which two of three given numbers to combine first in order to make a ten, when more than one valid pairing exists.
Solve a two-step word problem within 20 involving three whole numbers by sequencing an addition and a subtraction (or two additions).
Apply the correct within-10 or within-20 strategy to a novel mixed problem set presented in an unfamiliar picture format with no strategy label.
This unit gives a name to the bundle of ten your child has been making since Unit 1 and using in Unit 4's make-a-ten work: a ten. Every two-digit number becomes a story of some tens and some leftover ones, built entirely with bundles and base-ten pictures before any digit appears.
Given a picture of a bundled group of ten objects, the child names the group 'a ten'.
Given a pile of 11-19 loose objects and a rehearsed prompt ('make a ten, count what's left'), the child bundles ten and states the leftover count, using the exact routine modeled in guided practice.
Given a base-ten picture showing some bundles of ten and some loose ones (up to 9 bundles, 9 loose), the child taps the matching two-digit numeral.
The child recites the counting sequence from 1 to 20, in the exact rote order rehearsed daily since Unit 1, when asked to 'count as high as you can.'
The child counts aloud starting at any given number below 120, continuing at least ten counts forward.
Given the spoken number word for a decade number (e.g. 'seventy'), the child taps the base-ten picture showing that many full tens and zero loose ones.
Given the picture of exactly ten loose objects (no bundle drawn yet), the child taps the numeral 10 rather than a numeral suggesting 'one and zero' as separate leftover groups.
Given two two-digit numbers with the same digits in reversed order (e.g. 34 and 43), the child taps the base-ten picture matching each, showing the amounts differ.
Given a spoken two-digit number in an unfamiliar context (a shelf of toy count, a page count) with no bundle picture shown, the child taps the matching group of objects arranged in an unfamiliar layout (a ten-frame array instead of straw bundles).
Given a numeral between 100 and 120, the child taps the picture with ten full bundles plus the matching loose ones.
Children use tens-and-ones thinking from Unit 5 to compare two two-digit numbers (check tens first, then ones) and to add a one-digit number to a two-digit number (check whether the ones cross past ten).
Given two two-digit numbers shown as base-ten block pictures, child taps which number has more tens.
When two two-digit numbers have the same number of tens, child taps which has more ones to decide which number is greater.
Child explains, using tens and ones language, why a number with more tens is always greater regardless of its ones digit.
Given a picture story of a two-digit number of blocks with a one-digit number of blocks added, child taps the numeral that names the total when no new ten is formed.
Given a picture story where the ones pile reaches or passes ten, child taps the numeral total after bundling a new ten.
Before adding, child predicts whether a given two-digit-plus-one-digit picture story will cross a new ten, without completing the addition.
Child sorts a mixed set of two-digit comparison problems and two-digit-plus-one-digit addition problems by which strategy applies, without solving them.
Given a new context never used in instruction (comparing two piles of coins where one pile has fewer coins but a coin looks physically bigger), child taps which pile has more value using tens-and-ones reasoning transferred from blocks.
One shared idea runs through this whole unit: measuring means laying same-size units end to end with no gaps and counting them. That logic applies to length (cubes, paperclips) and then to clocks, where the same idea of 'fair, consistent units' shows up as hours and half-hours.
Child orders three pictured objects from shortest to longest by direct visual comparison.
Child identifies which of two objects is longer when they cannot be placed side by side, by comparing each to a third object.
Child counts how many same-size units (cubes) span a pictured object, laid end to end with no gaps.
Child explains why measuring the same object with a bigger unit gives a smaller number than measuring with a smaller unit.
Child compares the measured lengths of two different objects using the same unit and says which is longer using 'more/fewer' language.
Child taps the analog clock picture that shows a spoken time to the hour.
Child explains, using the picture of a clock, why the little hand moves much more slowly than the big hand.
Child taps the analog clock picture that shows a spoken time to the half hour.
Child decides whether a spoken time is closer to 'just started the hour' or 'halfway through the hour' by looking at where the big hand points on an unfamiliar clock picture.
The last unit of the year, split into two halves that share one idea: a rule applied consistently is what makes a sorted group or a split shape trustworthy. First half: sorting objects by one rule, building simple picture graphs, and comparing counts. Second half: combining small shapes into bigger ones, and splitting circles and rectangles into equal halves and quarters.
When shown a set of up to 10 mixed pictured objects and one stated sorting rule (e.g. by color), the child taps the correct bin for each object.
Given a picture graph of three categories (up to 10 total objects), the child taps the category with more, fewer, or the same number, using 'is the same as' language from Unit 2.
Given the same set of 9 pictured objects sorted first by color and then by shape, the child explains that the total count of objects stays the same even though the category picture looks different.
Given two small 2D shapes (e.g. two triangles), the child taps the picture showing the larger shape they combine to make (e.g. a square).
Given a pictured composite shape made of 3-4 small shapes not seen in instruction, the child taps which two named 3D solids (e.g. cube, cone) could stack to make a similarly shaped tower.
Given a picture of a circle or rectangle cut into two pieces, the child taps whether the pieces are halves (equal) or not equal shares.
Given a picture of a rectangle split into four pieces of different sizes, the child explains why it is not split into fourths even though there are four pieces.
Given a circle already split into two equal halves, the child taps the picture showing how one half could be split again to make four equal quarters.
The child recalls that a picture graph has bars or pictures that stand for objects being counted, when asked to identify a picture graph among other pictures.
From the parent guide
A full year of first-grade math in short daily sessions, run by you rather than by a textbook. You get a script to read and your child answers by tapping, so no teaching background is needed. Your child starts by counting objects and comparing groups, learns what the equals sign actually means, gets quick at adding and subtracting within 10 and then within 20 using a make-a-ten trick, comes to see two-digit numbers as bundles of tens and ones, compares and adds them, measures things, reads clocks, and finishes by sorting data and cutting shapes into equal pieces. Every new idea begins with objects your child can touch, counters and straws and bundles, before a single number or symbol shows up on paper.
Unit 1 · what to expect
This is the on-ramp for the whole year. Your child stretches counting from small sets up to 120, learns to count on from any number instead of always starting at 1, and meets the number line as a picture of counting they already know how to do. It also builds the words 'more, fewer, same' and the idea of a group of ten as a bundle — both come back constantly 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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