← All courses

Tens, Ones, and Adventures: Grade 1 Mathematics

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.

What your child will learn

The whole year, in plain English. Tap any unit to see every skill inside, nothing is hidden.

Counting, Comparing, and the Number Linepeek inside ▸

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.

  1. One-to-one correspondence in counting a set of objects up to 20

    Child counts a set of up to 20 pictured objects by touching or tapping each one exactly once and states the total.

  2. The count sequence to 120 applied to bundled sets of objects

    Child extends one-to-one counting to sets of up to 120 objects arranged in bundled groups of ten plus extra ones.

  3. Order-irrelevance and conservation of number when counting a fixed set

    Child explains that counting the same set in a different order or arrangement gives the same total.

  4. The counting-on strategy starting from a nonzero number

    Child counts on from a stated number between 1 and 20 to find a total, without restarting the count at 1.

  5. Comparison of two counted groups using more/fewer/same

    Child compares two pictured groups of objects and taps which has more, fewer, or the same amount, after counting both.

  6. The number line as a counting path with one-to-one hops mapped to numbers in order

    Child locates a stated number on a number line by hopping forward one mark at a time from zero or another known point.

  7. Transfer of the counting-on-a-number-line strategy to an unfamiliar real-world counting context

    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.

  8. The standard count sequence from 1 to 20

    Child recalls the count sequence in order from 1 to 20 without skipping or repeating a number.

What the Equals Sign Really Meanspeek inside ▸

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.

  1. The equals sign as a statement that two groups have the same count

    Child taps 'same' for a pictured equation like 4 objects = 4 objects and 'not same' for 4 objects = 5 objects.

  2. True and false number sentences with the equals sign in varied positions

    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.

  3. The equals sign with the sum on the left side of the sentence

    Child explains, using objects, why 5 = 2 + 3 is true even though the sum is on the left.

  4. A missing addend found by making both sides of an equation match

    Child finds the missing number of objects needed so that 3 + __ = 5 using counters.

  5. Missing-number position within an equation

    Child identifies the missing-number card that makes a pictured equation true when the blank appears in different positions (start, middle, end).

  6. Equivalence of a single group and a two-part grouping of the same total

    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.

  7. The spoken phrase attached to the equals sign

    Child recalls that the equals sign is read aloud as 'is the same as,' not 'makes' or 'equals the answer.'

  8. Contrast between bare-match and computed equations of the same magnitude

    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.

Adding and Subtracting Within 10, Fluentlypeek inside ▸

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.

  1. Joining (adding to) situations with totals within 10

    Given an object picture showing two groups joining (e.g. 3 ducks and 4 ducks), the student taps the numeral card showing the total.

  2. Separating (taking from) situations within 10

    Given an object picture showing a group with some taken away, the student taps the numeral card showing how many are left.

  3. The fact-family relationship between addition and subtraction within 10

    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.

  4. Unknown-addend structure linking addition and subtraction facts

    Given one addition fact within 10, the student generates the matching subtraction fact using the same three numbers.

  5. Joining versus separating situation types

    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.

  6. The counting-on strategy for addition within 10

    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.

  7. Distinguishing joining from separating in an unfamiliar object scenario

    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.

  8. Fluent recall of within-10 addition and subtraction facts

    The student recalls the sum or difference for within-10 facts quickly (within about 3 seconds) without counting all objects one by one.

Making a Ten: Addition and Subtraction Within 20peek inside ▸

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.

  1. Ten's partner facts (pairs of numbers that sum to 10)

    Recall the ten-partner (addend pair summing to 10) for any number 1-9, shown with objects.

  2. The full ten-frame as a single countable unit

    Recognize a full ten-frame picture as the quantity ten without recounting each unit.

  3. Conservation of quantity under regrouping in the make-a-ten strategy

    Explain why moving counters to fill a ten-frame does not change the total number of objects in a make-a-ten addition problem.

  4. The make-a-ten addition procedure (decompose an addend, fill the ten, add the remainder)

    Execute the make-a-ten strategy to solve an addition fact within 20 using a ten-frame and loose counters.

  5. The take-apart-a-ten subtraction procedure

    Execute the take-apart-a-ten strategy to solve a subtraction fact within 20 by removing loose ones before the ten.

  6. Correct versus incorrect ten-frame regrouping representations

    Identify which of two pictured ten-frame regroupings correctly represents a given make-a-ten addition or subtraction.

  7. Associative/commutative reordering of three addends

    Compare two different orders of adding the same three numbers and determine both totals are the same.

  8. Strategic pairing choice among three addends with ambiguous ten-partner options

    Select which two of three given numbers to combine first in order to make a ten, when more than one valid pairing exists.

  9. Two-step word problems with three whole numbers, within 20

    Solve a two-step word problem within 20 involving three whole numbers by sequencing an addition and a subtraction (or two additions).

  10. Strategy selection between within-10 recall and within-20 make-a-ten/take-apart procedures

    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.

Tens and Ones to 120peek inside ▸

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.

  1. A bundle of ten ones as a single unit called a ten

    Given a picture of a bundled group of ten objects, the child names the group 'a ten'.

  2. The bundle-then-count-leftovers routine for teen numbers

    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.

  3. Two-digit numbers as tens-and-ones groupings

    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.

  4. The memorized counting sequence from 1 to 20

    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.'

  5. The counting sequence to 120

    The child counts aloud starting at any given number below 120, continuing at least ten counts forward.

  6. Decade numbers as whole tens with no leftover ones

    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.

  7. Ten as the special case of ten ones with no leftovers

    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.

  8. Digit position as the record of tens versus ones

    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.

  9. Two-digit place value applied to a new representation of tens and ones

    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).

  10. Two-digit-style grouping extended to numbers past 100

    Given a numeral between 100 and 120, the child taps the picture with ten full bundles plus the matching loose ones.

Comparing and Adding Two-Digit Numberspeek inside ▸

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).

  1. The tens digit as the first thing checked when comparing two two-digit numbers

    Given two two-digit numbers shown as base-ten block pictures, child taps which number has more tens.

  2. Comparing the ones digit only after a tie in the tens digit

    When two two-digit numbers have the same number of tens, child taps which has more ones to decide which number is greater.

  3. The rule that tens always outweigh ones in determining which two-digit number is greater

    Child explains, using tens and ones language, why a number with more tens is always greater regardless of its ones digit.

  4. Adding a one-digit number to a two-digit number without regrouping, using base-ten pictures

    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.

  5. Adding a one-digit number to a two-digit number when the ones total crosses ten, forming a new ten

    Given a picture story where the ones pile reaches or passes ten, child taps the numeral total after bundling a new ten.

  6. Recognizing in advance whether an addition will cause the ones to cross ten

    Before adding, child predicts whether a given two-digit-plus-one-digit picture story will cross a new ten, without completing the addition.

  7. Telling apart comparison problems from addition problems by their picture structure

    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.

  8. Applying tens-first comparison reasoning to an untaught concrete context

    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.

Measuring Length and Telling Timepeek inside ▸

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.

  1. Ordering of three objects by length

    Child orders three pictured objects from shortest to longest by direct visual comparison.

  2. Indirect comparison of two lengths using a third object

    Child identifies which of two objects is longer when they cannot be placed side by side, by comparing each to a third object.

  3. Length measured as a count of repeated same-size units

    Child counts how many same-size units (cubes) span a pictured object, laid end to end with no gaps.

  4. Inverse relationship between unit size and unit count

    Child explains why measuring the same object with a bigger unit gives a smaller number than measuring with a smaller unit.

  5. Comparison of two measured lengths expressed as unit counts

    Child compares the measured lengths of two different objects using the same unit and says which is longer using 'more/fewer' language.

  6. Clock face reading for times on the hour

    Child taps the analog clock picture that shows a spoken time to the hour.

  7. Relative speed of the hour hand and minute hand on an analog clock

    Child explains, using the picture of a clock, why the little hand moves much more slowly than the big hand.

  8. Clock face reading for times at the half hour

    Child taps the analog clock picture that shows a spoken time to the half hour.

  9. Discrimination between hour and half-hour clock positions in a new context

    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.

Organizing Data and Composing Shapespeek inside ▸

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.

  1. Sorting objects into categories using one stated rule

    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.

  2. Comparison of category counts in a picture graph

    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.

  3. Invariance of total count under different sorting rules

    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.

  4. Composing a new 2D shape from two smaller shapes

    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).

  5. Composing a 3D composite shape from smaller solids

    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.

  6. Equal versus unequal partitioning into two shares

    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.

  7. The requirement that fourths/quarters be equal-size shares, not merely four pieces

    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.

  8. Relationship between halves and quarters as nested equal partitions

    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.

  9. The picture graph as a representation of counted categories

    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.

Ready when you are

Free for 30 days · then $29/mo or $290/yr for the whole family · Cancel anytime, no questions asked.

Start your family's account
Tens, Ones, and Adventures: Grade 1 Mathematics, Grade 1 Homeschool Curriculum