Skills your child needs first

Looking at two groups of things, counting or matching them one to one, and saying which has more, which has less, or that they are the same.

Counting a group of up to ten things by touching each one once, saying one number for each touch, and knowing the last number said is how many.

Starting a count at a number your child already has, like seven, and saying the next numbers, eight, nine, without going back to one.

Saying the counting words in order from one to twenty, out loud and without skipping, and knowing what comes next from any point along the way.

Counting the filled holes in the box of ten holes and seeing that the empty holes are the partner that makes ten, like seven and three or four and six.

Saying the new how-many when one more thing joins a group, without counting the whole group again, and knowing one more is the next counting number.

Putting one finger on one exact thing in a picture when a grown-up names it, and holding it there long enough to be seen.

Laying the marks 0 to 20 in a row with nothing skipped, knowing the neighbor just before and just after each mark, and naming a missing one.

Seeing each number from eleven to nineteen as one packed box of ten plus some extra ones, and reading the 1 in a teen mark as that packed ten.

Knowing that the box of ten holes always has two rows of five, that a full top row is five, and that empty holes still belong to the ten.

Showing eight on the box of ten holes as a full top row with three leftovers underneath, which leaves two empty holes, and matching it to the mark 8.

Showing five as one hand of fingers, a line of five things, or a full top row in the box of ten holes, and knowing it is still five when the things move. Matching it to the mark 5.

Making four as three and one more, counting it by touching, and knowing four is still four in a line, a pile or a square. Matching it to the mark 4.

Showing nine on the box of ten holes as a full top row and four more underneath, an almost full box with exactly one empty hole, and matching it to the mark 9.

Picking out a single thing, touching it as you say one, and matching it to the mark 1.

Showing seven on the box of ten holes as a full top row and a pair of extras underneath, five and two more, and matching it to the mark 7.

Showing six on the box of ten holes as a full top row of five and one leftover bean in the bottom row, and matching it to the mark 6.

Showing ten on the box of ten holes by filling every hole in both rows, so the box is packed, and matching it to the mark 10, a 1 beside a 0.

Making a group of three as two and one more, counting it by touching, and knowing the last number said is how many. Matching it to the mark 3.

Counting a pair by touching each one, saying one and then two, stopping, and knowing the group is two. Matching a pair to the mark 2.

Looking at two numbers, saying which one is bigger, and working out how much bigger by taking the smaller away from the larger.

Counting a group of real objects one by one, moving each as it is counted, so the last number said is how many there are.

Keeping count of things as they happen by making one mark for each, bundling every five marks together so the total is quick to add up.

Laying a ruler along something with the zero mark at one end, reading the mark at the other end to the nearest centimeter, and writing the unit after the number.

Finding where a point sits on a line of evenly spaced marks, including marks with no number beside them, by working out what one small step is worth.

Finding one fact in a grid of rows and columns by running a finger along one row and down one column until they meet.

Reading a timer or stopwatch that shows minutes and seconds with a colon between them, and turning that reading into plain seconds, so 2:40 becomes 160 seconds.

Reading the heading on each box of a form and putting the right piece of information in that box, and only in that box.

Reading a short set of written steps and carrying out each one, in order, without a grown-up saying them out loud first.

Changing a noun that names one thing into the word for more than one, like cat to cats, box to boxes, berry to berries and child to children.

Picking out the words in a sentence that name a person, a place, a thing or an idea, like sister, kitchen, spoon or kindness.

Spotting the small word that shows where something is, which way it moves, or when it happens, like under in "under the bed" or after in "after lunch."

Spotting the short words that stand in for a noun, like he, she, it, they, him, them, my and their, so a name does not have to repeat.

Finding the word in a sentence that tells what someone or something does, like runs or baked, or what it is, like is or was.

Finding the verb that tells what someone or something did, like carried, washed or waited, including quiet actions where nothing moves fast.

Spotting the word that describes a noun by telling what kind, which one, or how many, like red in "the red cup" or three in "three dogs."

Spotting the word that tells how, when, or where something happens, like slowly in "she walked slowly" or soon in "we leave soon."

Writing letters that are the right shape, sit on the line, and have space between words, so another person can read them without asking.

Reading a whole sentence out loud at a steady pace, in word groups rather than one word at a time, so the ear can hear what it says and whether it sounds right.

Reading five or six sentences about one thing, keeping track of what happened, and finding a particular detail in it afterward.

Finding the important words in the small print on the back of a package: what it is for, the warnings, and what to do if something goes wrong.

Reading a word, deciding which heading it belongs under, and writing it in that column, while keeping several headings in mind at once.

Hearing whether a group of words is a whole sentence, with someone or something that does or is something and a finished thought, or only a piece of one.

Finding the person, animal or thing a sentence is about, the doer, before looking for anything else in it.

Writing a complete thought that names who or what it is about, says what happened or what is true, starts with a capital letter and ends with a period.

Writing a sentence that asks instead of tells, starting with a question word or a flipped verb and ending with a question mark.

Adding ed to a verb to show that something already happened, and spelling it right: walked, hoped, stopped, carried.

Writing a guess in the shape If I do this, then that will happen, because of this reason, before finding out what really happens.

Holding two things side by side and naming, one feature at a time, what is the same about them and what is different.

Looking at a real object on the table and drawing what is actually there, its true shape, parts and marks, instead of a picture from memory.

Knowing the five senses, sight, hearing, touch, smell and taste, and being able to say which one brought in a piece of information about the world.

Arranging the steps of a job so each one comes when it should, and knowing why some steps have to come before others.

Putting each item in a set into one of a few named groups by checking it against a rule, and being able to say why each item went where it did.

Finding how much flat space a rectangle covers by multiplying its length by its width, and writing the answer in square units, like 6 x 4 = 24 square feet.

Deciding which of two numbers is greater, writing it with the less than and greater than symbols, and putting a list of whole numbers and decimals in order from least to greatest.

Splitting a number into equal parts on paper, carrying the division past the decimal point when something is left over, and dividing by a decimal like 2.5 by moving both decimal points first.

Knowing that 1/2, 2/4 and 3/6 name the same amount, and making a new equal fraction by multiplying or dividing the top and the bottom by the same number.

Putting a number in place of the letter in an expression like 3n + 2, then working it out in the right order to get one number.

Listing every number that divides a given number with nothing left over, which are its factors, and listing the numbers you land on when you skip count by it, which are its multiples.

Finding where a fraction like 3/4 or a decimal like 2.5 sits on a number line by cutting the space between whole numbers into equal parts and counting.

Reading a fraction like 3/4 as one whole cut into 4 equal parts with 3 of them taken, and knowing the bottom number counts the equal parts the whole was cut into.

Knowing which operation undoes which. Subtracting undoes adding, adding undoes subtracting, dividing undoes multiplying, and multiplying undoes dividing. It is the move behind every equation your child will solve.

Two ways to give one number for the middle of a list. The mean is the fair share: add every value and divide by how many there are. The median is the middle value once the list is in order.

Knowing every multiplication from 1 x 1 to 12 x 12 quickly and without counting, and knowing each one backwards as a division.

Finding a fraction of a whole number, like 3/4 of 20 or 30/100 of 70, and knowing the answer comes out smaller when the fraction is less than one.

Multiplying a fraction by a fraction by multiplying the tops and multiplying the bottoms, after turning any mixed number into a fraction, then simplifying the answer.

Multiplying numbers with two or more digits on paper, and multiplying three or more numbers together two at a time, with an estimate to check the answer is about the right size.

The agreed order for working out math with more than one operation: parentheses, then powers, then multiplication and division left to right, then addition and subtraction left to right.

Knowing what each digit in a decimal is worth, from the tens and ones on the left of the point to the tenths, hundredths and thousandths on the right.

Plotting points like (-2, 5) on a grid that runs both ways from zero. A negative first number goes left, a negative second number goes down, and the signs tell you which of the four quadrants the point is in.

Finding a point on a grid from an ordered pair like (3, 4): start at the corner, go across 3, then up 4, and mark the spot. The first number is always across and the second is always up.

Reading a picture where each dot stands for one answer, stacked above its value on a number line. Your child counts the dots, finds the tallest stack, and reads the smallest and largest values.

Reading a table of answers to one question, such as hours of sleep for each person in the family, well enough to count the answers, find any one of them, and pull out the smallest and the largest.

Reading the temperature where the red line stops by finding zero, working out what each small mark is worth, and counting in the right direction, including below zero.

Knowing that 3 x (4 + 5) is the same as 3 x 4 + 3 x 5, because the number outside the parentheses multiplies every piece inside, not only the first.

Turning a phrase like "5 more than a number" or "4 tickets at t dollars each" into math like n + 5 or 4t, with the pieces in the right order.