Why is math taught differently now with Common Core?

Common Core math is a set of grade-level standards that asks children to understand place value before they lean on shortcuts. Strategies such as making ten, number bonds, the open number line and the area model show why a method works. The standard algorithm still arrives: grade 4 for adding and subtracting, grade 5 for multiplying and grade 6 for long division.

Is Common Core math a curriculum?

Common Core math is a set of standards, which means a list of what a child should understand and be able to do by the end of each grade. The standards document says it does not dictate curriculum or teaching methods. Your district picks the textbook, and the textbook picks the strategies and the look of the worksheets.

Can I teach my child to carry the one?

Carrying the one is part of the standard algorithm, which Common Core requires by the end of grade 4, so you are not teaching anything forbidden. Timing is the thing to watch. If this week's homework asks for a number line or a drawing, let your child do it that way first, then show how carrying records the same regrouping.

What is a number bond?

A number bond is a small diagram that shows one number split into two parts, such as 10 at the top and 7 and 3 below it. Number bonds teach children that numbers can be taken apart and put back together, which is the move behind making ten and, later, behind regrouping in the standard algorithm.

Why does my child have to show their thinking?

Showing their thinking lets the teacher see whether a child understands the method or only remembers the steps. The standards name the ability to explain why a rule works as a hallmark of understanding. A wrong answer with clear thinking is also much easier to fix than a wrong answer with no working.

Do all states still use Common Core?

Most US states adopted the Common Core standards around 2010, and many have since reviewed, revised or renamed their own versions. The strategies in your child's homework usually come from the textbook your district chose, so the class worksheet and your state's standards document are the best guides to what is expected.

Common Core Math Explained for Parents

What is Common Core math?

Common Core math is a set of standards: a grade-by-grade list of what children should understand and be able to do. It is not a textbook, and it is not one teaching method. The standards document says so plainly: "These Standards do not dictate curriculum or teaching methods."

That one sentence explains a lot of kitchen-table confusion. The standards say what a child should reach by the end of grade 2 or grade 4. The textbook your district picked decides how, and that is where number bonds, ten frames and open number lines come from.

Common Core also arrived in a lot of places at once. All but five states adopted it at first, and many have since reviewed, revised or renamed their own versions. Whatever your state calls its standards today, the strategies on the homework page tend to look the same.

Why is math taught differently than when I was in school?

Math is taught differently because the standards put understanding of place value first and the fast written method second. Children still learn to carry and borrow. They meet those steps after they have seen why the steps work.

The standards describe understanding as the ability to explain "why a particular mathematical statement is true or where a mathematical rule comes from", and they add that understanding and procedural skill are "equally important." Think of carrying the one. The "one" is a ten. A child who knows that can check their own answer. A child who only remembers "write the small 1 up top" has nothing to check with when the numbers get bigger.

The National Council of Teachers of Mathematics makes a similar case in its position statement on procedural fluency: fluency means using procedures "efficiently, flexibly, and accurately," and every student should learn more than one method so they can pick the one that fits the problem. For 98 + 35, the flexible move is 100 + 35 − 2 = 133. No stacking required.

Play free in your browserPlace ValueGrade 1–2

What do the new math strategies mean?

The new math strategies are all ways of splitting numbers into friendly pieces, usually tens and ones, so the arithmetic happens in steps a child can see. Each one maps onto a method you already know.

Strategy	What it looks like	Grade	The old method it leads to
Number bonds	10 split into 7 and 3; 5 split into 2 and 3	K–1	Knowing pairs that make 10
Making ten	8 + 5 = 8 + 2 + 3 = 10 + 3 = 13	1	Carrying a ten
Open number line	53 − 27: jump from 27 to 30, to 50, to 53	2	Borrowing a ten
Area model	23 × 14 = 200 + 80 + 30 + 12 = 322	4	Long multiplication
Partial quotients	372 ÷ 6 = 50 + 12 = 62	4–5	Long division

Number bonds. A number bond is a circle with a number in it and two circles below for its parts. Kindergarten standards ask children to decompose numbers up to 10 into pairs in more than one way, for example 5 = 2 + 3 and 5 = 4 + 1. The pairs that make 10 matter most, because every later strategy leans on them. A few rounds of number bonds practice make those pairs automatic.

Making ten. Making ten turns a hard fact into an easy one. For 8 + 5, the 8 needs 2 more to reach 10, so the 5 splits into 2 and 3: 8 + 2 = 10, and 10 + 3 = 13. The grade 1 standard names this strategy with nearly the same example: 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14. When your child later carries a ten in 48 + 35, it is the same move on paper.

Open number line. An open number line is a blank line with jumps drawn on it, and no ruler marks. For 53 − 27, start at 27 and count up in friendly jumps: +3 lands on 30, +20 lands on 50, +3 lands on 53. The jumps add to 3 + 20 + 3 = 26, so 53 − 27 = 26. Grade 2 asks children to represent sums and differences within 100 on a number line diagram. The What Works Clearinghouse practice guide for struggling students, Assisting Students Struggling with Mathematics, recommends the number line as a tool for learning concepts and procedures. Once regrouping clicks, addition with regrouping is good follow-up practice.

Area model. An area model draws multiplication as a rectangle cut into parts. For 23 × 14, split 23 into 20 and 3 and 14 into 10 and 4. The four boxes hold 20 × 10 = 200, 20 × 4 = 80, 3 × 10 = 30 and 3 × 4 = 12, and 200 + 80 + 30 + 12 = 322. Written in a column, the same four numbers are called partial products. The old method finds exactly those pieces in two rows: 23 × 4 = 92 and 23 × 10 = 230, and 92 + 230 = 322. Grade 4 asks children to explain multiplication using equations, rectangular arrays and area models.

Partial quotients. Partial quotients let a child divide in chunks they are sure of. For 372 ÷ 6, take away 50 sixes (300) and 72 is left; take away 12 sixes (72) and nothing is left. The answer is 50 + 12 = 62, and 6 × 62 = 372 checks it.

Play free in your browserNumber BondsGrade 1–2

Does Common Core ban the standard algorithm?

Common Core does not ban the standard algorithm; it requires it, by name, at three points in the standards. The Common Core standards for mathematics say:

Grade 4 (4.NBT.B.4): "Fluently add and subtract multi-digit whole numbers using the standard algorithm."
Grade 5 (5.NBT.B.5): "Fluently multiply multi-digit whole numbers using the standard algorithm."
Grade 6 (6.NS.B.2): "Fluently divide multi-digit numbers using the standard algorithm."

So carrying and borrowing are coming. What changes is the timing. In grades 1 to 3, the standards ask for strategies "based on place value" and for children to "relate the strategy to a written method." The drawings are the bridge, and they tend to fade once the written method makes sense. A child in grade 2 drawing jumps is on schedule. A child in grade 5 who has never seen column addition is a question for the teacher.

How can I help with homework I don't understand?

The most useful help is to let your child teach the strategy to you. Explaining a method out loud is the skill the homework is practicing.

Ask before you show. "What did your teacher do with this one?" Most children can explain a strategy they half-understand, and talking it through often finishes the job.
Find the worked example. Worksheets and textbook pages usually open with a model problem. Copy its layout for the next question, step for step.
Translate into tens and ones. Whatever the diagram, ask "how many tens, how many ones?" That question fits number bonds, number lines and area models alike.
Hold the shortcut for later. If the assignment asks for a number line, a shortcut that skips it earns a wrong mark and a confused child. Show your method afterwards as a way to check the answer.
Write a note. When neither of you can crack the page, a short note to the teacher ("we got stuck on the open number line") is useful information for the next lesson.

A second grader practicing regrouping on paper can use an addition worksheet for 2nd graders, which comes with an answer key. For the bigger picture of what each year covers, see what math each grade should know.

Where do math facts fit in?

Math facts still have to be memorized, and the standards set clear deadlines for them. Every strategy above runs faster when the small facts come without counting.

Grade 2 (2.OA.B.2): "By end of Grade 2, know from memory all sums of two one-digit numbers."
Grade 3 (3.OA.C.7): "By the end of Grade 3, know from memory all products of two one-digit numbers."

Both lines are in the Common Core standards for mathematics. The strategies help children get there. NCTM's procedural fluency statement recommends teaching basic facts through number relationships such as making 10, and the What Works Clearinghouse guide Assisting Students Struggling with Mathematics recommends regular short timed activities as one way to build fluency once the idea is understood.

At home, a few minutes a day works better than a long weekend session. The pairs that make 10 come first, then doubles, then the rest of the addition facts. When multiplication arrives in grade 3, how to learn the times tables fast sets out an order that shrinks the grid to ten hard facts. MathIt is a free app for iOS and Android with about 90 game types and adaptive difficulty, and a math game for parents and kids turns fact practice into a short two-player round at the table.