Why is math taught differently now? What changed, and when the "old way" comes back
By 15Q20M Editorial · Last updated
Math homework looks different because the Common Core standards, published in 2010, expect both understanding and procedural skill, calling them "equally important," and several grade 4 and 5 standards ask students to show place value strategies. The standard algorithm is still there: it becomes a grade-level expectation, from 4th grade addition to 6th grade division.
Why is math taught differently now?
Many of the methods that surprise parents are written into the Common Core math standards themselves. In grade 4, for example, the multiplication standard asks students to use "strategies based on place value and the properties of operations" and to "illustrate and explain the calculation by using equations, rectangular arrays, and/or area models." That is where the boxes on your child's worksheet come from. The standards expect students to be able to explain a calculation as well as carry it out, and they call understanding and procedural skill "equally important."
The standards' introduction gives two reasons. One is depth: research on high-performing countries pointed to the conclusion that U.S. math "must become substantially more focused and coherent," instead of "a mile wide and an inch deep." The other is understanding: the introduction contrasts a student who can recite a memorized trick with one who can "explain where the mnemonic comes from." The same document also says the standards "do not dictate curriculum or teaching methods." That is why two schools in the same grade can hand out very different-looking homework. The goals are shared. The textbook, the order of lessons, and what a teacher asks your child to show are decided locally.
Do schools still teach the standard algorithm?
Yes. The phrase "standard algorithm," meaning the conventional written method for multi-digit arithmetic that most parents learned, appears by name in the Common Core math standards. Each one is tied to a grade where fluency with it becomes the expectation. Teachers may introduce it earlier. The table shows where the expectation lands in grades 4 to 6.
| Operation | Standard algorithm expected by | What the standards ask for in earlier grades | Standard |
|---|---|---|---|
| Add and subtract multi-digit whole numbers | Grade 4 | Place value strategies in grades 1 to 3 (grade 3 adds "algorithms based on place value" within 1000) | 4.NBT.B.4 |
| Multiply multi-digit whole numbers | Grade 5 | Grade 4: strategies based on place value, shown with equations, arrays, or area models (4.NBT.B.5) | 5.NBT.B.5 |
| Divide multi-digit whole numbers | Grade 6 | Grades 4 and 5: strategies based on place value and the link between multiplication and division (4.NBT.B.6, 5.NBT.B.6) | 6.NS.B.2 |
| Add, subtract, multiply, and divide decimals | Grade 6 | Grade 5: models, drawings, and place value strategies, related to a written method (5.NBT.B.7) | 6.NS.B.3 |
Read the table from your child's grade. A 4th grader multiplying with boxes is working on the grade 4 expectation, because fluency with the multiplication algorithm is a grade 5 expectation. A 5th grader dividing with a list of partial answers down the side is in the same position, because the division algorithm is named in grade 6. The grade 5 decimal standard even describes the bridge between the two: students use strategies and then "relate the strategy to a written method and explain the reasoning used."
New math vs old math: the same problem both ways
The strategies and the standard algorithms rest on the same place value facts, so the numbers in one can usually be matched to the numbers in the other. Here are three problems worked both ways. The answers are the same every time.
| Problem | The way your child may show it | The way you may have learned it |
|---|---|---|
| 23 × 14 (grade 4 area model) | Split into 20 + 3 and 10 + 4. Four boxes: 20 × 10 = 200, 20 × 4 = 80, 3 × 10 = 30, 3 × 4 = 12. Add: 322 | 23 × 4 = 92, then 23 × 10 = 230 on the next row. Add: 322 |
| 156 ÷ 6 (grade 4–5 partial quotients) | Take away 6 × 20 = 120, leaving 36. Take away 6 × 6 = 36, leaving 0. Add the parts: 20 + 6 = 26 | Long division: 6 into 15 is 2 (that's 12, with 3 left). Bring down the 6 to make 36. 6 into 36 is 6. Answer: 26 |
| 2.4 × 3 (grade 5 decimal strategy) | 2 × 3 = 6 and 0.4 × 3 = 1.2. Add: 7.2 | 24 × 3 = 72, then count one decimal place: 7.2 |
The multiplication row is the easiest one to match. In this example the four boxes group into your two rows: 80 + 12 = 92 is your first row, and 200 + 30 = 230 is your second. Partial quotients is a different method from long division, but both take away groups of 6 until nothing is left, and the 20 and the 6 add up to the answer. Once you can see a match like that, you can check a lot of grade 4 and 5 homework even when the method is new to you.
A step-by-step walkthrough of the area model, and where its four boxes sit inside the column method
How can I help with math homework I don't understand?
- Solve it your way first, on scrap paper. Now you know the answer the worksheet is heading toward, and you can stay calm while your child works.
- Find the class example. Look in the notebook, the textbook page, or the class website for the problem the teacher worked in class, and match tonight's problem to it step by step.
- Once things are calm, ask your child to walk you through one problem. Several grade 4 and 5 standards ask students to illustrate or explain particular calculations, so talking it through is practice for the assignment.
- Set a stopping point. If it is still not working after a reasonable stretch, stop, and write a short note on the page saying what your child could do and where you both got stuck. That tells the teacher more than a page of forced answers.
Should I teach my child the old way?
Check the table first. If your child is in or past the grade where the standard algorithm is expected, it is part of what they are supposed to learn, and showing how it connects to the strategy they already know can help. If your child is a grade or two earlier, look at what the assignment asks for. If it asks for a model or an explanation, an answer on its own may be marked incomplete, which is frustrating when the math is right. It is fair to ask the teacher what a particular assignment needs to show. Either way, your method stays useful at home as a way to check answers.
What changes in Common Core math from 4th to 6th grade, with the critical areas for each year
Frequently asked questions
What's the difference between new math and old math?
Mostly the order and the amount written down. Common Core asks for place value strategies, such as area models and partial quotients, in the grades before fluency with the standard algorithm is expected. The answers are the same, and the standard algorithm is still a grade-level expectation: addition and subtraction in grade 4, multiplication in grade 5, and division in grade 6.
When did schools start teaching math differently?
The Common Core State Standards were presented as final on June 2, 2010, on behalf of 48 states, two territories, and the District of Columbia. Whether and when this change reached your child's school depends on your state's standards and your district, and the standards leave curriculum and teaching methods to them.
Why won't my child's teacher let them use the regular way?
In grades 4 and 5, several standards ask students to illustrate and explain calculations with place value strategies, equations, arrays, or area models, and an assignment may be checking that explanation. Fluency with the standard algorithm is expected for multiplication in grade 5 and for division in grade 6. For a specific assignment, ask the teacher what it needs to show.
Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
15Q20M is an independent product and is not affiliated with, sponsored, or endorsed by NGA Center or CCSSO.
Sources
- Common Core State Standards for Mathematics (official PDF), Introduction, pp. 3–5 — p. 5: "These Standards do not dictate curriculum or teaching methods." p. 3: research on high-performing countries points to the conclusion that the U.S. mathematics curriculum "must become substantially more focused and coherent"; "a curriculum that is 'a mile wide and an inch deep.'" p. 4: "There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from." "Mathematical understanding and procedural skill are equally important." (verified 2026-09-25)
- Common Core State Standards for Mathematics (official PDF), Grade 4 NBT, Grade 5 NBT, Grade 6 NS, pp. 29–30, 35, 42 — 4.NBT.B.4 "Fluently add and subtract multi-digit whole numbers using the standard algorithm." 4.NBT.B.5 and 4.NBT.B.6: strategies based on place value; "Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models." 5.NBT.B.5 "Fluently multiply multi-digit whole numbers using the standard algorithm." 5.NBT.B.6: division with two-digit divisors using strategies. 5.NBT.B.7: decimals using models, drawings, and strategies; "relate the strategy to a written method and explain the reasoning used." 6.NS.B.2 "Fluently divide multi-digit numbers using the standard algorithm." 6.NS.B.3 "Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation." (verified 2026-09-25)
- Common Core State Standards Initiative, Introduction to the Common Core State Standards (June 2, 2010) — CCSSO and the NGA Center "are pleased to present the final Kindergarten-12 Common Core State Standards documents" produced "on behalf of 48 states, two territories, and the District of Columbia." (verified 2026-09-25)
Research citations link to the original papers. Statistics are checked against their primary source.
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