The standards behind it
California's State Board of Education adopted its current math standards on August 2, 2010, and the published version was modified in January 2013 (CDE: Mathematics; content standards). They're California's version of the Common Core State Standards for Mathematics.
Two parts of the standards explain most of what's new about homework:
- Methods are introduced in a sequence. Children add, subtract, multiply and divide with strategies based on place value for several years before the standard algorithm is expected.
- Explaining is part of the math. The eight Standards for Mathematical Practice include "Construct viable arguments and critique the reasoning of others" and "Look for and make use of structure" (practices). That's where "explain your thinking" comes from.
When each method appears
| Grade | What the standards ask | Standard |
|---|---|---|
| 1st | Add and subtract within 20 with strategies such as counting on and "making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14)" | 1.OA.C.6 |
| 2nd | Add and subtract within 1000 "using concrete models or drawings and strategies based on place value," and "relate the strategy to a written method"; "Explain why addition and subtraction strategies work" | 2.NBT.B.7, 2.NBT.B.9 |
| 3rd | Add and subtract within 1000 "using strategies and algorithms based on place value"; a footnote adds that "A range of algorithms may be used" | 3.NBT.A.2 |
| 4th | "Fluently add and subtract multi-digit whole numbers using the standard algorithm." Multiply and divide with place-value strategies, and "Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models" | 4.NBT.B.4–B.6 |
| 5th | "Fluently multiply multi-digit whole numbers using the standard algorithm." Divide by two-digit numbers with strategies, arrays and area models | 5.NBT.B.5–B.6 |
| 6th | "Fluently divide multi-digit numbers using the standard algorithm," and use the standard algorithm for all four operations with decimals | 6.NS.B.2–B.3 |
So a 3rd grader drawing base-ten blocks and a 6th grader doing long division are both doing what their grade's standards ask.
What the pictures on the page mean
| You see | What it is | Example |
|---|---|---|
| Making ten | Breaking a number apart to reach 10 first | 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14 |
| Number line jumps | Adding or subtracting in friendly chunks | 63 − 28: jump back 20 to 43, then 3 to 40, then 5 to 35 |
| Expanded form | Adding by place value | 345 + 278 = (300 + 200) + (40 + 70) + (5 + 8) = 500 + 110 + 13 = 623 |
| Array or area model | A rectangle split by place value | 23 × 14 = (20 × 10) + (20 × 4) + (3 × 10) + (3 × 4) = 200 + 80 + 30 + 12 = 322 |
| Partial quotients | Division by subtracting easy multiples | 156 ÷ 6: take away 6 × 20 = 120, then 6 × 6 = 36, so 20 + 6 = 26 |
Each of these is the same arithmetic the standard algorithm does, written out so the place value shows. For 23 × 14, the standard algorithm adds the same partial products combined into two rows: 23 × 4 = 92 (80 + 12) and 23 × 10 = 230 (200 + 30).
How to help without the old way
- Ask your child to teach you the method. Explaining it out loud is part of the assignment, and you'll see where it breaks down.
- Ask what a digit stands for. "What does the 2 in 23 mean?" is the question behind most of these methods.
- Use the model on the page. Draw the number line or rectangle with your child rather than switching methods mid-assignment.
- Connect your method once the idea is solid. If you show the standard algorithm, point to the partial products or the regrouping it hides.
- Check the teacher's examples. Many assignments ask for a specific strategy, and the class notes or textbook page show which one.
If math homework turns into a nightly struggle, the signs a child needs a tutor guide covers what to look for and who to ask first. Fractions, the next big step in grades 3–5, are in the fractions guide, and the addition and multiplication facts these methods rest on are in how to get faster at math facts.
Questions parents ask
Why can't my child just use the standard algorithm?
California's standards expect the standard algorithm in 4th grade for adding and subtracting multi-digit numbers, in 5th grade for multiplying and in 6th grade for dividing. Before that, children learn place-value strategies they can explain, and the algorithm builds on them.
When do kids learn long division in California?
In 6th grade: "Fluently divide multi-digit numbers using the standard algorithm." In 4th and 5th grade, division uses place-value strategies, and children show their work with equations, rectangular arrays or area models.
What is an area model in math?
A rectangle split into parts by place value. For 23 × 14, the parts are 20 × 10, 20 × 4, 3 × 10 and 3 × 4, which add up to 200 + 80 + 30 + 12 = 322. The standard algorithm combines the same partial products into two rows, 92 and 230.
Should I teach my child the way I learned?
Showing a method you know can help once your child understands the place-value idea behind it. Ask the teacher whether it's fine to use on homework, since some assignments ask for a specific strategy.
Sources
- CDE: Mathematics, undated. Opened October 13, 2026.
- CDE: Content Standards, last reviewed May 7, 2026. Opened October 13, 2026.
- Grade 1 Operations and Algebraic Thinking, standards text. Opened October 13, 2026.
- Grade 2 Number and Operations in Base Ten, standards text. Opened October 13, 2026.
- Grade 3 Number and Operations in Base Ten, standards text. Opened October 13, 2026.
- Grade 4 Number and Operations in Base Ten, standards text. Opened October 13, 2026.
- Grade 5 Number and Operations in Base Ten, standards text. Opened October 13, 2026.
- Grade 6 The Number System, standards text. Opened October 13, 2026.
- Standards for Mathematical Practice, standards text. Opened October 13, 2026.