Teacher standing in front of class teaching finding factors.

In What Order Should Students Learn Math Facts?

Learn the Basics (add, subtract, multiply, divide) first.

 

Basic, optional, and alternative—there are a lot of different Rocket Math programs to help students learn math facts. A common question teachers ask is in what sequence should they teach the various Rocket Math programs? The basic programs of Addition, Subtraction, Multiplication, and Division (1s-9s) have priority and must be mastered by all students. Addition in the first grade. Addition and Subtraction in the second grade. Multiplication (as well as Addition and Subtraction) by the third grade. Then, all four, including Division by fourth grade. If a student is on track, those basics have first priority.

 

Optional programs if the basics are already on track

 

The rest of the programs are optional and should be offered to students once the basics have been mastered and only then. The only exception would be in a school where Kindergarteners did not get a chance to learn how to quickly and easily write numerals, through using the Rocket Writing for Numerals program. In that case, you might take the first two months of the first grade year to run students through Rocket Writing for Numerals before beginning Addition (1s-9s).

Here’s a link to a printable version of the graphic above.

 

First-grade Students Should Learn Addition Facts

 

Students practicing their math facts together.If first-grade students are taking all year to get through sets A-Z in Addition, they need some extra help. You should intervene to help students who take more than a week to pass a level. Often they need to practice better or with a better partner, and some may need to practice a second time during the day or at home in the evening. 

Another intervention would be to use Rocket Math Online Game for Addition facts, as students seem to progress much more quickly in the online game.  The Online Game has an adjustable game speed for first-grade students who are having trouble (their difficulty score is over 3) moving their fingers fast enough. First-grade students who finish the 1s-9s can move on to the Add to 20 programs for the remainder of the year.

 

Second-grade Students Must Know Both Addition & Subtraction Facts

 

The Rocket Math Online Game Additions fact family example page.

Second-grade students must have completed Addition before starting on Subtraction (1s-9s).  They can also test out of Addition through the Placement Probes which are available within the Addition drawer in the Rocket Math Worksheet program virtual filing cabinet. Addition has priority for second graders who can not test out of Addition in first grade or didn’t complete it in first grade. Only after getting through Set Z of Addition should they move into Subtraction. Second-grade students who complete Addition and Subtraction 1s-9s can move on to Subtract from 20. Students who finish Subtract from 20 can do Skip Counting, which does a great job of preparing students to learn Multiplication facts.

 

Fact Families is Another Way to Learn Addition & Subtraction Math Facts

 

 

A chart showing the Addition and Subtraction fact family of 2, 3, and 5.There is another way to learn facts, which is called Fact Families. Instead of learning all Addition facts, students can learn Addition and Subtraction facts at the same time. A fact family consists of four related facts, for example: 3+2 = 5, 2 + 3 = 5, 5 – 3 = 2, 5 – 2 = 3.  

 

It is challenging for students to switch between Addition and  Subtraction. But it does drive home the reciprocal nature of the two. There is no evidence that it is better to learn in fact families than it is to separate the operations. That’s why we offer both alternatives. Students can learn fact families up to 10 in first grade. Then the upper fact families, from 11 in second grade.

 

Third-grade Students Must Learn Multiplication Facts

 

In third grade, Multiplication has priority, even if students have not mastered Addition and Subtraction. Multiplication facts are so integral to the rest of higher math that students are even more crippled without Multiplication facts than they are having to count Addition and Subtraction problems on their fingers. So do Multiplication first, then if there’s time, students who need to can go back to master Addition and Subtraction.

 As in Addition and Subtraction, students can learn Multiplication and Division by fact families. In third grade, just the fact families through 20 need to be mastered. Once all three of these basic operations are under their belt students can go on to 10s, 11s, 12s in Multiplication. If that is done and there is still some school year left I’d recommend the Identifying Fractions program next followed by Factors.

 

Fourth-grade Students Should Know Both Multiplication and Division Facts

Effective math teaching strategies help students of all levels be successful at math.

Fourth-grade students need to have completed Multiplication before going on to Division.  They can also do Fact Families for Multiplication and Division, starting with facts to 20 and then part two is fact families from 21 on. If they complete Multiplication and Division, they should go back and do Addition and Subtraction. If those are not mastered, either straight up by operation or in families. Then students can go on to Identifying Fractions, then Factors, then Equivalent Fractions. They can go on to 10s, 11s, 12s Division, but it is less valuable than the pre-algebra skills of factors and fractions.

 

Fifth-grade Students & Up Need to Know All Basic Operations First, Then Branch Out

 

Fifth-grade students should have completed all four basic operations (1s-9s). If students have not completed these basics (and cannot test out of them with the Placement Probes), then the sequence they should follow is Multiplication, followed by Division, then go back and complete Addition followed by Subtraction. Again, as an alternative, students can learn the basic facts in families. The same recommendations hold for students in any grade after fifth.

Once students have mastered the basics (1s-9s add, subtract, multiply, divide) the supplemental pre-algebra programs are recommended. These will help more than learning the 10s, 11s, 12s facts. I would recommend this order: Identifying Fractions, then Factors, followed by Equivalent Fractions, followed by Learning to Add Integers, Learning to Subtract Integers, then Mixed Integers.

 

Rocket Math Worksheet & Online Game

 

Learn more about Rocket Math: in just 2 minutes!  Rocket Math has a fun video for you to learn more about how Rocket Math works. Or check out our website at www.rocketmath.com 

Here is a quick and easy chart to help understand which operation/skill students need to learn in which grade level and which Rocket Math Worksheet and Rocket Math Online Game Level they should be at.

Age Grade Operation/Skill Rocket Math Worksheet Rocket Math Online Game Level
5-6 Kindergarten Writing Numerals Beginning Numerals

Rocket Writing for Numerals

In development
6-7 First Writing Numerals

Addition

Rocket Writing for Numerals

Addition 1s through 9s

Fact Families 1 to 10 Add and Subtract

Add to 20

Addition

Fact Families (+, -) to 10

Add to 20

7-8 Second Addition

Subtraction

Addition 1s through 9s

Fact Families 1 to 10 Add and Subtract

Add to 20

Subtraction 1s through 9s

Fact Families 11 to 18 Add & Subtract

Skip Counting

Subtract from 20

Addition

Subtraction

Fact Families (+, -) to 10

Fact Families (+,-) from 11

Add to 20

Subtract from 20 

8-9 Third Multiplication Multiplication 1s to 9s

Multiplication 10s, 11s, 12s

Identify Fractions

Multiplication

Fact Families (x,division) to 20

Multiplication 10s-11s-12s

Identify Fractions

9-10 Fourth Multiplication

Division

Multiplication 1s to 9s

Division 1s through 9s

Multiplication 10s, 11s, 12s

Division 10s, 11s, 12s

Identify Fractions

Equivalent Fractions

Factors

Multiplication

Division

Fact Families (x,division) to 20

Fact Families (x, division) from 21

Multiplication 10s-11s-12s

Division 10s-11s-12s

Identify Fractions

Equivalent Fractions

Factors & Primes

10+ Fifth and up All Basic Operations

Fractions

Positive/Negative Numbers

Basic Addition, Subtraction, Multiplication, and Division

Equivalent Fractions

Factors

Learning to Add Integers

Learning to Subtract Integers

Mixed Integers

Basic Addition, Subtraction, Multiplication and Division 

Identify Fractions,

Equivalent Fractions,

Factors & Primes,

Fraction & Decimal Equivalents (coming soon)

 

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