In fourth grade, students learn how to multiply 2-digit by 2-digit numbers (ex: 42 x 87) and 4-digit by 1-digit numbers (ex: 8,264 x 5). They learn two strategies to solve these types of problems: the area model strategy, and the partial products strategy. These strategies are key stepping stones in the conceptual development of long multiplication, serving as a bridge towards the standard algorithm, which they will learn in 5th grade. (Students who jump straight to the standard algorithm without first focusing on concept development will memorize a bunch of steps without any meaningful understanding of why the standard algorithm works.) The resources below will help you understand the area model and partial products strategy so you can support your child's learning at home. 

After each unit’s math assessment, students complete an “error analysis” to help them understand why they made particular mistakes and how to prevent them in the future. I created this routine after seeing many students miss problems they clearly understood—often because of preventable errors rather than gaps in understanding.

As part of the rollout, we introduced the mathematical practice of attending to precision (as described by the Common Core Standards for Mathematical Practice). We discussed:

1. What is precision? Why does it matter?

2. What are the 3 types of errors, and how are they different?

3. What strategies can I use to prevent these errors in the future?

During the routine, students categorize each incorrect problem:

1. Conceptual Error: I wasn’t fully sure how the math concept works or how to approach this problem.

2. Computational Error: I knew what to do, but I made a calculation mistake.

3. Careless Error: I made an avoidable slip—copying incorrectly, misreading directions, writing sloppily, etc.

They then correct each problem to show accurate thinking and reflect on patterns in their errors. Over time, this helps them build metacognition, strengthen precision, and develop habits that reduce preventable mistakes.

We also revisited the idea of productive struggle and reinforced that making mistakes is a normal—and important—part of learning. Students are beginning to engage thoughtfully with their errors as opportunities for growth.

Please explore the resources below to learn more about this routine!

Core Program: Fluency By Heart

Number sense is crucial to all aspects of mathematics, so we have set up students with a Fluency by Heart (FBH) account to practice basic math facts in a way that will reinforce their conceptual understanding of operations.

FBH flash cards include both equations and visual representations, including 10-frames, number cards, number bars, and number lines for addition, as well as dot arrangements, area models, and prime factor circles for multiplication. This helps students use different brain pathways – one that is numerical and symbolic, and another that involves more intuitive and spatial reasoning – to make sense of operations.

Fourth graders will start with multiplication through 12 x 12, and throughout the year will progress into division.

Using the theory of spaced repetition, students will practice the facts they are most likely to forget more frequently. When students correctly answer a fact, they will not see that same fact again for 1–2 days to a few weeks, depending upon how many times they have already correctly answered that fact. If students answer a fact incorrectly, they will see that fact again the next time they practice. Student progress will be monitored by teachers.

Students will log in and get 30 cards to practice each day. This daily practice is untimed and takes approximately 2-10 minutes to complete. It is embedded into the school day, and we will aim for students to log in at least 3 times each week.  

Of course, students can benefit from additional practice at home, so you are welcome to bookmark the site: fluency.amplify.com. Students must click “Sign In” and then click “Continue with Google” using their Lab Google Drive login credentials, including the @ucls.uchicago.edu part. 

If they do not click "Sign In," the homepage is just feeding them random card sets, and it is not tracking their progress. They need to "sign in" in order to access their latest individualized assignment and to record their practice session.

Recommended Supplemental Program: Time4MathFacts

Another program I highly recommend is "Time4MathFacts." I used it for many years, and it remains my favorite online learning tool for building math fact fluency.

Fluency By Heart is excellent for introducing students to math facts using visual models—it helps children understand what multiplication and division mean. However, it does not measure automaticity. For example, a student might see a flashcard for 6×7 with a visual cue and take 30 seconds to answer “42.” While that visual helps build conceptual understanding, it doesn’t develop the instant recall students need to free up working memory for more complex math in 5th grade and beyond.

Time4MathFacts, on the other hand, focuses precisely on that skill. The program measures each student’s base typing speed, then uses it to calculate how quickly they can recall each math fact. It introduces facts in a systematic way and repeats them (through fun, fast-paced games!) until the student’s response time shows true automaticity. Once a fact is mastered, the program marks it as “memorized.”

Because it’s gamified, students love it—it feels like playing computer games rather than doing flashcards! If your child is reluctant to use Fluency By Heart, they will almost certainly enjoy Time4MathFacts. The detailed progress reports for parents are also outstanding and give a clear picture of your child’s growth.

This program is a fantastic companion to Fluency By Heart, helping your child achieve both conceptual understanding and automatic recall of multiplication and division facts. While Lab does not currently provide subscriptions, families can purchase a one-year home account for about $55.

Having taught 5th grade before, I can confidently say that math becomes far more challenging—and frustrating—when students don’t yet know their facts automatically. Helping your child master them now is truly one of the greatest academic “gifts” you can give for their future success in math!