Fourth Grade · Ages 9-10 · Upper West Side
4th grade math is where multi-digit arithmetic, fractions, and the first real algebra reasoning come together. Small groups of 6, Upper West Side, Harvard- and Kellogg-trained teachers.
Book a free 30-minute evaluation →The curriculum
Fourth grade math extends the operational fluency built in 3rd grade to multi-digit numbers: multi-digit multiplication (up to 4-digit by 1-digit and 2-digit by 2-digit), long division, and fluent addition and subtraction of multi-digit whole numbers. Fractions expand to include addition and subtraction with like denominators, comparison of fractions with different denominators, and equivalent fractions. Decimals enter for the first time as an extension of fractions (tenths and hundredths). Angle measurement and lines of symmetry appear in geometry. This is also the second year of NY State Math testing.
Where kids get stuck
Long division is the most complex procedure a 4th grader has ever learned — it requires multiplication, subtraction, place value, and estimation all working together. The most common failure is that any weakness in the underlying operations (usually multiplication facts) becomes catastrophic in long division. A student who is 85% fluent with multiplication facts hits a wall the first time division asks them to test 7 x 8, 8 x 8, 9 x 8 in sequence. The prerequisite work is fact fluency, not more division practice.
Understanding that 1/2 = 2/4 = 3/6 = 4/8 is conceptually simple but procedurally slippery. Fourth graders often can identify equivalent fractions on a visual model but fail to apply the concept when they need to compare 3/4 vs. 5/8 or add 1/2 + 1/4. The stronger habit is always converting to a common denominator first — even for problems the student thinks they can solve mentally.
Most 4th grade curricula introduce decimals in a separate unit from fractions, which leads students to treat them as different things. In reality, 0.5 and 1/2 are the same number, and every operation on decimals is an operation on fractions. Students who learn decimals procedurally without connecting them to fractions consistently make errors like 0.3 + 0.4 = 0.34 (adding the way they would with whole numbers, ignoring place value).
Milestones by month
How SOMATH teaches it
Our Kid Einsteins class runs in small groups of six on the Upper West Side, 90 minutes once a week, taught in person by Harvard- and Kellogg-trained educators. Every session works on grade-level content plus extension work for stronger students and gap-filling for kids catching up. We wrote our own 48-class syllabus for this level — no worksheet packets, no improvised lessons. See the full Kid Einsteins syllabus →
Every new student starts with a free 30-minute in-person evaluation, at the end of which we send you a written report on your child's specific strengths and gaps. No pitch, no pressure — you get the report either way.
NYC schools we work with
SOMATH sees 4th graders from PS 87, PS 199, PS 452, PS 9, Anderson, NEST+m, and Special Music School, plus Trinity, Ethical Culture Fieldston, Rodeph Sholom, and Manhattan Country School. Long division pacing varies noticeably — some schools have it fluent by winter break, others don't reach it until spring.
Common questions
For families targeting selective NYC middle schools, a Level 4 (top level) is the goal — it keeps every door open including screened programs and specialized progress tracks. A Level 3 is on-grade-level and acceptable for most placement decisions. A Level 2 is a signal to look at where the gaps are before 5th grade, when the last year of elementary math consolidates before middle school.
The math on the SHSAT includes topics that first appear in 4th grade — fraction operations, decimal fluency, multi-step word problems, and basic geometry. The SHSAT itself is taken in fall of 8th grade, but the students who score highest are typically those who built solid 4th and 5th grade fluency and never had to catch up. Starting SHSAT-style problem solving in 4th grade is not too early — but it should layer on top of grade-level work, not replace it.
Because it is harder. Long division combines four skills — multiplication, subtraction, place value, estimation — that were separate in 3rd grade. It requires holding multiple partial results in working memory. Students who struggle typically struggle in one of the four skills, not in division itself. The right diagnostic is to isolate which underlying skill is weak.
Not for planning, though not for pressure. Most NYC middle school placement decisions are made based on 5th and 6th grade performance, but the foundations are built in 4th. A 4th grader who is solid on multi-digit arithmetic, fluent with fractions, and comfortable with multi-step word problems has every option open in 5th grade. A 4th grader with gaps in these areas is spending 5th grade fixing them rather than moving forward.
Related reading
Bring your child in for a one-on-one evaluation with one of our teachers. You'll leave with a written report on your child's specific strengths and gaps. No pitch, no pressure.
Book the evaluation → Or call us: (646) 668-6151 · 226 W 79th St, 1st Floor, NY 10024