Grade 4 · Level 39 · Foundational mastery
MATH 39
Algorithms as application.
Meridian Note
Multi-digit algorithms are KS-7 application of facts now held at KS-5 or better — a student still finger-counting 7 × 8 cannot afford the working-memory tax the algorithm charges. Fraction equivalence is the year's KS-6 centerpiece: why does 1/2 equal 2/4?
The Fix Registry
Skills of This Course
Every skill is pinned to the meridian by fix notation — where along the scale, and at what depth. The highlighted state is this course's target: the state an honest instrument must certify before the skill counts as covered here.
| Skill | Fixes | Target at Level 39 |
|---|---|---|
| Place value | 14-KS439-KS760-KS10 | KS-7Applied |
| Multiplication facts | 27-KS539-KS750-KS10 | KS-7Applied |
| Multi-digit multiplication & long division | 39-KS750-KS8 | KS-7Applied |
| Fractions as numbers | 27-KS439-KS660-KS9 | KS-6Understood |
| Decimal notation | 39-KS650-KS8 | KS-6Understood |
| Angles & geometric classification | 39-KS660-KS8 | KS-6Understood |
Course of Instruction
Units
Unit 1.Place Value to a Million
6 practice itemsThis year your numbers get big — into the hundred thousands and beyond. The good news: big numbers follow the exact same rule as small ones. Every place in a number is worth ten times the place to its right. Once you truly understand that one rule, you can read, build, compare, and round any number, no matter how long it is.
Multiple choiceFill in the blankMultiple choice (misconception distractors)Problem solvingTransfer problem
Unit 2.Multi-Digit Multiplication
14 practice itemsLast year you learned your multiplication facts. This year those facts become power tools. To multiply big numbers like 27 × 34, you never need a brand-new skill — you break the big problem into small fact-sized pieces, solve each piece, and add. This unit shows you why that breaking-apart trick always works.
Multiple choiceFill in the blankMultiple choice (misconception distractors)Problem solvingTransfer problem
Unit 3.Long Division Foundations
8 practice itemsDivision is multiplication running backward. 96 ÷ 4 asks: "4 groups of WHAT makes 96?" With big numbers you answer in stages — handing out easy chunks first, then smaller ones, until nothing (or almost nothing) is left. That stage-by-stage sharing is exactly what long division is. Learn the idea here, and next year's full algorithm will feel obvious.
Multiple choiceFill in the blankMultiple choice (misconception distractors)Short answerProblem solving
Unit 4.Fraction Equivalence: Same Number, Different Name
8 practice itemsHere is this year's biggest idea in fractions: two fractions that look completely different can be the exact same number. 1/2 and 2/4 and 4/8 all sit on the very same spot on the number line. This unit is about WHY that is true — not a trick to memorize, but a reason you can see and explain.
Multiple choiceFill in the blankMultiple choice (misconception distractors)Short answerProblem solving
Unit 5.Decimals: Tenths and Hundredths
8 practice itemsDecimals are not a new kind of number. They are fractions wearing place-value clothing. Just as places to the LEFT of the ones get ten times bigger, places to the RIGHT of the decimal point get ten times smaller: tenths, then hundredths. If you understand place value and fractions, you already own decimals — this unit just introduces you.
Multiple choiceFill in the blankMultiple choice (misconception distractors)Short answerProblem solving
Unit 6.Angles and Shape Families
6 practice itemsAn angle measures a TURN — how far one ray swings away from another. Once you can measure turns in degrees, you can sort every shape by its angles and sides, and you will discover something surprising: shapes belong to families, and one shape can belong to several families at once.
MatchingMultiple choiceFill in the blankProblem solvingMultiple choice (misconception distractors)