Grade 4 · printable course

Grade 4 Mathematics: Place Value, Operations, and Fractions

Grade 4 · 348 pages · 74 lessons · PDF, print at home

A full-year grade 4 mathematics course built on CCSS. Students extend place value to one million, build fluency with multi-digit addition, subtraction, multiplication, and long division, and reason about multiplicative comparison. The year moves into fraction equivalence, addition and subtraction of like-denominator fractions, and decimal notation for tenths and hundredths, then closes with measurement conversion, angle measurement, and geometric classification. Every new idea is introduced with a picture, array, area model, number line, or fraction bar, before any symbol is attached to it. The course is designed for a home setting where a parent checks finished work but does not teach the lesson.

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What is inside

Every unit and lesson in this book, in order. The same lessons are taught online at lettersanddevotion.com, so a family can move between paper and screen.

Grade 4 Mathematics: Place Value, Operations, and Fractions

74 lessons · try a lesson online free

Unit 1: Place Value to One Million8 lessons
  1. 1.Place value of a digit within a number up to 1,000,000
  2. 2.Standard, expanded, and word form of multi-digit numbers
  3. 3.Periods (ones, thousands, millions) as a grouping structure in the base-ten system
  4. 4.Comparison of multi-digit numbers using place value
  5. 5.The relationship between digit count and number size
  6. 6.Rounding multi-digit numbers to a specified place
  7. 7.Justification of a rounding decision using benchmark position
  8. 8.Place value, comparison, and rounding applied to an unfamiliar real-world numeric context
Unit 2: Multi-Digit Addition and Subtraction9 lessons
  1. 9.Regrouping ten ones as one ten in addition
  2. 10.Standard addition algorithm with multiple regroupings
  3. 11.Standard subtraction algorithm with regrouping across zeros
  4. 12.The trade of ten units for one unit of the next higher place
  5. 13.Rounding-based estimation of sums and differences
  6. 14.Reasonableness of a computed answer relative to an estimate
  7. 15.Selection of operation within a multi-step word problem
  8. 16.Multi-step addition/subtraction reasoning applied to an unpracticed context
  9. 17.Efficiency comparison between standard algorithm and compensation strategy
Unit 3: Multiplicative Comparison and Multi-Step Problems8 lessons
  1. 18.Multiplicative comparison represented as repeated copies of a bar
  2. 19.The structural difference between additive and multiplicative comparison problems
  3. 20.Equations representing multiplicative comparison with a symbol for the unknown
  4. 21.The relationship between comparison language and equation structure
  5. 22.The intermediate quantity in a two-operation word problem
  6. 23.Multi-step word problems combining the four operations with multiplicative comparison
  7. 24.Choosing additive versus multiplicative comparison in a novel context
  8. 25.The phrase 'times as many' as a signal for multiplication-based comparison
Unit 4: Multi-Digit Multiplication10 lessons
  1. 26.Place-value decomposition of a 2-digit number into tens and ones
  2. 27.Area model for one-digit by multi-digit multiplication
  3. 28.Reading partial products directly off a fully labeled area model
  4. 29.Partial products for 1-digit by 4-digit multiplication tied to the area model
  5. 30.Area model for two-digit by two-digit multiplication
  6. 31.The distributive property as the reason partial products sum to the exact product
  7. 32.Standard algorithm for two-digit by two-digit multiplication as a shortcut for the area model
  8. 33.Estimating products by rounding factors before multiplying
  9. 34.Multiplication word problems requiring a justified choice between exact computation and estimation
  10. 35.The relationship between area model size and total computational work required
Unit 5: Division with Remainders8 lessons
  1. 36.The missing-side (quotient) in an area model given total area and one factor
  2. 37.The correspondence between long division steps and area-model partial quotients
  3. 38.The standard long division algorithm for 1-digit divisors
  4. 39.The multiplication check for a division computation
  5. 40.Remainder interpretation matched to problem context (drop, round up, express as fraction)
  6. 41.Multistep word problems combining multiplicative comparison (Unit 3) and division with remainders
  7. 42.Estimation of a quotient using compatible numbers, as a reasonableness check
  8. 43.The situational feature that determines which remainder interpretation a problem requires
Unit 6: Factors, Multiples, and Patterns8 lessons
  1. 44.Factor pairs of numbers up to 100
  2. 45.The role of 1 and the number itself in every factor pair
  3. 46.Multiples of a number
  4. 47.The taught surface tell distinguishing factor questions from multiple questions
  5. 48.Prime versus composite numbers
  6. 49.Numerical patterns generated by multiples on a hundred chart
  7. 50.The generating rule behind a numerical pattern
  8. 51.Prime versus composite classification of a number resistant to quick mental testing
Unit 7: Fraction Equivalence, Operations, and Decimal Notation11 lessons
  1. 52.Equivalence of fractions shown by partitioning a fraction bar into smaller equal pieces
  2. 53.The relationship between equal partitioning and equivalent fraction amount
  3. 54.Comparison of fractions with unlike denominators using benchmark fractions
  4. 55.Common denominators found using multiples of the denominators
  5. 56.Addition and subtraction of like-denominator fractions shown on a fraction bar
  6. 57.The condition under which fractions must share a denominator before being added or subtracted
  7. 58.Multiplication of a fraction by a whole number as repeated addition of the fraction
  8. 59.The difference between the fraction-addition procedure and fraction-times-whole-number procedure
  9. 60.Decimal notation for fractions with denominator 10 or 100 shown on a hundredths grid
  10. 61.Comparison of decimals to hundredths using shaded grid area
  11. 62.Application of decimal grid comparison to an unfamiliar measurement context
Unit 8: Measurement Conversion, Angles, and Classifying Shapes12 lessons
  1. 63.Relative sizes of measurement units within a system (km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec)
  2. 64.Conversion from a larger to a smaller unit of length, weight, or time
  3. 65.The multiplicative relationship between a measurement's numeric value and its unit size
  4. 66.Multi-step word problems involving distance, time, liquid volume, mass, or money with unit conversion
  5. 67.Area and perimeter formulas for rectangles, used to solve for a missing dimension
  6. 68.Angle measurement in whole-number degrees using a protractor
  7. 69.Angle measure as a fraction of a circular arc
  8. 70.Angle measure as additive across adjacent angles in a diagram
  9. 71.Classification of two-dimensional figures by line relationships and angle types
  10. 72.Classification of quadrilaterals using multiple simultaneous properties (parallel sides and angle type)
  11. 73.Lines of symmetry in two-dimensional figures
  12. 74.The distinction between additive and multiplicative comparison applied to measurement conversion problems

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