A full year of 4th grade math in 15 units and 127 lessons, free to print. Every lesson has a one-page lesson plan (how to teach it, the words to use, the mistakes to watch for) and an exit ticket, and every unit has a pre-check, a review and a test in two forms. Each lesson plan points to the worksheets, worksheet makers, teaching tools and quizzes that practice it. The plan below counts one lesson a day, with a day for the pre-check, the review and the test of each unit: 172 days, which leaves room in a 180-day year for catching up, holidays and seasonal packs.
15 units127 lessons172 days35 weeks
Students read, write, compare and order whole numbers to 1,000,000. They learn the periods and the commas between them, find the value of a digit from its place, and see that each place is worth ten times the place to its right, so a digit one place to the left is worth 10 times as much. They write numbers in standard, word and expanded form, rename a number in other units (3,400 is 34 hundreds or 340 tens), place numbers on number lines, and compare and order them with >, = and <. Place value opens the year because rounding, the column algorithms and multi-digit multiplying and dividing all lean on it. Lesson 1.7 (numbers to 999,999,999) is for the states that teach the millions period in 4th grade.
Students round whole numbers to any place, first on a number line and then by the digit to the right of the rounding place, with a number exactly halfway rounding up. Then they add and subtract numbers to 1,000,000 with the standard algorithm: lining up the places, regrouping, trading across zeros, and adding to check a difference. They estimate to decide whether an answer is reasonable, and solve one- and two-step stories with strip diagrams and a letter for the unknown. Rounding comes before the algorithms so that an estimate can check every sum and difference. Lesson 2.8 (estimate or exact?) is for the states that teach it in 4th grade.
Students see multiplication as comparing: 30 = 6 × 5 means 30 is 6 times as many as 5. They solve times as many stories with strip diagrams, multiplying to find the larger amount and dividing to find the smaller amount or the number of times, and tell times as many from how many more. Then they find factor pairs from rectangles of squares, list every factor pair of a number to 100, find multiples, and sort numbers into prime and composite. The facts come back all unit, and factors and multiples set up multi-digit multiplying and dividing, and later equivalent fractions. Lessons 3.1 (facts through 12 × 12) and 3.9 (common factors and the greatest common factor) are for the states that teach them in 4th grade.
Students multiply by 10, 100 and 1,000 and see each digit move one place to the left for each 10, then multiply multiples of 10, 100 and 1,000 with a basic fact (6 × 600 is 36 hundreds). They multiply 2-, 3- and 4-digit numbers by a 1-digit number with base-ten blocks, area models and partial products, then with the standard algorithm, and two 2-digit numbers with a four-part area model, partial products and the standard algorithm. They round each factor to estimate a product and decide whether an answer is reasonable, and they solve equal groups and times as many stories with an equation. Ask “what is each part worth?” every day: every method in the unit splits a number by place value. Lesson 4.7 (3-digit times 2-digit) is for the states that teach it in 4th grade.
Students divide tens, hundreds and thousands with a basic fact (4,200 ÷ 7 is 42 hundreds ÷ 7) and learn what a remainder is. Then they divide 3- and 4-digit numbers by a 1-digit number four ways: sharing base-ten blocks, area models, partial quotients and long division, with a 0 in the quotient where a place has no groups. They estimate quotients with numbers that divide easily, check by multiplying, decide what a remainder means in a story, and divide to compare two amounts with times as many. Ask “how many groups of the divisor fit?” every day: every method in the unit takes away equal groups, place by place.
Students solve stories in two and more steps with all four operations: they draw strip diagrams, write one equation with a letter for the unknown, and estimate to check that an answer is reasonable. Then they make number and shape patterns from a rule and look for what the rule does not say, such as odd and even numbers taking turns, and explain why it happens. In some states the unit also covers the equal sign with all four operations (= and ≠), a letter in any place of an equation, input-output tables, and rules that give a value from its position (lessons 6.3, 6.4, 6.7 and 6.8). Ask “what does the letter stand for?” and “why does the pattern do that?” every day.
Students find equivalent fractions with paper strips, area models and hundredths grids, and see why multiplying the numerator and denominator by the same number names the same amount: every part is cut into that many smaller parts. They find equal fractions on number lines past 1 and by dividing. Then they compare fractions with different numerators and denominators by renaming them to a common denominator or a common numerator, or by comparing each with one half or 1, and they order fractions and mixed numbers, always as parts of wholes the same size. Denominators are 2, 3, 4, 5, 6, 8, 10, 12 and 100. Cut every paper strip from one length, so the wholes always match.
Students see a fraction as a count of unit fractions (3/5 is 1/5 + 1/5 + 1/5) and break fractions apart in more than one way. Then they add and subtract fractions with the same denominator: the parts are the same size, so only the numerators change. They rename mixed numbers and fractions greater than 1 both ways, add and subtract mixed numbers, trading 1 whole when the parts run over or run short, check answers with the benchmarks 0, one half and 1, and solve story problems with models and equations. Every problem keeps one denominator; adding fractions with unlike denominators is 5th grade work.
Students see a fraction as copies of a unit fraction: 5/4 is 5 copies of 1/4, or 5 × 1/4. They multiply a whole number by a unit fraction with jumps on a number line, then by any fraction with strips and equations: 3 × 2/5 is 6 copies of 1/5, or 6/5. They find which two whole numbers a product is between, with the fraction first too, and solve story problems about equal groups of a fraction. In some states the unit ends with a fraction as sharing: 3 muffins shared equally by 5 friends is 3/5 of a muffin each. Multiplying a fraction by a fraction is 5th grade work.
Students meet decimals as a new way to write tenths and hundredths. They shade tenths strips and hundred grids and write each amount as a fraction, a decimal and in words, rename tenths as hundredths (4/10 = 40/100) so they can add tenths and hundredths, and place decimals in a place value chart and on number lines. Money ties it together: a dime is a tenth of a dollar and a penny a hundredth. Then they compare and order decimals by place value, checking with grids. In some states the unit goes on to halves, fourths and fifths as decimals with benchmarks, thousandths, and adding and subtracting decimals with money. Decimals come right after the fraction units, as fractions with denominators 10 and 100.
Students learn how the units of one system compare: kilometers, meters, centimeters and millimeters; kilograms and grams; liters and milliliters; miles, yards, feet and inches; pounds and ounces; gallons, quarts, pints and cups; and days, hours, minutes and seconds. They record each relation in a two-column table, change a larger unit to a smaller one by multiplying, and compare two amounts by writing both in the smaller unit. Then they find elapsed time across the hour, and start and end times, and solve measurement stories in all four operations, with number line and bar diagrams, fractions and decimals. Measurement comes after the fraction and decimal units, so its stories can use them. Some states add measuring to the nearest eighth inch and millimeter, and choosing a unit and a tool.
Students move from counting squares to the area and perimeter formulas for rectangles: A = l × w and P = 2 × l + 2 × w, with A = s × s and P = 4 × s for a square. They use them with two-digit side lengths, splitting a rectangle at the tens to multiply, work back from the area or the perimeter to a missing side, and solve stories by deciding whether a job covers a shape or goes around it. The unit uses the multiplying and dividing of Units 4 and 5. Some states add rectangles that share a perimeter or an area, shapes made of rectangles, and a first look at volume with unit cubes.
Students measure lengths to the nearest eighth of an inch and show them on line plots marked in halves, quarters and eighths, then add and subtract fractions to answer questions about the data. These two lessons can also close Unit 8 instead, right after adding and subtracting fractions. The rest of the unit is taught in 4th grade in some states: collecting data in a frequency table, stem-and-leaf plots with the mode, median and range, bar graphs whose scales count by halves, line graphs, the possible outcomes of an event and how likely it is, and probability as a fraction from 0 to 1.
Students name points, lines, segments and rays with symbols, find and draw parallel and perpendicular lines, and sort angles as acute, right or obtuse. They learn that an angle is a turn and a degree is 1/360 of a full turn, measure and draw angles with a protractor, and add the parts of an angle to find an unknown part. Then they sort triangles by their angles and shapes by their sides and angles, and find lines of symmetry. Two lessons are taught in 4th grade in some states: the quadrilateral family, and the faces, edges and vertices of solid figures.
Students count bills and coins to $20 and make an amount with the fewest pieces, decide whether there is enough money, and make change from up to $20 by counting on or subtracting. Then come the financial literacy lessons: fixed and variable expenses, profit, the pros and cons of three ways to save, a weekly allowance plan for spending, saving, college and sharing, and what banks do. Every lesson in this unit is taught in 4th grade in some states only, so teach the ones your state lists; the unit can be spread through the year. The banks and businesses in the lessons are made up, and the lessons teach how money works, not what to choose.
Lessons marked ★ are taught in 4th grade in some states and in other grades elsewhere; skip them if your state does not teach them in 4th grade (without them and Unit 15 the year is 93 lessons, which leaves time to spend two days on the multiplication, division and fraction lessons). The two line plot lessons that open Unit 13 can close Unit 8 instead, after adding and subtracting fractions. Unit 15 (money and financial literacy) is for the states that teach it in 4th grade, and it can be spread through the year.
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