A full year of 3rd grade math in 14 units and 125 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: 167 days, which leaves room in a 180-day year for catching up, holidays and seasonal packs.
14 units125 lessons167 days34 weeks
Students learn what multiplying means: equal groups, a multiplication sentence (the first number tells how many groups, the second how many in each), arrays in rows, skip counting and equal jumps, and turn-around facts. Then they learn the facts for 2, 5 and 10 by their patterns and the rules for 0 and 1, and they solve equal groups and array stories. Ask “how many groups, and how many in each?” every day: the whole unit rests on it. Lesson 1.9 (one fact shown many ways) is for the states that teach it in this unit.
Students learn division two ways: sharing equally (how many in each group) and making equal groups (how many groups). They write division sentences and name the dividend, divisor and quotient, divide with arrays and with jumps back to 0, and find a quotient as a missing factor. Then they write fact families, divide by 2, 5 and 10 and with 0 and 1, find missing numbers in × and ÷ equations, and solve division stories. Ask “do we know how many groups, or how many in each?” every day: it tells sharing from grouping.
Students learn the rest of the facts, each family with a strategy that leans on a fact they already know: the 3s as 2 groups and 1 more, the 4s as double the 2s, the 6s as 5 groups and 1 more, the 7s as the 5s and the 2s, the 8s as double the 4s and the 9s as 10 groups minus 1. They break a fact apart with an array, group three factors to make a 10, and divide by thinking of the times fact. The unit ends with the facts from memory. Ask “which fact do you know that is close?” every day. Lesson 3.11 (facts with 11 and 12) is for the states that teach it in 3rd grade.
Students learn what area is: how many unit squares cover a flat shape with no gaps and no overlaps. They count square units, name them (square centimeters, square inches, square feet, square meters) and draw shapes with a given area. Then they see that a covered rectangle is rows of squares, so its area is the rows times the squares in a row, and that the side lengths give the same two numbers: length times width. They solve area stories, one with a missing side, split a rectangle into two parts to multiply (the break apart strategy of the facts unit, now as area), and find the area of shapes made of two rectangles. Area comes right after the facts so the times tables get used, and before perimeter, so the two can be told apart later.
Students review place value to 1,000 (the value of a digit, expanded form and number words), then learn to round: to the nearest ten and to the nearest hundred, first on a number line and then by looking at the digit to the right, with a number exactly halfway rounding up. They use rounding to estimate sums and differences and to decide whether an answer is reasonable, which sets up the next unit on adding and subtracting within 1,000. In some states the unit also goes past 1,000: thousands, comparing and ordering numbers to 10,000, one number shown many ways, and rounding to the nearest thousand.
Students become fluent adding and subtracting within 1,000. They add by place value with partial sums, then in columns, regrouping ones, tens or both. They subtract by breaking apart the number taken away and by counting up on an open number line, then in columns, trading a ten, a hundred or both, and across zeros. Mental math with a friendly hundred and one- and two-step story problems, checked with an estimate from the last unit, finish the lessons every class teaches. In some states the unit adds four-digit numbers and deciding whether two sums or differences are equal.
Students multiply a one-digit number by a multiple of 10 by thinking in tens (2 × 70 is 2 × 7 tens, 14 tens, 140) and find missing factors with tens. Then they solve story problems with all four operations: equal groups and arrays with the unknown in any place, measurement stories in centimeters, liters and kilograms, two-step stories with a step for each operation, and equations with a letter for the unknown. They round to the nearest hundred to decide whether an answer is reasonable. In some states the unit also multiplies a 2-digit number by a 1-digit number, solves times as many stories, and decides whether equations with × and ÷ are true.
Students look for patterns in the addition table and the multiplication table and explain why they work: a row goes up by 1, the sums down a line from top right to bottom left stay the same, the 5s row ends in 0 or 5, and the 4s row is double the 2s row. They predict whether a sum or product is odd or even without working it out, and say which rules are always true. In some states the unit goes on to number patterns: finding a rule and keeping a pattern going, finding a mistake and the number at a position, growing and shrinking shape patterns, and input-output tables.
Students learn what a fraction is as a number. A unit fraction is one of the equal parts of a whole, and a/b is a of those parts, written in numbers and in words. They cut shapes into parts with the same area and see that equal parts can look different, then put fractions on a number line, where the space from 0 to 1 is the whole. In some states the unit also takes in fractions of a set and sharing, fractions greater than 1 as mixed numbers, and a fraction as a sum of unit fractions. Paper strips folded into equal parts are the model to come back to every day.
Students find fractions that name the same amount: with paper strips and area models, on number lines lined up one under another, and by cutting every part into the same number of pieces to find a missing number. They write whole numbers as fractions. Then they compare fractions with the same denominator (same size parts, so more parts is more) and with the same numerator (fewer parts in the whole means bigger parts), and compare in stories, where the wholes must be the same size. In some states the unit ends with 0, 1/2 and 1 as benchmarks. Cut every strip from one length, so the wholes always match.
Students read and write time to the minute and choose a.m. or p.m., then find elapsed time in minutes with jumps on an open number line: to the next quarter hour, by 15s, then the rest. They find a missing start or end time and solve time stories. Then they measure mass in grams and kilograms on dial scales and liquid volume in milliliters and liters, choose the better unit, and solve mass and liquid volume stories with all four operations. In some states the unit ends with customary units (ounces, pounds, cups and gallons), reading a thermometer, and choosing the tool and the unit for a job.
Students read and make picture graphs where each picture stands for 2, 5 or 10, then read and make bar graphs with a scale, and answer how many more, how many fewer and two-step questions from both. They measure to the nearest half and quarter inch and show the lengths on line plots marked in halves and quarters. In some states the unit ends with surveys and frequency tables, and listing the possible outcomes of an event.
Students find perimeter as the distance around: they count units around shapes on grid paper, add side lengths and find a missing side. They compare rectangles with the same perimeter and different areas, and decide whether a story asks for area or perimeter. Then they describe quadrilaterals by their right angles and parallel sides, sort rhombuses, rectangles and squares, and draw quadrilaterals in none of those groups. Some states add polygons, lines and angles, symmetry and solids.
Students count bills and coins and write amounts with $ and a point, decide whether there is enough money to buy something, compare amounts, and make change by counting on from the price, with every amount $5.00 or less. Then come the financial literacy lessons: how skills and training raise pay, how scarcity and plenty change a price, planned and unplanned spending, borrowing with interest, and a plan to save and give. Every lesson in this unit is taught in 3rd grade in some states only, so teach the ones your state lists.
Lessons marked ★ are taught in 3rd grade in some states and in other grades elsewhere; skip them if your state does not teach them in 3rd grade (without them and Unit 14 the year is 89 lessons, which leaves time to spend two days on the fact lessons of Unit 3, the fractions units and the word problems of Unit 7). Unit 14 (money and financial literacy) is for the states that teach it in 3rd grade, and it can be spread through the year.
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