A full year of 5th grade math in 16 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: 175 days, which leaves room in a 180-day year for catching up, holidays and seasonal packs.
16 units127 lessons175 days35 weeks
Students see that each place is worth ten times the place to its right and one tenth of the place to its left, from the millions to the thousandths. They write powers of ten with exponents, multiply and divide whole numbers and decimals by 10, 100 and 1,000 by moving every digit, and read and write thousandths in standard, word and expanded form, with decimals and with fractions. Then they compare and order decimals to thousandths and round them to the nearest whole number, tenth and hundredth. Place value opens the year because adding, subtracting, multiplying and dividing decimals all stand on it. Lesson 1.5 (one number many ways, and 0.1, 0.01 and 0.001 more or less) is for the states that teach it in 5th grade.
Students add and subtract decimals to hundredths, first on hundred grids, where a model shows the equation, then in columns with the decimal points lined up, writing zeros in empty places and regrouping as with whole numbers. They estimate first by rounding to whole numbers and use the estimate to judge an answer, add and subtract money for totals, change and the better buy, and solve one- and two-step stories. The unit follows place value at once: lining up the points is lining up the places. Classes whose standards ask for it go on to thousandths in lesson 2.2.
Students multiply multiples of 10, 100 and 1,000 with a basic fact and the zeros of both factors (80 × 900 is 72 thousands) and write powers of ten with exponents. They round each factor to its greatest place to estimate a product and decide whether an answer is reasonable. Then they multiply 2-, 3- and 4-digit numbers by a 2-digit number with area models and partial products, move to the standard algorithm, go on to 4-digit times 2-digit and 3-digit times 3-digit with zeros in a factor, and solve stories of one and more steps. Ask “what is each part worth?” every day: each row of the standard algorithm is a row of the area model.
Students divide multiples of 10, 100 and 1,000 by multiples of 10 with a basic fact (4,200 ÷ 70 is 420 tens ÷ 7 tens) and estimate quotients with compatible numbers. Then they divide 3-, 4- and 5-digit numbers by 2-digit numbers with area models and partial quotients, then with the standard algorithm, rounding the divisor to estimate each digit and fixing one that is too big or too small, and writing a 0 in the quotient where a place has no groups. They decide what a remainder means in a story and solve division stories of one and more steps. Ask “about how many groups of the divisor fit?” every day: every method in the unit takes away equal groups, place by place. Lesson 4.7 (a remainder as a fraction or a decimal) is for the states that teach it in 5th grade.
Students learn that grouping symbols decide what is done first. The same numbers grouped two ways can have different values; multiplying and dividing come before adding and subtracting, each from left to right; brackets and braces are worked from the inside out, one step on each line. Then they write expressions from words and compare expressions without working them out: 6 × (a big sum) is 3 times as large as 2 × (the same sum). In some states the unit goes on to true or false equations with a value put in, where a pair of parentheses goes, equivalent expressions with the properties, expressions and equations with a letter, and multi-step stories with a letter for the unknown (lessons 5.5 to 5.8). Ask “what do you do first, and how do you know?” every day.
Students multiply and divide decimals to hundredths with models first: tenths strips and hundred grids for a decimal times a whole number and for tenths times tenths, base-ten blocks and grids for sharing a decimal equally. Then they work as with whole numbers and place the point two ways, by estimating and by counting decimal places. They multiply in columns, money too, divide by 2-digit numbers to a quotient in hundredths, and divide by a decimal by asking how many tenths or hundredths fit. The unit ends with stories that use all four operations. In some states it also covers times and divided by 0.1 and 0.01 (lesson 6.5). Ask “about how big should the answer be?” before every problem.
In some states the unit opens with prime numbers and factor trees. Then factors and multiples go to work on fractions: the greatest common factor writes a fraction in simplest form in one step, and the least common multiple of the denominators is the least common denominator, for renaming and comparing. Students add and subtract fractions with unlike denominators, on strips and then by renaming; add and subtract mixed numbers, renaming fractions that make 1 or more as a whole and trading 1 whole when the top fraction is too small; estimate with 0, one half and 1; and solve story problems in one and two steps. Denominators go to 12. Ask “what size parts can both fractions be written in?” every day.
Students see a fraction as a division: 3 pizzas shared equally by 4 friends is 3 ÷ 4, or 3/4 of a pizza each. Then they multiply: a fraction of a whole number on tape diagrams, a fraction of a fraction on area models, where the overlap is the product, and then by the rule, numerators times numerators and denominators times denominators, in simplest form. They find areas of rectangles with fraction sides by tiling them with unit-fraction squares, multiply mixed numbers, decide without multiplying whether a product is more or less than a factor, and solve story problems and recipes. Ask “is the product more or less than what you started with?” every day: times a fraction less than 1 makes a number smaller.
Students divide with unit fractions two ways. A unit fraction divided by a whole number cuts a part into equal pieces: on an area model, 1/2 ÷ 3 is one of 6 equal pieces of the whole, so 1/6. A whole number divided by a unit fraction asks how many fit: there are 10 tenths in every whole, so 6 ÷ 1/10 = 60. Students check every division by multiplying, find missing numbers and write equations for division stories. In some states the unit goes on to dividing a fraction by a fraction with common denominators, fractions as decimals and back (thirds, eighths and the factors of 100), comparing and ordering fractions, mixed numbers and decimals on one number line, and percents as parts of 100. Ask “is the answer more or less than the number I started with?” every day.
Students convert within one measurement system. Metric units go by powers of ten, so changing kilometers to meters, or grams to kilograms, moves the digits: 2.9 km = 2,900 m and 270 cm = 2.7 m. Customary units do not, so students use the facts (12 inches in a foot, 3 feet in a yard, 16 ounces in a pound, 4 quarts in a gallon) with fractions: 2 1/3 ft = 28 in. They fill in tables, compare amounts in two units by writing both in one unit, and solve conversion stories in two and three steps. In some states the unit also takes in units of time and elapsed time, choosing a metric unit and estimating before measuring, and measuring to the nearest sixteenth inch and millimeter. Ask “will there be more or fewer of the new unit?” before every conversion.
Students name solid figures by their faces, edges and vertices and match nets to the solids they fold into. Then they find volume: they fill boxes with unit cubes, count cubic centimeters, inches and feet, multiply the bottom layer by the number of layers, and use V = l × w × h and V = B × h. They find a missing edge, build different boxes with the same volume, add the volumes of two prisms joined together, solve volume stories, and decide whether a job needs perimeter, area or volume. Volume comes after the multiplying of Unit 3 and the conversions of Unit 10, and stands on the area of 4th grade: a base is an area, and the layers stack on it. Some states add solid figures and nets, missing edges, and choosing the measure.
Students sort polygons by their sides, right angles and parallel sides and tell regular polygons from the rest. They name triangles by their sides and by their angles and give every name that fits a quadrilateral, reading the marks for equal sides, parallel sides and right angles. Then they see that a shape in a smaller group has every property of the larger group (every square is a rectangle) and arrange quadrilaterals in a hierarchy, deciding whether a statement is always, sometimes or never true. On Animal Math a trapezoid has at least one pair of parallel sides, so a parallelogram is a trapezoid too. Three lessons are taught in 5th grade in some states: measuring and sorting angles, the angles of a triangle, and circles.
Students go past rectangles with whole number sides. They find the area and perimeter of rectangles with fraction and decimal sides, and of shapes made of two rectangles, finding a missing side from the sides across from it. They see a right triangle as half a rectangle, then find the area of a parallelogram (a triangle cut off and moved makes a rectangle), of any triangle (half a parallelogram) and of a trapezoid split into a rectangle and triangles. They answer stories in the right units and estimate perimeters, curved ones too. The unit uses the decimal and fraction multiplying of Units 6 and 8. Every lesson is one that some states teach in 5th grade: teach the ones your class learns.
Students learn the first quadrant of the coordinate plane: the x-axis, the y-axis, the origin and ordered pairs. They read and plot points, join points into shapes and find lengths along grid lines, and tell what a point means on a map or a graph. Then they make two number patterns from two rules, compare the terms that line up, and graph the pairs. Three lessons are taught in 5th grade in some states: input-output rules written with n, telling adding patterns from multiplying ones, and patterns with fractions and decimals. Say “across, then up” every day.
Students measure to the nearest eighth of an inch and show the data on line plots marked in halves, quarters and eighths, then add, subtract and share the total equally to answer questions about it. The rest of the unit is taught in 5th grade in some states: planning how to collect data, the mean as a fair share, the median, mode and range and which measure fits, stem-and-leaf plots and frequency tables, line graphs and double bar graphs, scatterplots, histograms and circle graphs, probability as a number from 0 to 1, and sample spaces in tree diagrams, counted by multiplying.
Students learn the four kinds of taxes and add sales tax to a price, find gross and net income, compare paying by check, debit card, credit card and electronic payment, and keep a record of deposits and payments with a running balance. Then they find what helps when a family’s expenses are more than its income, and balance a simple budget. Every lesson in this unit is taught in 5th grade in some states only, so teach the ones your state lists; the unit can be spread through the year. The people, 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 5th grade in some states and in other grades elsewhere; skip them if your state does not teach them in 5th grade (without them the year is 81 lessons in 14 units, which leaves time to spend two days on the long division, decimal and fraction lessons). The two line plot lessons that open Unit 15 can close Unit 9 instead. Units 13 (area and perimeter of polygons) and 16 (money and financial literacy) are for the states that teach them in 5th grade, and Unit 16 can be spread through the year.
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