Grade 5 math

Units

1. 1

   Expressions and patterns

   3 lessons

   1. Parentheses, brackets and braces: evaluating expressionsFind the value of math with groups in it, and explain how the groups change the answer.
   2. Writing and interpreting numerical expressionsTurn word instructions into math with the right parentheses, and compare two of them by how they are built, without working them out.
   3. Numerical patterns with two rules and graphing ordered pairsMake two number patterns, explain how the numbers in the same week are related, and put each pair of numbers on a grid.
2. 2

   Place value and decimals

   9 lessons

   1. Each place is ten times the place to its rightCompare what the same digit is worth in different places by counting jumps of ten.
   2. Multiplying and dividing by powers of tenUse place value to multiply and divide whole numbers and decimals by 10, 100 and 1,000.
   3. Reading, writing and comparing decimals to thousandthsRead and write decimals in digits, in words and in expanded form, and compare them to thousandths.
   4. Rounding decimals to any placeRound a decimal to the place you're asked for, and explain your answer using the two numbers on either side and the halfway mark.
   5. Multiplying multi-digit whole numbers with the standard algorithmMultiply big whole numbers in columns, and check the answer with a quick estimate.
   6. Dividing by two-digit divisorsDivide whole numbers by taking away easy chunks, show the chunks in a rectangle, and check any leftover.
   7. Adding and subtracting decimals to hundredthsAdd and subtract decimals to hundredths by lining up the places and trading pieces of the same worth.
   8. Multiplying decimals to hundredthsMultiply decimal side lengths, explain which place the area lands in, and check that its size makes sense.
   9. Dividing decimals to hundredthsDivide by whole numbers or easy decimals by counting equal groups or making equal shares, then check by multiplying.
3. 3

   Adding and subtracting fractions

   3 lessons

   1. Adding and subtracting fractions with unlike denominatorsChange two fractions so they have the same bottom number, then add or subtract, and check that the answer makes sense.
   2. Adding and subtracting mixed numbersAdd and subtract numbers like 3 1/4, a whole number with a fraction, by making the fraction parts the same size and trading a whole when you need to.
   3. Fraction word problems and estimating with benchmarksSolve fraction story problems where the parts share one whole: guess first, draw a tape or write a number sentence, then check that the answer makes sense.
4. 4

   Multiplying and dividing fractions

   6 lessons

   1. A fraction is a division: a/b = a ÷ bSolve fair-sharing problems with a fraction or mixed number answer, and find which two whole numbers the answer is between.
   2. Multiplying a fraction by a whole number or a fractionFind a fraction of a whole number, or a fraction of a fraction, with a picture and a number sentence.
   3. Area of rectangles with fractional side lengthsFind a rectangle's area when its sides are fractions, and explain the answer with small tiles that are all the same size.
   4. Multiplication as scalingGuess how multiplying by a fraction changes a photo's width, and explain why multiplying by a fraction like 2/2 changes nothing.
   5. Real-world problems multiplying fractions and mixed numbersSolve story problems that multiply mixed numbers, with a picture or a number sentence, then check the answer.
   6. Dividing unit fractions by whole numbers and whole numbers by unit fractionsDraw and solve both kinds of fraction division, then check by multiplying.
5. 5

   Measurement, data and volume

   4 lessons

   1. Converting measurement units within one systemChange measurements to a different unit, in metres and centimetres or in feet and inches, then use matching units to solve problems.
   2. Line plots with fractional measurementsMake a line plot marked in eighths, and use it to find a total, a fair share, and a difference.
   3. Volume as packing unit cubesCount all the cubes that fill a box, even the hidden ones, and give its volume in cubic units.
   4. Volume formulas and additive volumeFind a box's volume or its missing height, and add the volumes of two boxes that don't overlap.
6. 6

   The coordinate plane

   2 lessons

   1. The coordinate system: axes, origin and ordered pairsPlot and name points on a grid, including points that sit right on one of the lines.
   2. Graphing points to solve problemsPut points on a graph with labelled lines and a scale, and use them to answer questions about a story.
7. 7

   Classifying shapes

   2 lessons

   1. Attributes belong to every subcategoryUse what each shape name means to explain what shapes share, and decide if “all,” “some” or “no” sentences are true.
   2. Classifying two-dimensional figures in a hierarchyPut four-sided shapes and triangles into bigger and smaller groups, and give a reason for each one.