What is my kid learning?
It isn’t always easy to know what’s happening in math class. We’ll break it down for you.
What your child learns in Pre-K
Numbers & Place Value · 8 skillsCounting to 20, writing 0 to 5, and comparing small groups.
- Counting to 20 out loudSay the counting numbers in order from 1 to 20.
- Writing a number 0 to 5 to show how manyShow how many objects are in a small group by writing a numeral from 0 to 5, and write 0 when there is nothing.
- Counting each thing once: one number for each objectCount objects by touching or pointing to each one once while saying one number.
- The last number counted tells how manyThe last number said when counting tells how many objects there are, and moving or reordering the objects does not change the total.
- Each number in the count is one moreEach counting number means one more than the number before it.
- Counting groups of up to 10 thingsCount up to 10 objects in a line, grid, or circle; find the number of scattered objects; and count out a requested number of things.
- Comparing groups: which has more, which has fewerTell whether one small group has more, fewer, or the same number of objects as another, by matching or counting groups of up to 5.
- Using the words "first" and "last"Use the words "first" and "last" to describe order and position, such as the first child in line or the last block on a tower.
Problem Solving · 3 skillsAdding and taking away with real objects, and simple patterns.
- Adding with objects and fingersPut small groups of real things together, show adding on their fingers, and answer everyday questions about how many there are in all.
- Subtracting with objects and fingersTake some things away from a small group, show taking away by folding down fingers, and tell how many are left.
- Spotting and continuing simple patternsCopy and continue simple repeating patterns made with real objects, such as red, blue, red, blue.
Measurement & Data · 2 skillsDescribing size and weight, and sorting things into groups.
- Describing length and weight: longer, heavier, tallerNotice what can be measured about everyday objects and describe it with words like big, small, tall, short, full, empty, heavy, and light.
- Sorting things into groups and counting themSort objects into groups by a shared feature, such as color or kind, and count how many are in each group, up to 10.
Geometry · 4 skillsNaming shapes, flat versus solid, and words for position.
- Naming shapes around us and saying where things areName the shapes they see around them and describe where things are, using words like top, bottom, in front of, behind, over, under, and next to.
- Naming shapes whatever their sizeName circles, squares, triangles, and rectangles correctly, whether the shape is tiny or very large.
- Comparing and sorting flat and solid shapesCompare and sort flat shapes and solid objects of different sizes, and describe in their own words how they are alike and different.
- Building shapes from parts, like sticks and clayMake shapes from parts, such as building a triangle from three sticks or a square from four.
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Numbers & Place Value · 9 skillsCounting to 100, writing numbers to 20, and teen numbers.
- Counting to 100 by onesCount aloud by ones from 1 to 100, saying every number in order, including the turns from one ten to the next, such as 29 to 30.
- Counting to 100 by tensCount by tens from 10 to 100, saying 10, 20, 30, and on up to 100 in order.
- Counting on from any numberStart counting from any number, such as 7 or 23, instead of always beginning at 1.
- Writing numbers from 0 to 20Write the numbers 0 to 20 and use them to record how many objects are in a group, including 0 for an empty group.
- How counting tells you how manyEach object gets one number, the last number counted tells how many, and each next number is one more.
- Counting groups of up to 20 thingsCount up to 20 objects in a line, grid, or circle; count up to 10 scattered objects; and count out any number from 1 to 20.
- Which group has more, fewer, or the sameTell whether one group of objects is greater than, less than, or equal to another, by matching the objects up or by counting each group.
- Comparing numbers from 1 to 10Compare two written numbers between 1 and 10 and say which is greater or less, without needing objects to count.
- Teen numbers as ten and some moreThe numbers 11 to 19 are made of ten ones and some more ones, such as 18 = 10 + 8.
Problem Solving · 7 skillsAdding and subtracting within 10, and making ten.
- Showing addition in many waysShow adding with objects, fingers, drawings, claps, and acting out; explain it in words; and write it as an equation like 3 + 2 = 5.
- Showing subtraction in many waysShow taking away with objects, fingers, drawings, and acting out; explain what is left in words; and write it as an equation like 5 - 2 = 3.
- Adding and subtracting story problems within 10Solve addition and subtraction story problems within 10 and show what happens in the story with objects or drawings.
- Splitting numbers up to 10 into two partsBreak numbers up to 10 into two parts in more than one way, such as 5 = 2 + 3 and 5 = 4 + 1.
- Finding the number that makes 10Find the number that makes 10 when added to any number from 1 to 9, such as knowing that 7 needs 3 more.
- Adding fluently within 5Add numbers with totals of 5 or less, such as 2 + 3 = 5 and 1 + 3 = 4, quickly and accurately, without counting every time.
- Subtracting fluently within 5Subtract within 5 quickly and accurately, such as 5 - 2 = 3 and 4 - 1 = 3, without counting back every time.
Measurement & Data · 3 skillsComparing length and weight, and sorting things to count.
- Describing how long or heavy things areDescribe what can be measured about an object, such as its length or weight, and notice that one object can be measured in several ways.
- Comparing which is longer, taller, or heavierCompare two objects directly to see which is longer, taller, or heavier, or which holds more; and describe the difference in words.
- Sorting things into groups and counting themSort objects into given groups, count how many are in each group, and put the groups in order from most to fewest.
Geometry · 6 skillsNaming, comparing, building, and combining flat and solid shapes.
- Spotting shapes and saying where things areName shapes in the objects around them and describe where things are with words like above, below, beside, in front of, behind, and next to.
- Naming shapes turned any which wayName shapes correctly however they are turned and whatever their size, including a triangle pointing down and a tilted square.
- Telling flat shapes from solid shapesTell flat shapes, like a square drawn on paper, from solid shapes, like a block or a ball; and call them two-dimensional or three-dimensional.
- Comparing shapes by their sides and cornersCompare flat and solid shapes by describing their parts, such as how many sides and corners they have, and say how the shapes are alike and different.
- Building and drawing shapesModel shapes from the world around them by building them from sticks and clay balls and by drawing them.
- Putting shapes together to make new shapesPut simple shapes together to make larger shapes, such as joining two triangles along a full side to make a rectangle.
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Numbers & Place Value · 6 skillsCounting to 120, tens and ones, and adding within 100.
- Counting, reading, and writing numbers to 120Count to 120 starting from any number and read and write numerals up to 120.
- Tens and ones in two-digit numbersA two-digit number like 34 means 3 tens and 4 ones, 14 is a ten and 4 ones, and 60 is 6 tens and no ones.
- Comparing two-digit numbers with >, =, and <Compare two-digit numbers by checking the tens before the ones and recording the result with >, =, or <.
- Adding two-digit numbers within 100Add within 100 by combining tens with tens and ones with ones, make a new ten when needed, and explain their method.
- 10 more or 10 less in your headFind 10 more or 10 less than a two-digit number in their heads and explain why only the tens digit changes.
- Subtracting tens, like 70 - 30Subtract tens from tens, as in 70 - 30 = 40; show it with models; and explain how their strategy connects to the written problem.
Problem Solving · 9 skillsAdding and subtracting within 20, story problems, and the equal sign.
- Adding and subtracting story problems within 20Solve addition and subtraction story problems within 20, including ones where the missing number comes at the start or in the middle.
- Story problems that add three numbersSolve story problems that add three numbers with a total of 20 or less and combine the groups in a sensible order.
- Adding in any order to make it easierAdd numbers in any order or grouping and use facts they already know to make adding easier.
- Subtracting by finding the missing partThink of subtraction as finding a missing part, so 10 - 8 becomes the question "what do I add to 8 to make 10?"
- Counting on and back to add and subtractAdding 2 means counting on two more and subtracting 2 means counting back two.
- Adding within 20Add within 10 quickly and accurately, count on from the larger number, and make ten or use a double for harder sums within 20.
- Subtracting within 20Subtract within 10 quickly and accurately; find differences, the answers to subtraction problems, within 20 by stopping at ten; and use addition facts they know.
- What the equal sign really meansThe equal sign means "the same amount as" and an equation like 5 + 2 = 2 + 5 can be checked as true or false.
- Missing numbers, like 8 + ? = 11Find the missing number in equations like 8 + ? = 11 or 5 = ? - 3 by thinking about how the three numbers relate.
Measurement & Data · 4 skillsMeasuring length, telling time to the half hour, and simple charts.
- Ordering three things from shortest to longestOrder three objects from shortest to longest and compare two lengths by using a third object.
- Measuring length by lining up same-size objectsMeasure length by laying same-size objects end to end without gaps or overlaps and counting them.
- Telling time to the hour and half hourTell and write time to the hour and half hour on both analog and digital clocks.
- Sorting, tallying, and reading simple chartsSort information into up to three groups, show it in a simple chart or tally, and answer questions about totals and which group has more or fewer.
Geometry · 3 skillsWhat makes a shape, building shapes, and halves and quarters.
- What makes a triangle a triangleWhich features make a shape what it is, like three straight sides for a triangle; and which do not matter, like color, size, or which way it is turned.
- Building bigger shapes from smaller onesPut flat shapes or solid shapes together to make new, larger shapes.
- Halves and quarters of circles and rectanglesSplit circles and rectangles into two or four equal parts and name them halves, fourths, and quarters.
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Numbers & Place Value · 13 skillsPlace value to 1,000, and adding and subtracting within 1,000.
- Hundreds, tens, and ones in numbers like 706The three digits of a number like 706 stand for hundreds, tens, and ones.
- Counting within 1,000Count by ones from any number up to 1,000, cross into a new hundred without stopping, and count past numbers with zeros in them.
- Skip-counting by 5s, 10s, and 100sSkip-count by 5s, like 5, 10, 15; by 10s, like 40, 50, 60; and by 100s, like 300, 400, 500.
- Reading and writing numbers to 1,000Read and write numbers up to 1,000 as numerals, in words, and in expanded form, like 400 + 30 + 6.
- Comparing three-digit numbers with >, =, and <Compare two three-digit numbers by looking at hundreds, then tens, then ones, and record the result with >, =, or <.
- Adding within 100Add numbers when the total is 100 or less, such as 47 + 38, by working with tens and ones in flexible ways.
- Subtracting within 100Subtract numbers within 100, such as 82 - 56, by counting up, taking numbers apart into tens and ones, and using what they know about adding.
- Adding up to four two-digit numbersAdd up to four two-digit numbers, such as 23 + 45 + 17 + 30, using place value and smart grouping.
- Adding within 1,000Add within 1,000 by adding hundreds, tens, and ones separately; make a new ten or hundred if needed; and connect drawings or blocks to written steps.
- Subtracting within 1,000Subtract within 1,000 by taking hundreds from hundreds, tens from tens, and ones from ones; break apart a ten or a hundred; and check by adding.
- Adding or taking away 10 or 100 mentallyAdd or subtract 10 or 100 in their heads from numbers between 100 and 900, seeing which digit changes.
- Explaining why addition strategies workExplain why an addition strategy works, show it with tens and ones, and say why changing the order of the numbers keeps the sum the same.
- Explaining why subtraction strategies workExplain why a subtraction strategy works, show why a ten can become ten ones, and say why adding back checks the answer.
Problem Solving · 5 skillsStory problems within 100, facts by heart, and odd and even.
- One- and two-step story problems within 100Solve one- and two-step addition and subtraction word problems within 100, plan their steps, and show each story with a drawing or an equation.
- Adding fluently within 20Add within 20 using mental strategies, and know every sum of two one-digit numbers, like 8 + 7, from memory by the end of the year.
- Subtracting fluently within 20Subtract within 20 in their heads, quickly and accurately, and use an addition fact they know, like 8 + 6 = 14, find 14 - 8.
- Odd and even numbersTell whether a group of up to 20 objects is odd or even and write an even number as a double, like 8 = 4 + 4.
- Counting objects in equal rows by addingTotal an array of up to 5 rows and 5 columns by adding the rows, writing equations like 4 + 4 + 4 = 12.
Measurement & Data · 11 skillsRulers, time to five minutes, money, and bar graphs.
- Measuring with a ruler, yardstick, or tapeMeasure length with rulers, yardsticks, meter sticks, and measuring tapes; choose the right tool for the job; and read it correctly.
- Measuring in inches and in centimetersMeasure one object in both inches and centimeters and explain why the smaller unit gives the larger number.
- Estimating lengths in inches, feet, and metersEstimate lengths in inches, feet, centimeters, and meters before they measure.
- Measuring how much longer one thing isMeasure two objects and find how much longer one is than the other, in a standard unit like inches or centimeters.
- Story problems about lengthSolve word problems about length within 100 by adding and subtracting, often drawing a ruler or number line to show the problem.
- Adding and subtracting on a number lineShow whole numbers as distances from 0 on a number line and use number lines to add and subtract within 100.
- Telling time to the nearest five minutesTell and write time to the nearest five minutes on analog and digital clocks and use a.m. and p.m. for the time of day.
- Solving story problems by counting bills and coinsCount dollar bills and coins, write the total with the $ or ¢ symbol, and solve story problems about how much there is in all.
- Solving story problems about how much money is leftFind how much money is left after buying something, work out the change from a dollar, and write the answer with the $ or ¢ symbol.
- Measuring things and making a line plotMeasure several objects to the nearest whole unit and show the measurements on a line plot.
- Making and reading picture graphs and bar graphsDraw picture graphs and bar graphs with up to four categories; and solve put-together, take-apart, and compare problems using what they show.
Geometry · 3 skillsNaming shapes; rows of squares; and halves, thirds, and fourths.
- Naming triangles, hexagons, cubes, and moreRecognize and draw shapes by their features, such as how many angles or faces they have; and name triangles, quadrilaterals, pentagons, hexagons, and cubes.
- Splitting a rectangle into rows of squaresDivide a rectangle into rows and columns of equal squares and count them.
- Halves, thirds, and fourths of shapesSplit circles and rectangles into two, three, or four equal shares; name them halves, thirds, or fourths; and see that equal shares can have different shapes.
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Numbers & Place Value · 8 skillsRounding, adding within 1,000, and what fractions like 3/4 mean.
- Rounding to the nearest 10 or 100Round whole numbers to the nearest 10 or 100, such as 347 to 350 or 300, using place value to decide which is closer.
- Adding within 1,000Add numbers when the total is 1,000 or less, such as 456 + 278, quickly and accurately, working with hundreds, tens, and ones.
- Subtracting within 1,000Subtract numbers within 1,000, such as 503 - 267, quickly and accurately, including numbers with zeros like 400 - 156.
- Multiplying by tens, like 4 x 70Multiply one-digit numbers by multiples of ten, such as 4 x 70 = 280, by thinking of it as 4 groups of 7 tens.
- What a fraction like 3/4 meansA fraction like 3/4 means 3 parts of size 1/4, where the whole has been split into 4 equal parts.
- Fractions on a number lineFractions are numbers with their own places on a number line, so 3/4 sits three fourths of the way from 0 to 1.
- Finding equal fractions, like 1/2 = 2/4Spot fractions of the same size, like 1/2 and 2/4; make equal fractions, like 2/3 and 4/6; and write whole numbers as fractions, like 3 = 3/1.
- Comparing fractions by sizeTell which of two fractions is greater when they share a denominator (bottom number), like 2/6 and 5/6, or a numerator (top number), like 3/4 and 3/8.
Problem Solving · 10 skillsMultiplying and dividing, times tables, and two-step story problems.
- Multiplication as equal groupsMultiplication means equal groups, so 5 x 7 is the total number of things in 5 groups of 7.
- Division as sharing into equal groupsDivision means sharing a total into equal groups, so 56 ÷ 8 tells how many each of 8 shares gets, which is 7.
- Multiplying and dividing in story problemsRead a word problem about equal groups, rows, or measurements and decide whether it calls for multiplication or division within 100.
- Finding the missing number, like 7 x ? = 56Find the missing number in equations like 7 x ? = 56 or ? ÷ 3 = 6, using how multiplication and division fit together.
- Shortcuts that make times tables easierMake harder facts easier by rearranging or breaking apart numbers, such as finding 4 x 7 as 4 x 5 plus 4 x 2.
- Using times tables to divideTreat division as a missing-factor question, solving 32 ÷ 8 by asking what number times 8 makes 32.
- Knowing the times tables by heartRecall every product (the answer to a multiplication) of two one-digit numbers from memory, such as 7 x 8 = 56, in any order and without counting.
- Dividing within 100Divide numbers within 100 quickly and accurately, such as 56 ÷ 7 = 8, using the multiplication facts they already know.
- Story problems with two stepsSolve two-step word problems using addition, subtraction, multiplication, or division, and write an equation with a letter standing for the unknown.
- Spotting patterns in times tablesFind patterns in addition and multiplication tables, such as every multiple of 4 being even, and explain why each pattern happens.
Measurement & Data · 9 skillsTime to the minute, area, perimeter, graphs, and measuring.
- Telling time to the minuteRead a clock with hands to the nearest minute, such as 4:37; say the time out loud; and write it the way a digital clock shows it.
- Working out how many minutes have passedFind how many minutes pass between two times, like 3:45 to 4:10; find when something starts or ends; and solve story problems that add or subtract minutes.
- Weighing things and measuring liquidsMeasure and estimate weights in grams and kilograms and liquids in liters, and solve one-step story problems with those amounts.
- Reading picture graphs and bar graphsDraw and read picture graphs and bar graphs where each symbol or square stands for more than one, and answer questions about how many more or fewer.
- Measuring to the nearest quarter inchMeasure lengths to the nearest half or quarter inch and show their measurements on a line plot.
- Area: how much flat space a shape coversWhat area is: the amount of flat space a shape covers, measured by how many equal squares fit inside without gaps or overlaps.
- Finding area by counting squaresFind the area of a shape by counting unit squares, such as square centimeters, square inches, square feet, square meters, or squares they make up themselves.
- Finding the area of a rectangleFind a rectangle's area by multiplying its length by its width, and find the area of L-shaped figures by splitting them into rectangles.
- Perimeter: the distance around a shapeFind the perimeter of a shape, work out a missing side length, and see that rectangles with the same perimeter can have different areas.
Geometry · 2 skillsSorting four-sided shapes and splitting shapes into equal parts.
- Sorting four-sided shapes into familiesSort shapes into bigger groups by shared features, so squares, rectangles, and rhombuses are all quadrilaterals, or four-sided shapes; and draw quadrilaterals that fit none of those.
- Splitting shapes into equal partsSplit shapes into parts with equal area and name each part as a unit fraction, such as 1/4 for each of 4 equal parts.
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Numbers & Place Value · 16 skillsBig numbers; multiplying and dividing them; and fractions and decimals.
- Why each place is worth ten times the nextEach place in a number is worth ten times the place to its right, so the 7 in 700 is ten times the 7 in 70.
- Reading and writing numbers up to a millionRead and write whole numbers up to a million in digits, such as 305,120; in words; and in expanded form.
- Comparing numbers up to a millionCompare two numbers up to a million, place by place from the left, and record the result with >, =, or <.
- Rounding big numbers to any placeRound large whole numbers to any place, like 6,812 to 7,000 for the nearest thousand, and use rounding to make quick estimates.
- Adding numbers up to a millionAdd whole numbers up to a million on paper, such as 46,372 + 28,519, by lining up the places and regrouping when a column makes 10 or more.
- Subtracting numbers up to a millionSubtract whole numbers up to a million on paper, such as 60,205 − 37,418, by lining up the places and regrouping, even across zeros.
- Multiplying large numbers by a one-digit numberMultiply a number of up to four digits by a one-digit number, such as 3,045 × 8, by breaking the larger number apart by place value.
- Multiplying two two-digit numbersMultiply two two-digit numbers, such as 64 × 38, by splitting each one into tens and ones and adding the four smaller products.
- Dividing with remainders, like 87 ÷ 5Divide numbers up to four digits by one-digit numbers, like 87 ÷ 5 = 17 with 2 left over, and explain it with a drawing or an equation.
- Why fractions like 3/4 and 6/8 are equalWhy multiplying the top and bottom of a fraction by the same number gives an equal fraction, like 3/4 = 6/8, and how to show it with a picture.
- Comparing fractions like 2/3 and 5/6Compare fractions with different denominators, like 2/3 and 5/6, using a common denominator or numerator, or comparing to 1/2; and record and explain the result with >, =, or <.
- Adding and subtracting fractions and mixed numbers5/4 is five one-fourths, which can also be split as 2/4 + 3/4; and how to use that to add and subtract fractions and mixed numbers with like denominators.
- Multiplying a fraction by a whole numberMultiply a fraction by a whole number, like 2 × 3/4, by seeing it as repeated groups of the same fraction.
- Adding tenths and hundredths togetherRename tenths as hundredths, like 3/10 = 30/100, and add a tenths fraction and a hundredths fraction together, such as 3/10 + 4/100.
- Writing fractions as decimals, like 0.62Write fractions with denominators of 10 or 100 as decimals, such as 4/10 = 0.4 and 62/100 = 0.62.
- Comparing decimals like 0.09 and 0.1Compare decimals to hundredths, like 0.09 and 0.1, by their size rather than how many digits they have; and record the result with >, =, or <.
Problem Solving · 6 skills"Times as many," multi-step problems, factors, and patterns.
- Reading multiplication as "times as many"Read a multiplication fact like 35 = 5 × 7 as a comparison: 35 is 5 times as many as 7, and 7 times as many as 5.
- Story problems about "times as many"Solve "times as many" word problems, telling them apart from "more than" ones, by choosing to multiply or divide and showing each with a drawing and an equation.
- Multi-step story problems and leftoversSolve word problems that take more than one step, using adding, subtracting, multiplying, and dividing; and decide what a leftover remainder means in the story.
- Finding factors and multiples up to 100Find every factor pair of a number up to 100, see that it is a multiple of each factor, and spot multiples of one-digit numbers.
- Spotting prime numbersTell whether a whole number up to 100 is prime, with exactly two factors, or composite, with more than two.
- Number patterns that follow a ruleBuild number and shape patterns from a rule, like "start at 3 and add 6," and notice and explain features the rule does not state.
Measurement & Data · 7 skillsConverting units, area and perimeter, and measuring angles.
- Converting feet to inches and kilograms to gramsHow units of measure compare in size and how to convert a larger unit into a smaller one in the same system, like 4 feet to 48 inches.
- Story problems about distance, time, and moneySolve word problems about distance, time, liquid volume, weight, and money using all four operations, including some with simple fractions or decimals.
- Using area and perimeter to solve real problemsUse the area and perimeter formulas for rectangles to solve real problems, and find a missing side when the area or perimeter is known.
- Charting measurements in halves, fourths, and eighthsMake line plots of measurements in halves, fourths, and eighths of a unit; and add and subtract those fractions to answer questions about the data.
- What angles are and how degrees measure themAn angle is formed where two rays meet at a point, and angles are measured in degrees as parts of a full 360-degree turn.
- Measuring and drawing angles with a protractorMeasure angles to the nearest whole degree with a protractor and draw angles of a given size, such as 65 degrees.
- Adding angles together to find a missing oneAn angle split into parts that do not overlap equals the sum of those parts, and how to use this to find a missing angle.
Geometry · 3 skillsLines, angles, sorting shapes by their sides, and symmetry.
- Spotting lines, rays, angles, and parallel linesDraw and identify points, lines, line segments, and rays; right, acute, and obtuse angles; and parallel and perpendicular lines, both on their own and inside shapes.
- Sorting shapes by their sides and anglesSort flat shapes by whether they have parallel sides, perpendicular sides, or angles of a certain size; and recognize right triangles as their own group.
- Finding lines of symmetryWhat a line of symmetry is, a line where a shape folds into two matching halves, and how to find and draw lines of symmetry on shapes.
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Numbers & Place Value · 17 skillsDecimals, multiplying and dividing big numbers, and fraction math.
- What each digit is worth, including decimalsEach place in a number is worth ten times the place to its right, including decimals, so 0.09 is one tenth of 0.9.
- Multiplying and dividing by 10, 100, and 1,000Why multiplying and dividing by 10, 100, and 1,000 shifts digits and moves the decimal point; and how to write those numbers as powers of 10, like 10³.
- Reading and writing decimals to thousandthsRead decimals to thousandths by their place names; write them in digits; and break them into expanded form, such as 0.362 = 0.3 + 0.06 + 0.002.
- Comparing decimals to thousandthsCompare two decimals to thousandths by the value of each digit, and record the result with >, =, or <.
- Rounding decimals, like 4.68 to 4.7Round decimals to any place, like 4.68 to the nearest tenth, using place value to decide which nearby number is closer.
- Multiplying big numbers, like 213 × 32Multiply larger whole numbers, like 213 × 32, using the standard written method.
- Dividing by two-digit numbers, like 480 ÷ 16Divide numbers up to four digits by two-digit numbers, like 480 ÷ 16, using place value and multiplication, and explain the steps with a drawing or an equation.
- Adding and subtracting decimals to hundredthsAdd and subtract decimals to hundredths, like 3.4 + 1.25 and 6 - 2.75, using drawings and place value, and explain how a drawing matches the written steps.
- Multiplying decimals to hundredthsMultiply decimals to hundredths, like 4 × 0.75 and 0.2 × 0.3, using drawings and place value, and explain where the decimal point lands in the written answer.
- Dividing decimals to hundredthsDivide decimals to hundredths, like 3.6 ÷ 4 and 3 ÷ 0.5, by sharing equally or by counting how many groups fit, and explain how that matches the written steps.
- Adding and subtracting fractions like 2/3 + 1/4Add and subtract fractions with different denominators, like 2/3 + 1/4, by first renaming them with the same denominator.
- Story problems that add and subtract fractionsSolve word problems that add and subtract fractions of the same whole, and check with estimates that their answers make sense.
- Fractions as sharing, like 3 ÷ 4 = 3/4See a fraction as a division, so 3 ÷ 4 equals 3/4, and solve sharing problems whose answers are fractions or mixed numbers.
- Multiplying fractions, like 2/3 × 4/5Multiply by a fraction, like 2/3 × 4/5 or 5/8 × 16, by thinking of "a fraction of" an amount; and find the area of a rectangle with fraction sides.
- When multiplying makes a number smallerSee multiplication as resizing, and tell without calculating whether multiplying by a fraction makes a number bigger or smaller.
- Multiplying fractions in real life, like recipesSolve real-world problems that multiply fractions and mixed numbers, like scaling a recipe or finding the area of a garden with fractional sides.
- Dividing with fractions, like 1/2 ÷ 4Divide a unit fraction by a whole number, like 1/2 ÷ 4, and divide a whole number by a unit fraction, like 5 ÷ 1/3.
Problem Solving · 3 skillsParentheses, writing number sentences, and comparing patterns.
- Solving number sentences with parenthesesWork out number sentences with parentheses and brackets, and do the grouped part first.
- Turning words into number sentencesTurn words like "add 5 and 7, then triple it" into number expressions, and read what an expression means before calculating.
- Comparing two number patterns on a gridBuild two number patterns from two rules, compare them side by side and explain why they are linked, and plot the matching pairs on a grid.
Measurement & Data · 5 skillsConverting units, line plots, and the volume of a box.
- Converting feet to yards and grams to kilogramsConvert between units in the same system, like feet to yards or grams to kilograms, and use conversions in multi-step problems.
- Measurement charts with halves, quarters, and eighthsMake line plots of measurements in halves, quarters, and eighths; and add, subtract, and share those fractions to answer questions about the data.
- Volume: how much space is inside a solidWhat volume is: the amount of space inside a solid, measured by how many same-size cubes fill it with no gaps or overlaps.
- Finding volume by counting cubesMeasure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and everyday objects as units.
- Finding the volume of a boxFind the volume of a box by multiplying length × width × height, and add the volumes of two boxes joined together.
Geometry · 4 skillsPoints on a grid and sorting shapes into families.
- Finding points on a grid, like (6, 3)Locate points on a coordinate grid, reading (6, 3) as six steps from 0 along the x-axis and three steps up the y-axis, so 6 is its x-coordinate.
- Plotting real-life points on a gridGraph points from real situations on a coordinate grid, and explain what each point means, such as a plant's height after a certain week.
- Why a square is also a rectangleEvery feature of a shape category belongs to all the shapes inside it, so a square has every feature of a rectangle, because it is one.
- Sorting four-sided shapes into a family treeSort shapes into a family tree by their sides and angles, showing how quadrilaterals, parallelograms, rectangles, rhombuses, and squares fit inside each other.
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