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- Mathematics: Key Stage 2 Year 5

# United Kingdom Curriculum - Mathematics: Key Stage 2 Year 5

## Programme of Study | Adopted: 2013

### NPV: : Number - number and place value

NPV.1: : read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit

Cannonball Clowns (Number Line Estimation)

Launch clowns from a circus cannon and try to hit the target. Drag digit cards on the control panel to set the launch distance and choose an appropriate unit of distance. After practicing your clown-launching skills on a number line, move on to the Big Top, Football Field, School Buses, the Golden Gate Bridge, and more! 5 Minute Preview

Fraction Garden (Comparing Fractions)

Plant flowers in two gardens to help develop fraction sense. The two gardens act as number lines, from 0 to 1. Use the flowers in the gardens to compare fractions and to explore equivalent fractions. Chalk marks can be drawn to divide the garden into equal sections. 5 Minute Preview

Rounding Whole Numbers (Number Line)

Place points on a number line. Round these values to the nearest ten or hundred. Visualize rounding by showing the number line as a hill or series of hills. These hills cause the points to roll to the nearest valley (nearest multiple of ten or one hundred). 5 Minute Preview

Target Sum Card Game (Multi-digit Addition)

Play an addition card game! The goal is to create a sum that is as close as possible to the target sum. Students will deepen their understanding of place value as they get better at playing the game. Many game options allow students to vary the game for more practice. The game can be played with one or two players. 5 Minute Preview

NPV.5: : solve number problems and practical problems that involve all of the above

Rounding Whole Numbers (Number Line)

Place points on a number line. Round these values to the nearest ten or hundred. Visualize rounding by showing the number line as a hill or series of hills. These hills cause the points to roll to the nearest valley (nearest multiple of ten or one hundred). 5 Minute Preview

### NAS: : Number - addition and subtraction

NAS.1: : add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)

Adding Whole Numbers and Decimals (Base-10 Blocks)

Use base-10 blocks to model two numbers. Then combine the blocks to model the sum. Blocks of equal value can be exchanged from one area of the mat to the other to help understand carrying when adding. Four sets of blocks are available to model different place values. 5 Minute Preview

Cargo Captain (Multi-digit Subtraction)

You are the captain of an interplanetary cargo ship, delivering important supplies to the outer planets. The cargo can be stored in barrels, crates, and holds. (There are 10 barrels in a crate, and 10 crates in a hold.) Model multi-digit subtraction by unloading cargo on each planet. 5 Minute Preview

Number Line Frog Hop (Addition and Subtraction)

Live a frog's life as you hop along a number line in search of flies. Learn how addition and subtraction can be represented as movement along a number line. Fred the frog may even help you get better at adding and subtracting two-digit numbers in your head by decomposing them into tens and ones. 5 Minute Preview

Subtracting Whole Numbers and Decimals (Base-10 Blocks)

Use base-10 blocks to model a starting number. Then subtract blocks from this number by dragging them into a subtraction bin. Blocks of equal value can be exchanged from one section of the mat to the other to help understand regrouping and borrowing. Four sets of blocks are available to model different place values. 5 Minute Preview

Target Sum Card Game (Multi-digit Addition)

Play an addition card game! The goal is to create a sum that is as close as possible to the target sum. Students will deepen their understanding of place value as they get better at playing the game. Many game options allow students to vary the game for more practice. The game can be played with one or two players. 5 Minute Preview

NAS.2: : add and subtract numbers mentally with increasingly large numbers

Adding Fractions (Fraction Tiles)

Add fractions with the help of the Fractionator, a fraction-tile-making machine in the Gizmo. Model sums by placing the tiles on side-by-side number lines. Explore the usefulness of common denominators in adding. Express sums as improper fractions or mixed numbers. 5 Minute Preview

Adding Whole Numbers and Decimals (Base-10 Blocks)

Use base-10 blocks to model two numbers. Then combine the blocks to model the sum. Blocks of equal value can be exchanged from one area of the mat to the other to help understand carrying when adding. Four sets of blocks are available to model different place values. 5 Minute Preview

Cargo Captain (Multi-digit Subtraction)

You are the captain of an interplanetary cargo ship, delivering important supplies to the outer planets. The cargo can be stored in barrels, crates, and holds. (There are 10 barrels in a crate, and 10 crates in a hold.) Model multi-digit subtraction by unloading cargo on each planet. 5 Minute Preview

Fractions Greater than One (Fraction Tiles)

Explore fractions greater than one with the Fractionator, a fraction-tile-making machine in the Gizmo. Create sums of fraction tiles on two number lines. Sums greater than one are shown as improper fractions on the top number line, and as mixed numbers on the bottom number line. 5 Minute Preview

Number Line Frog Hop (Addition and Subtraction)

Live a frog's life as you hop along a number line in search of flies. Learn how addition and subtraction can be represented as movement along a number line. Fred the frog may even help you get better at adding and subtracting two-digit numbers in your head by decomposing them into tens and ones. 5 Minute Preview

Subtracting Whole Numbers and Decimals (Base-10 Blocks)

Use base-10 blocks to model a starting number. Then subtract blocks from this number by dragging them into a subtraction bin. Blocks of equal value can be exchanged from one section of the mat to the other to help understand regrouping and borrowing. Four sets of blocks are available to model different place values. 5 Minute Preview

NAS.4: : solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

Adding Whole Numbers and Decimals (Base-10 Blocks)

Use base-10 blocks to model two numbers. Then combine the blocks to model the sum. Blocks of equal value can be exchanged from one area of the mat to the other to help understand carrying when adding. Four sets of blocks are available to model different place values. 5 Minute Preview

Cargo Captain (Multi-digit Subtraction)

You are the captain of an interplanetary cargo ship, delivering important supplies to the outer planets. The cargo can be stored in barrels, crates, and holds. (There are 10 barrels in a crate, and 10 crates in a hold.) Model multi-digit subtraction by unloading cargo on each planet. 5 Minute Preview

Number Line Frog Hop (Addition and Subtraction)

Live a frog's life as you hop along a number line in search of flies. Learn how addition and subtraction can be represented as movement along a number line. Fred the frog may even help you get better at adding and subtracting two-digit numbers in your head by decomposing them into tens and ones. 5 Minute Preview

Subtracting Whole Numbers and Decimals (Base-10 Blocks)

Use base-10 blocks to model a starting number. Then subtract blocks from this number by dragging them into a subtraction bin. Blocks of equal value can be exchanged from one section of the mat to the other to help understand regrouping and borrowing. Four sets of blocks are available to model different place values. 5 Minute Preview

### NMD: : Number - multiplication and division

NMD.1: : identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers

Chocomatic (Multiplication, Arrays, and Area)

Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar. 5 Minute Preview

Factor Trees (Factoring Numbers)

The Factor Trees Gizmo has two modes. In Factor mode, you can create factor trees to factor composite numbers into primes. In Build mode, you can build numbers by multiplying primes together. Can you build all composite numbers up to 50? Any whole composite number up to 999 can be factored or built with the Gizmo. 5 Minute Preview

Pattern Flip (Patterns)

In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck! 5 Minute Preview

NMD.2: : know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers

Chocomatic (Multiplication, Arrays, and Area)

Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar. 5 Minute Preview

Factor Trees (Factoring Numbers)

The Factor Trees Gizmo has two modes. In Factor mode, you can create factor trees to factor composite numbers into primes. In Build mode, you can build numbers by multiplying primes together. Can you build all composite numbers up to 50? Any whole composite number up to 999 can be factored or built with the Gizmo. 5 Minute Preview

NMD.3: : establish whether a number up to 100 is prime and recall prime numbers up to 19

Chocomatic (Multiplication, Arrays, and Area)

Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar. 5 Minute Preview

Factor Trees (Factoring Numbers)

The Factor Trees Gizmo has two modes. In Factor mode, you can create factor trees to factor composite numbers into primes. In Build mode, you can build numbers by multiplying primes together. Can you build all composite numbers up to 50? Any whole composite number up to 999 can be factored or built with the Gizmo. 5 Minute Preview

NMD.4: : multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers

Critter Count (Modeling Multiplication)

Use groups of critters on leaves to model multiplication as repeated addition. Change the expression to change the number of groups or the number of critters per group. Display the critters either on leaves or as a rectangular array. 5 Minute Preview

NMD.5: : multiply and divide numbers mentally drawing upon known facts

Multiplying Decimals (Area Model)

Model the product of two decimals by finding the area of a rectangle. Estimate the area of the rectangle first. Then break the rectangle into several pieces and find the area of each piece (partial product). Add these areas together to find the whole area (product). 5 Minute Preview

NMD.6: : divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context

No Alien Left Behind (Division with Remainders)

The alien school children from the planet Zigmo travel to distant planets on a field trip. The goal is to select a bus size so that all buses are full and no aliens are left behind. This is a nice illustration of division with remainders. 5 Minute Preview

NMD.9: : solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes

Chocomatic (Multiplication, Arrays, and Area)

Critter Count (Modeling Multiplication)

Use groups of critters on leaves to model multiplication as repeated addition. Change the expression to change the number of groups or the number of critters per group. Display the critters either on leaves or as a rectangular array. 5 Minute Preview

Factor Trees (Factoring Numbers)

Pattern Flip (Patterns)

In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck! 5 Minute Preview

NMD.11: : solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

Critter Count (Modeling Multiplication)

Use groups of critters on leaves to model multiplication as repeated addition. Change the expression to change the number of groups or the number of critters per group. Display the critters either on leaves or as a rectangular array. 5 Minute Preview

Factor Trees (Factoring Numbers)

Multiplying Decimals (Area Model)

Model the product of two decimals by finding the area of a rectangle. Estimate the area of the rectangle first. Then break the rectangle into several pieces and find the area of each piece (partial product). Add these areas together to find the whole area (product). 5 Minute Preview

No Alien Left Behind (Division with Remainders)

The alien school children from the planet Zigmo travel to distant planets on a field trip. The goal is to select a bus size so that all buses are full and no aliens are left behind. This is a nice illustration of division with remainders. 5 Minute Preview

Pattern Flip (Patterns)

In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck! 5 Minute Preview

### NF: : Number - fractions (including decimals and percentages)

NF.1: : compare and order fractions whose denominators are all multiples of the same number

Factor Trees (Factoring Numbers)

Fraction Artist 2 (Area Models of Fractions)

Extend understanding of fractions by making modern paintings in the style of Piet Mondrian. Create and analyze paintings with different-sized sections. Compare the sizes of unit fractions. Find creative ways to color one-half of a painting. This can be a nice introduction to adding fractions with unlike denominators. 5 Minute Preview

Modeling Fractions (Area Models)

Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare fractions visually, on a number line, or numerically using the least common denominator. 5 Minute Preview

NF.2: : identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths

Adding Fractions (Fraction Tiles)

Add fractions with the help of the Fractionator, a fraction-tile-making machine in the Gizmo. Model sums by placing the tiles on side-by-side number lines. Explore the usefulness of common denominators in adding. Express sums as improper fractions or mixed numbers. 5 Minute Preview

Equivalent Fractions (Fraction Tiles)

Explore fractions using the Fractionator, the machine that makes fraction tiles. Compare fractions and find equivalent fractions by arranging the tiles on two horizontal rows. Explore simplifying fractions. Add fractions and express sums as improper fractions or mixed numbers. 5 Minute Preview

Factor Trees (Factoring Numbers)

Fraction Artist 1 (Area Models of Fractions)

Develop understanding of fractions by making modern paintings. Find different ways to divide a canvas into equal-sized sections. Make paintings to represent simple fractions and to find fractions that are equivalent to one-half. 5 Minute Preview

Fraction Artist 2 (Area Models of Fractions)

Extend understanding of fractions by making modern paintings in the style of Piet Mondrian. Create and analyze paintings with different-sized sections. Compare the sizes of unit fractions. Find creative ways to color one-half of a painting. This can be a nice introduction to adding fractions with unlike denominators. 5 Minute Preview

Fraction Garden (Comparing Fractions)

Plant flowers in two gardens to help develop fraction sense. The two gardens act as number lines, from 0 to 1. Use the flowers in the gardens to compare fractions and to explore equivalent fractions. Chalk marks can be drawn to divide the garden into equal sections. 5 Minute Preview

Fractions Greater than One (Fraction Tiles)

Explore fractions greater than one with the Fractionator, a fraction-tile-making machine in the Gizmo. Create sums of fraction tiles on two number lines. Sums greater than one are shown as improper fractions on the top number line, and as mixed numbers on the bottom number line. 5 Minute Preview

Modeling Fractions (Area Models)

Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare fractions visually, on a number line, or numerically using the least common denominator. 5 Minute Preview

Toy Factory (Set Models of Fractions)

Create a set of stuffed animals: monkeys, giraffes, and rabbits. Toys can be painted red, green, or blue. Describe the makeup of the set (animals or colors) with fractions. Arrange the toys into groups to simplify the fractions. 5 Minute Preview

NF.3: : recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 2/5 + 4/5 = 6/5 = 1 1/5]

Fractions Greater than One (Fraction Tiles)

Explore fractions greater than one with the Fractionator, a fraction-tile-making machine in the Gizmo. Create sums of fraction tiles on two number lines. Sums greater than one are shown as improper fractions on the top number line, and as mixed numbers on the bottom number line. 5 Minute Preview

NF.4: : add and subtract fractions with the same denominator and denominators that are multiples of the same number

Adding Fractions (Fraction Tiles)

Add fractions with the help of the Fractionator, a fraction-tile-making machine in the Gizmo. Model sums by placing the tiles on side-by-side number lines. Explore the usefulness of common denominators in adding. Express sums as improper fractions or mixed numbers. 5 Minute Preview

Fraction Artist 2 (Area Models of Fractions)

Extend understanding of fractions by making modern paintings in the style of Piet Mondrian. Create and analyze paintings with different-sized sections. Compare the sizes of unit fractions. Find creative ways to color one-half of a painting. This can be a nice introduction to adding fractions with unlike denominators. 5 Minute Preview

Fractions Greater than One (Fraction Tiles)

Modeling Fractions (Area Models)

Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare fractions visually, on a number line, or numerically using the least common denominator. 5 Minute Preview

NF.5: : multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

Factor Trees (Factoring Numbers)

NF.6: : read and write decimal numbers as fractions [for example, 0.71 = 10071]

Fraction, Decimal, Percent (Area and Grid Models)

Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview

Modeling Decimals (Area and Grid Models)

Model and compare decimals using area models. Set the number of sections in each model to 1, 10, or 100, and then click in the models to shade sections. Compare decimals visually and on a number line. 5 Minute Preview

NF.7: : recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

Fraction, Decimal, Percent (Area and Grid Models)

Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview

Modeling Decimals (Area and Grid Models)

Model and compare decimals using area models. Set the number of sections in each model to 1, 10, or 100, and then click in the models to shade sections. Compare decimals visually and on a number line. 5 Minute Preview

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Model numbers with base-10 blocks. Drag flats, rods, and individual cubes onto a mat to model a number. Blocks can be exchanged from one area of the mat to the other. Four sets of blocks are available to model a variety of whole numbers and decimals. 5 Minute Preview

NF.9: : read, write, order and compare numbers with up to three decimal places

Adding Whole Numbers and Decimals (Base-10 Blocks)

Modeling Decimals (Area and Grid Models)

Model and compare decimals using area models. Set the number of sections in each model to 1, 10, or 100, and then click in the models to shade sections. Compare decimals visually and on a number line. 5 Minute Preview

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Model numbers with base-10 blocks. Drag flats, rods, and individual cubes onto a mat to model a number. Blocks can be exchanged from one area of the mat to the other. Four sets of blocks are available to model a variety of whole numbers and decimals. 5 Minute Preview

Subtracting Whole Numbers and Decimals (Base-10 Blocks)

Treasure Hunter (Decimals on the Number Line)

Drive a desert highway searching for buried treasure. Learn to use the car's tens, ones, tenths, and hundredths gears, along with a GPS system (number line), to find the right place to dig. Plot your findings on a zoomable number line map. Can you become a master Treasure Hunter? 5 Minute Preview

NF.10: : solve problems involving number up to three decimal places

Fraction, Decimal, Percent (Area and Grid Models)

Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview

Modeling Decimals (Area and Grid Models)

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Model numbers with base-10 blocks. Drag flats, rods, and individual cubes onto a mat to model a number. Blocks can be exchanged from one area of the mat to the other. Four sets of blocks are available to model a variety of whole numbers and decimals. 5 Minute Preview

Multiplying Decimals (Area Model)

Model the product of two decimals by finding the area of a rectangle. Estimate the area of the rectangle first. Then break the rectangle into several pieces and find the area of each piece (partial product). Add these areas together to find the whole area (product). 5 Minute Preview

Treasure Hunter (Decimals on the Number Line)

Drive a desert highway searching for buried treasure. Learn to use the car's tens, ones, tenths, and hundredths gears, along with a GPS system (number line), to find the right place to dig. Plot your findings on a zoomable number line map. Can you become a master Treasure Hunter? 5 Minute Preview

NF.11: : recognise the per cent symbol (%) and understand that per cent relates to 'number of parts per hundred', and write percentages as a fraction with denominator 100, and as a decimal

Fraction, Decimal, Percent (Area and Grid Models)

NF.12: : solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25.

Fraction, Decimal, Percent (Area and Grid Models)

Modeling Decimals (Area and Grid Models)

### M: : Measurement

M.1: : convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)

Cannonball Clowns (Number Line Estimation)

Launch clowns from a circus cannon and try to hit the target. Drag digit cards on the control panel to set the launch distance and choose an appropriate unit of distance. After practicing your clown-launching skills on a number line, move on to the Big Top, Football Field, School Buses, the Golden Gate Bridge, and more! 5 Minute Preview

M.5: : estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water]

Balancing Blocks (Volume)

This Gizmo provides you with two challenges. First, use blocks to build a figure with a given volume. Then, try to balance the blocks on a platform that sits on the tip of a cone. The dimensions of the platform can be adjusted, and blocks can be added or deleted by clicking on the model. 5 Minute Preview

### GPS: : Geometry - properties of shapes

GPS.4: : identify:

GPS.4.a: : angles at a point and one whole turn (total 360°)

Classifying Quadrilaterals

Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview

GPS.4.b: : angles at a point on a straight line and 1/2 a turn (total 180°)

Classifying Quadrilaterals

Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview

GPS.4.c: : other multiples of 90°

Classifying Quadrilaterals

Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview

GPS.5: : use the properties of rectangles to deduce related facts and find missing lengths and angles

Classifying Quadrilaterals

### GPD: : Geometry - position and direction

GPD.1: : identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed.

Rock Art (Transformations)

Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview

### S: : Statistics

S.1: : solve comparison, sum and difference problems using information presented in a line graph

Graphing Skills

Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview

S.2: : complete, read and interpret information in tables, including timetables.

Mascot Election (Pictographs and Bar Graphs)

A brand new school is opening and it is time to elect the school mascot! Students can choose the Eagle, Lion, Bear, or Wolf. Voting results can be displayed in a table, tally chart, pictograph, bar graph, circle graph, or dot plot. You can change student votes by selecting a group of students and clicking a mascot. 5 Minute Preview

Reaction Time 2 (Graphs and Statistics)

Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean. 5 Minute Preview

Correlation last revised: 9/16/2020

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