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- Mathematics: Key Stage 2 Year 4

# United Kingdom Curriculum - Mathematics: Key Stage 2 Year 4

## Programme of Study | Adopted: 2013

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

NPV.1: : count in multiples of 6, 7, 9, 25 and 1000

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

NPV.2: : find 1000 more or less than a given number

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

NPV.4: : recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)

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

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

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: : order and compare numbers beyond 1000

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

NPV.6: : identify, represent and estimate numbers using different representations

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

NPV.8: : solve number and practical problems that involve all of the above and with increasingly large positive numbers

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

### NAS: : Number - addition and subtraction

NAS.1: : add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate

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.3: : solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

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

### NMD: : Number - multiplication and division

NMD.1: : recall multiplication and division facts for multiplication tables up to 12 × 12

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.2: : use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers

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

NMD.3: : recognise and use factor pairs and commutativity in mental calculations

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

NMD.5: : solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.

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

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

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

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)

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

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

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

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

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

NF.1: : recognise and show, using diagrams, families of common equivalent fractions

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)

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

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

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

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 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 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

Modeling Whole Numbers and Decimals (Base-10 Blocks)

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: : solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number

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, 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

NF.4: : add and subtract fractions with the same denominator

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)

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

NF.5: : recognise and write decimal equivalents of any number of tenths or hundredths

Fraction, Decimal, Percent (Area and Grid Models)

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)

NF.6: : recognise and write decimal equivalents to 1/4, 1/2, 3/4

Fraction, Decimal, Percent (Area and Grid Models)

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.9: : compare numbers with the same number of decimal places up to two decimal places

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

Modeling Decimals (Area and Grid Models)

Modeling Whole Numbers and Decimals (Base-10 Blocks)

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

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

### M: : Measurement

M.1: : Convert between different units of measure [for example, kilometre to metre; hour to minute]

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.3: : find the area of rectilinear shapes by counting squares

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

Fido's Flower Bed (Perimeter and Area)

Construct models of gardens on a grid using squares of sod. Fence the gardens to find and compare perimeters. Work with pre-built gardens made of 36 squares each to compare perimeters of shapes with equal areas. 5 Minute Preview

M.4: : estimate, compare and calculate different measures, including money in pounds and pence

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

### GPS: : Geometry - properties of shapes

GPS.4: : complete a simple symmetric figure with respect to a specific line of symmetry.

Quilting Bee (Symmetry)

Participate in an old-fashioned quilting bee and create a colorful, symmetrical quilt. Quilts can be created with a vertical, horizontal, or diagonal line of symmetry. Quilts can be folded to look for reflections, or rotated to test for rotational symmetry. 5 Minute Preview

### GPD: : Geometry - position and direction

GPD.1: : describe positions on a 2-D grid as coordinates in the first quadrant

City Tour (Coordinates)

Go sightseeing in fictional cities all over the world. Learn about coordinates on a graph by navigating around these cities on a grid-like city map. Some landmarks are shown on the map. For others, you are only given the coordinates. Can you find all of them? 5 Minute Preview

Elevator Operator (Line Graphs)

Operate an elevator in an old apartment building. Pick up and drop off residents where they want to go. A line graph shows where the elevator traveled over time. Operate the elevator either by using the standard up and down controls, or by building a graph to program where you want it to go. 5 Minute Preview

Function Machines 2 (Functions, Tables, and Graphs)

Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

### S: : Statistics

S.2: : solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

Forest Ecosystem

Observe and manipulate the populations of four creatures (trees, deer, bears, and mushrooms) in a forest. Investigate the feeding relationships (food web) in the forest. Determine which creatures are producers, consumers, and decomposers. Pictographs and line graphs show changes in populations over time. 5 Minute Preview

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

Movie Reviewer (Mean and Median)

Movie reviewers rate movies on a scale of 0 to 10. Each movie comes with a set of reviews that can be changed by the user. The mean of a data set can be explored using a see-saw balance model. Students can also find the median, mode, and range of the data set. 5 Minute Preview

Reaction Time 1 (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 1 Student Exploration focuses on range, mode, and median. 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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Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.

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Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.

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