data problem solving year 4

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Statistics Mastery Activities – Year 4

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

4 January 2020

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Click the link below for the complete Year 4 resource pack (all 42 objectives)

Year 4 Maths Mastery Pack

These are a range of activities/tasks to demonstrate mastery and develop deeper thinking and deeper understanding of year 4 Statistics objectives. For each objective there are at least 3 activities/tasks along with answers (where possible). The document is set up so that you can quickly jump to the objective you are covering and then simply print the appropriate pages. In addition, almost all the activities can be adapted to suit your class’s needs if necessary.

Finding or creating resources to evidence mastery and deeper understanding can take hours of time (and a lot of frustration). With this resource, you will have a handy bank of activities/tasks that you can choose from in seconds!

Objectives covered:

Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs

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This was excellent but not suitable for my class level but still good work.

Hi SueHotta. The year 3 resource (also free) is available here and may be more suitable for your class level: https://www.tes.com/teaching-resource/statistics-mastery-activities-year-3-11878982 Thanks for the review :)

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Your child will answer questions using time graphs. For example, they may need to work out the distance travelled in ten minutes, to find the total journey length, or to point out when the car was not moving.

Solve problems using information from bar charts, pictograms, tables, and other graphs

What is the total number of children who preferred apples and grapes? What is the difference in the number of children who preferred strawberries to oranges?

Your child will solve problems by comparing information from graphs. For example:

Using the graph, what is the difference in temperature between Monday and Friday last week?

Total and compare categorical data

Your child will ask and answer questions about data they collect, and will be able to make comparisons using the data. For example:

How many children took part in the survey? Which option was most popular? Which was least popular?

How to help at home

There are lots of everyday ways you can help your child to understand statistics. Here are just a few ideas.

1. Create a time graph

Time graphs show distance travelled over time. The vertical y -axis of a time graph shows the distance travelled, and the horizontal x -axis shows the time it has taken. Your child will learn to create time graphs by plotting points on the graph and then connecting these points to create a continuous line.

Your child will be given a table of data such as:

They will then plot this information as points on the graph and join the points to create a continuous line:

See if your child to create their own time graph. They can gather data themselves – for example, tracking a walk, a bike ride, or their journey to school. Can they present the data in a table and present the data in a time graph? Multiple lines representing different days could also show improvement at a distance sport like running.

2. Interpret data

There are many non-fiction books that present data in interesting ways. Discuss with your child why the author of the book has decided to present the information in a particular way.

Ask questions and encourage your child to ask their own questions about data. Pay careful attention to the scales on the graphs and support children to read these accurately. This can help your child learn to spot data that is shown in a potentially misleading way, a very useful life skill!

3. Create charts and graphs using a computer

Why not encourage your child to explore computer programs (like Excel or Google Sheets) to create their own tables and graphs?

For example, your child could compare different types of animals using statistics like population, size, or life expectancy. They could then come up with a series of questions for you to answer using their charts. Which animals are the most populous? How much bigger is the biggest animal than the smallest animal?

Once they have practised lots of ways of showing information, your child should be able to decide which ways of showing data are most appropriate to different situations and to be able to explain why.

Activity: Data handling

Use the bar graph to answer questions.

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Years 3 & 4: Data and Statistics

This list consists of activities, games and videos designed to support the new curriculum programme of study in Years 3 and 4. Containing tips on using the resources and suggestions for further use, it covers:

Year 3:  Interpret and present data using bar charts, pictograms and tables, solve one-step and two-step questions (for example, ‘How many more?’ and ‘How many fewer?’) using information presented in scaled bar charts and pictograms and tables.

Year 4 : Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs, solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

Visit the primary mathematics webpage to access all lists.

Data Handling

Quality Assured Category: Mathematics Publisher: Teachers TV

This video shows three ideas for use in class when teaching data handling. Creating a human bar graph is a great way of helping children learn about the scales on a bar graph and what they represent. 

Collecting data for a purpose helps show children one way in which maths is used in the real world. Have fun measuring and recording results from the long jump, high jump and target practice, then represent and analyse the data using Venn diagrams and graphs.

Another idea asks children to use a ‘Tardis’ in their classroom to estimate when 30 seconds have elapsed. After collecting the data, they produce a graph on the interactive whiteboard.

Starting Data Handling

Quality Assured Category: Mathematics Publisher: Unwin Hyman Ltd

A collection of 40 activity sheets which could be used in class to process, represent and interpret data using block graphs, pictograms and frequency tables. Aimed at Curriculum levels 1-3, there are opportunities for using them with the whole class or to support children with work in data handling.

Analysing and Interpreting Data

Quality Assured Category: Mathematics Publisher: SMILE

Two packs of games, investigations, worksheets and practical activities. The first pack asks children to interpret and answer questions on rainfall over a year. There is also a sheet which asks children to measure and collect data on hand span within a class. This idea could be adapted to measure and record forearm length within a class/across the school when learning about growth of humans in science. 

Handling Data: African Animal Maths (Age 7 to 11)

Quality Assured Category: Mathematics Publisher: Wildscreen ARK (previously ARKive)

Look at the practical application of data handling and analysis in this activity which explores measurement data for a range of species found in the African savannah. Children use data to fill in a table, and then construct and interpret bar charts for a range of different measurements (height, length, weight).

This is a great opportunity to link science and mathematics.

Handling Data

Quality Assured Category: Mathematics Publisher: Centre for Innovation in Mathematics Teaching

Designed for teachers to develop professionally and gain confidence in the teaching of mathematics, new teachers and those looking for a refresher will benefit greatly from Part A.  Page 16 starts looking at pictograms and bar charts as a way of representing discrete data, Page 29 looks at line graphs as a way of representing trends over time such as temperature change and rainfall.

The difference between the terms discrete and continuous data is often misunderstood by children with some trying to show a change over time using a bar chart. The worked examples in this booklet help to clarify the different charts used to represent data. Page 34 looks at histograms and how they are used to represent continuous data.

The booklet highlights some common misconceptions children may have and how to overcome these as well as examples for teachers to work through to gain confidence in this area of mathematics.

NRICH: Handling Data KS2

A collection of activities which allow children to investiagte problems centred around data handling.

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Handling Data KS2

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

How Big Are Classes 5, 6 and 7?

Use the two sets of data to find out how many children there are in Classes 5, 6 and 7.

Take Your Dog for a Walk

Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?

Real Statistics

Have a look at this table of how children travel to school. How does it compare with children in your class?

Venn Diagrams

How will you complete these interactive Venn diagrams?

The Car That Passes

What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?

Class 5's Names

Class 5 were looking at the first letter of each of their names. They created different charts to show this information. Can you work out which member of the class was away on that day?

The Domesday Project

Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?

If the World Were a Village

This activity is based on data in the book 'If the World Were a Village'. How will you represent your chosen data for maximum effect?

This problem explores the range of events in a sports day and which ones are the most popular and attract the most entries.

Going for Gold

Looking at the 2012 Olympic Medal table, can you see how the data is organised? Could the results be presented differently to give another nation the top place?

Now and Then

Look at the changes in results on some of the athletics track events at the Olympic Games in 1908 and 1948. Compare the results for 2012.

Problem solving

Part of KS2 Maths

How to solve maths problems

Find out how you can use maths to solve your problems.

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Discover how numbers can be connected in a pattern and see if you can solve the puzzle.

Play Guardians maths game!

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Data handling year 4

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DATA HANDLING - PROBLEM SOLVING YEAR 4

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Reasoning/Problem Solving Maths Worksheets for Year 4 (age 8-9)

This category is all about children choosing the most appropriate method to achieve a quick and accurate answer and to be able to explain their methods and reasoning.

Problem solving: finding the missing digits in 4-digit numbers. Tricky!

Problem solving: finding the values of missing counters. Logical thinking and careful work needed here!

Reasoning about numbers on a number line and rounding numbers.

More reasoning about number and place value.

Not only do the questions have to be answered, but explanations given. These pages really show how well children understand what they are doing.

More written explanations on which operation to use and whether the question should be done mentally or on paper.

Lots of questions, most of which can be done mentally. The important thing is to explain how they were tackled.

Decide which operation is needed (add, subtract, multiply, divide) and whether a calculator, or pencil and paper are needed, or whether it can be done, 'in your head'.

Solving problems

A selection of problem solving activities and word problems.

Here are some problems written in words. Fairly straightforward as they require just one mathematical step to work out the answer

Some word problems that need at least two steps to find the answer. This makes them much harder, so careful thinking is needed.

5 pages of word problems, all involving money. Some are suitable for calculator work as they are specially written to make the process the most important factor: it is no use having a calculator if you don't know what calculation to carry out!

A range of number and money problems, typical of those found in KS2 test papers.

More number and money problems, typical of those found in KS2 test papers.

Tricky word problems involving time and money.

More word problems; this time on measurement of length, mass and capacity. These really test children's understanding of when to use addition, subtraction, multiplication or division to solve a problem.

Time problems are especially tricky, especially when finding lengths of time that cross the hour boundary. A good knowledge of the number of days in each month is also needed.

Not many problems on a page, but there is an awful lot within each question. Each is a mini investigation, which can be explored in depth.

Number patterns, remainders, number machines and much more in this mixed selection of problems.

Working out the missing value.

More working out missing values.

Using the instructions on the packet what is the maximum number of bulbs that can be grown in the garden?

Using the instructions on the packet what is the maximum number of seeds that can be sown in the garden?

Using the instructions on the packet what is the maximum number of vegetables that can be grown in the garden?

An addition challenge suitable for year 4 on.

The fish are all called numbers. Can you work out their names by solving the clues?

Investigations

More open ended activities where children choose the approach to the task.

Making rules for sequences is an early step towards understanding algebra, and an important part of Year 5 maths. More 'How would you...?' type questions as well.

How many different three course meals can Sam choose?

Investigate patterns made by placing consecutive numbers in a number square.

A great little investigation which has plenty of extension possibilities.

Fun addition investigation using the date: 22.02.2022.

Some thoughts on how important this area of maths is.

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Year 4 Money Challenges Solving Money Problems

Welcome to our Year 4 Money Challenges page. Here you will find our selection of printable money problem worksheets to help your child learn to use their money skills to solve a range of problems.

These challenges are a great resource as an extension for more able pupils, or to consolidate and extend learning.

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Year 3 Money Learning

Knowing how to handle and calculate with money is a very important life-skill.

During Year 3, children build on their knowledge and skills they have achieved during Year 2.

By the time children reach the end of Year 3, they should be able to:-

• use decimal notation for amounts of money, e.g. £3.27
• change amounts in £ to amounts in pence and back;
• count money up to £10;
• calculate change for amounts of money up to £1 mentally;
• solve simple problems involving money;
• use informal methods to add and subtract money amounts in £ and pence.

Our worksheets will support your child with these objectives.

Year 4 Money Challenges Information

The following worksheets involve solving challenges involving money amounts. They are a great way to consolidate and extend money learning once children are confident with counting money amounts.

The challenges start off at a fairly easy level with problems that involve lower value coins and smaller money amounts. The challenges later on involve more complex problems with larger values to calculate.

If you are teaching a class or group of children, then these sheets should give you some great differentiated learning activities with a money theme.

An answer sheet is available for each challenge provided.

The money challenges in each section are carefully graded, allowing you to introduce concepts at an easier level before introducing harder work, or differentiate within your class.

Using the sheets in this section will help your child to:

• count money in coins;
• develop their reasoning and thinking skills;
• solve problems involving money.

All the money worksheets in this section will help your child to become more confident with money, and develop better problem solving skills.

These problems and challenges build on our Year 3 Money Challenges .

Year 4 Money Challenges Worksheets

There are 3 challenges - Tyger's Money Square Challenge, Row of Coins Challenge and How Much Money Challenge.

Each main challenge has several versions which start with the easiest level and progress onto harder levels of challenge.

Row of Coins Challenges

• Row of Coins Challenge 4:1
• PDF version
• Row of Coins Challenge 4:2

Tyger's Money Square Challenges

• Tyger's Money Square Challenge 4:1
• Tyger's Money Square Challenge 4:2
• Tyger's Money Square Challenge 4:3

How Much Money Challenges

• How Much Money Challenge 4:1
• How Much Money Challenge 4:2

Match the Coins

• Match the Coins 4:1
• Match the Coins 4:2

Extension Activity Ideas

If you are looking for a way to extend learning with the How Much Money challenge, why not...

Try playing 'How Much Money' in pairs.

One person chooses 2 or 3 coins and the other person has to ask questions which involve 'yes' or 'no' answers.

To make the game more interesting, have a maximum of 5 questions before you make a guess!

Looking for some more UK money worksheets?

We also have some counting money worksheets with amounts up to £1 or £5.

The sheets are at a more basic level than those on this page.

• Free UK Money Worksheets Coins up to £1
• Year 3 Money Worksheets Coins up to £5
• Year 3 Money Challenges

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Money Riddles

These puzzles are a great money starter activity to get children thinking and puzzling out which the correct answer is out of a set number of choices. They are great for partner work too.

UK Money Riddles

If you are looking for some fun learning puzzles involving money, then look no further.

The puzzle sheets in this section are designed primarily for children in Years 3 and 4 who need to develop their problem solving skills and mathematical language.

Using these challenges will help your child to:

• apply their existing skills to puzzle out clues;
• understand money terminology;
• develop their thinking skills.
• Money Riddles for Kids (UK coins)

Money Column Addition Worksheets

Here you will find a selection of Column Addition Money sheets designed to help your child add different amounts of money.

Using these sheets will help your child to:

• add up a range of money amounts involving decimals.

The worksheets in this section are aimed at children in Years 4 and 5.

• Column Addition Money Worksheets (UK)

Money Column Subtraction Worksheets

Here you will find a selection of Column Subtraction Money sheets designed to help your child subtract different amounts of money.

• subtract a range of money amounts involving decimals.
• Column Subtraction Money Worksheets (UK)
• Counting Money Games

Here is our collection of counting money games for kids.

All of these games are suitable for kids aged from 1st grade and upwards.

Playing games is a great way to practice math skills in a fun way. Games also help to develop reasoning, thinking and memory.

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What the data says about crime in the U.S.

A growing share of Americans say reducing crime should be a top priority for the president and Congress to address this year. Around six-in-ten U.S. adults (58%) hold that view today, up from 47% at the beginning of Joe Biden’s presidency in 2021.

We conducted this analysis to learn more about U.S. crime patterns and how those patterns have changed over time.

The analysis relies on statistics published by the FBI, which we accessed through the Crime Data Explorer , and the Bureau of Justice Statistics (BJS), which we accessed through the  National Crime Victimization Survey data analysis tool .

To measure public attitudes about crime in the U.S., we relied on survey data from Pew Research Center and Gallup.

Additional details about each data source, including survey methodologies, are available by following the links in the text of this analysis.

With the issue likely to come up in this year’s presidential election, here’s what we know about crime in the United States, based on the latest available data from the federal government and other sources.

How much crime is there in the U.S.?

It’s difficult to say for certain. The  two primary sources of government crime statistics  – the Federal Bureau of Investigation (FBI) and the Bureau of Justice Statistics (BJS) – paint an incomplete picture.

The FBI publishes  annual data  on crimes that have been reported to law enforcement, but not crimes that haven’t been reported. Historically, the FBI has also only published statistics about a handful of specific violent and property crimes, but not many other types of crime, such as drug crime. And while the FBI’s data is based on information from thousands of federal, state, county, city and other police departments, not all law enforcement agencies participate every year. In 2022, the most recent full year with available statistics, the FBI received data from 83% of participating agencies .

BJS, for its part, tracks crime by fielding a  large annual survey of Americans ages 12 and older and asking them whether they were the victim of certain types of crime in the past six months. One advantage of this approach is that it captures both reported and unreported crimes. But the BJS survey has limitations of its own. Like the FBI, it focuses mainly on a handful of violent and property crimes. And since the BJS data is based on after-the-fact interviews with crime victims, it cannot provide information about one especially high-profile type of offense: murder.

All those caveats aside, looking at the FBI and BJS statistics side-by-side  does  give researchers a good picture of U.S. violent and property crime rates and how they have changed over time. In addition, the FBI is transitioning to a new data collection system – known as the National Incident-Based Reporting System – that eventually will provide national information on a much larger set of crimes , as well as details such as the time and place they occur and the types of weapons involved, if applicable.

Which kinds of crime are most and least common?

Property crime in the U.S. is much more common than violent crime. In 2022, the FBI reported a total of 1,954.4 property crimes per 100,000 people, compared with 380.7 violent crimes per 100,000 people.  

By far the most common form of property crime in 2022 was larceny/theft, followed by motor vehicle theft and burglary. Among violent crimes, aggravated assault was the most common offense, followed by robbery, rape, and murder/nonnegligent manslaughter.

BJS tracks a slightly different set of offenses from the FBI, but it finds the same overall patterns, with theft the most common form of property crime in 2022 and assault the most common form of violent crime.

How have crime rates in the U.S. changed over time?

Both the FBI and BJS data show dramatic declines in U.S. violent and property crime rates since the early 1990s, when crime spiked across much of the nation.

Using the FBI data, the violent crime rate fell 49% between 1993 and 2022, with large decreases in the rates of robbery (-74%), aggravated assault (-39%) and murder/nonnegligent manslaughter (-34%). It’s not possible to calculate the change in the rape rate during this period because the FBI  revised its definition of the offense in 2013 .

The FBI data also shows a 59% reduction in the U.S. property crime rate between 1993 and 2022, with big declines in the rates of burglary (-75%), larceny/theft (-54%) and motor vehicle theft (-53%).

Using the BJS statistics, the declines in the violent and property crime rates are even steeper than those captured in the FBI data. Per BJS, the U.S. violent and property crime rates each fell 71% between 1993 and 2022.

While crime rates have fallen sharply over the long term, the decline hasn’t always been steady. There have been notable increases in certain kinds of crime in some years, including recently.

In 2020, for example, the U.S. murder rate saw its largest single-year increase on record – and by 2022, it remained considerably higher than before the coronavirus pandemic. Preliminary data for 2023, however, suggests that the murder rate fell substantially last year .

How do Americans perceive crime in their country?

Americans tend to believe crime is up, even when official data shows it is down.

In 23 of 27 Gallup surveys conducted since 1993 , at least 60% of U.S. adults have said there is more crime nationally than there was the year before, despite the downward trend in crime rates during most of that period.

While perceptions of rising crime at the national level are common, fewer Americans believe crime is up in their own communities. In every Gallup crime survey since the 1990s, Americans have been much less likely to say crime is up in their area than to say the same about crime nationally.

Public attitudes about crime differ widely by Americans’ party affiliation, race and ethnicity, and other factors . For example, Republicans and Republican-leaning independents are much more likely than Democrats and Democratic leaners to say reducing crime should be a top priority for the president and Congress this year (68% vs. 47%), according to a recent Pew Research Center survey.

How does crime in the U.S. differ by demographic characteristics?

Some groups of Americans are more likely than others to be victims of crime. In the  2022 BJS survey , for example, younger people and those with lower incomes were far more likely to report being the victim of a violent crime than older and higher-income people.

There were no major differences in violent crime victimization rates between male and female respondents or between those who identified as White, Black or Hispanic. But the victimization rate among Asian Americans (a category that includes Native Hawaiians and other Pacific Islanders) was substantially lower than among other racial and ethnic groups.

The same BJS survey asks victims about the demographic characteristics of the offenders in the incidents they experienced.

In 2022, those who are male, younger people and those who are Black accounted for considerably larger shares of perceived offenders in violent incidents than their respective shares of the U.S. population. Men, for instance, accounted for 79% of perceived offenders in violent incidents, compared with 49% of the nation’s 12-and-older population that year. Black Americans accounted for 25% of perceived offenders in violent incidents, about twice their share of the 12-and-older population (12%).

As with all surveys, however, there are several potential sources of error, including the possibility that crime victims’ perceptions about offenders are incorrect.

How does crime in the U.S. differ geographically?

There are big geographic differences in violent and property crime rates.

For example, in 2022, there were more than 700 violent crimes per 100,000 residents in New Mexico and Alaska. That compares with fewer than 200 per 100,000 people in Rhode Island, Connecticut, New Hampshire and Maine, according to the FBI.

The FBI notes that various factors might influence an area’s crime rate, including its population density and economic conditions.

What percentage of crimes are reported to police? What percentage are solved?

Most violent and property crimes in the U.S. are not reported to police, and most of the crimes that  are  reported are not solved.

In its annual survey, BJS asks crime victims whether they reported their crime to police. It found that in 2022, only 41.5% of violent crimes and 31.8% of household property crimes were reported to authorities. BJS notes that there are many reasons why crime might not be reported, including fear of reprisal or of “getting the offender in trouble,” a feeling that police “would not or could not do anything to help,” or a belief that the crime is “a personal issue or too trivial to report.”

Most of the crimes that are reported to police, meanwhile,  are not solved , at least based on an FBI measure known as the clearance rate . That’s the share of cases each year that are closed, or “cleared,” through the arrest, charging and referral of a suspect for prosecution, or due to “exceptional” circumstances such as the death of a suspect or a victim’s refusal to cooperate with a prosecution. In 2022, police nationwide cleared 36.7% of violent crimes that were reported to them and 12.1% of the property crimes that came to their attention.

Which crimes are most likely to be reported to police? Which are most likely to be solved?

Around eight-in-ten motor vehicle thefts (80.9%) were reported to police in 2022, making them by far the most commonly reported property crime tracked by BJS. Household burglaries and trespassing offenses were reported to police at much lower rates (44.9% and 41.2%, respectively), while personal theft/larceny and other types of theft were only reported around a quarter of the time.

Among violent crimes – excluding homicide, which BJS doesn’t track – robbery was the most likely to be reported to law enforcement in 2022 (64.0%). It was followed by aggravated assault (49.9%), simple assault (36.8%) and rape/sexual assault (21.4%).

The list of crimes  cleared  by police in 2022 looks different from the list of crimes reported. Law enforcement officers were generally much more likely to solve violent crimes than property crimes, according to the FBI.

The most frequently solved violent crime tends to be homicide. Police cleared around half of murders and nonnegligent manslaughters (52.3%) in 2022. The clearance rates were lower for aggravated assault (41.4%), rape (26.1%) and robbery (23.2%).

When it comes to property crime, law enforcement agencies cleared 13.0% of burglaries, 12.4% of larcenies/thefts and 9.3% of motor vehicle thefts in 2022.

Are police solving more or fewer crimes than they used to?

Nationwide clearance rates for both violent and property crime are at their lowest levels since at least 1993, the FBI data shows.

Police cleared a little over a third (36.7%) of the violent crimes that came to their attention in 2022, down from nearly half (48.1%) as recently as 2013. During the same period, there were decreases for each of the four types of violent crime the FBI tracks:

• Police cleared 52.3% of reported murders and nonnegligent homicides in 2022, down from 64.1% in 2013.
• They cleared 41.4% of aggravated assaults, down from 57.7%.
• They cleared 26.1% of rapes, down from 40.6%.
• They cleared 23.2% of robberies, down from 29.4%.

The pattern is less pronounced for property crime. Overall, law enforcement agencies cleared 12.1% of reported property crimes in 2022, down from 19.7% in 2013. The clearance rate for burglary didn’t change much, but it fell for larceny/theft (to 12.4% in 2022 from 22.4% in 2013) and motor vehicle theft (to 9.3% from 14.2%).

Note: This is an update of a post originally published on Nov. 20, 2020.

• Criminal Justice

John Gramlich is an associate director at Pew Research Center

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