The 10 best chocolate bars, Epicurean – s Answer, what is the

Epicurean s Answer

What is the answer to life

Scrivens sat at the end of an elongated red brick shoebox row of shops. There was a hardware store, a greengrocers, a hairdressers, a rather strange woman’s clothes shop – which for some reason sold toys – and finally Scrivens, a strange L-shaped grocery cum newsagents. It was here where you spent your pocket money. You’d lean your bike against the window and head in, straight to the angled display of chocolate bars. A sensory overload of colours, shapes and tastes. There are so many memories tied up with the first thrill of autonomy, to hold in your hand that coin which is yours, to do with what you want. What do you spend your money on? Sweets obviously!

They claim that 70% of chocolate bar purchases are impulse driven but there’s so much more to confectionery than the confectionery itself. Often those decisions are based just as much on what happened years ago, as it is on what is in the present. The texture and luxurious taste are only one small part of the nostalgic feeling that one associates with that indulgence.

Despite manufacturers constantly rebranding and repackaging trusted franchises, people have grown up with them and they are an integral part of peoples lives. You can’t underestimate the joy of running ones fingernail along the foil covered crevices of a four bar KitKat. The disappointment of getting the letter p, again, on your Smarties lid. The thrill of a free piece of cardboard with a Bounty or the anticipation of laying your Mars Bar on its front and disrobing it, revealing bit by bit your opulent quarry.

Whilst I have become a self-confessed chocolate snob, I acknowledge and appreciate the role that these bars have had in my life. So in a tribute to the everyday enemy foot solider in the battle of obesity, I decided to find the best ten chocolate bars of Britain. Obviously there has to be criteria. Without rules we’d be looking at confectionery chaos.

No solid chocolate bars – Dairy Milk, Yorkies and Buttons are all out.

It has to cost under a pound – so no fancy continental creation, or family sized treats.

No seasonal products – Cream Eggs a no go, despite being an annual event these bad boys are only (supposedly) available between Boxing Day and Easter.

Has to be currently available – No place for Drifters, Spiras or Treets.

Most importantly it has to be chocolate based – Jelly Tots, Tooty Frooties and Haribo are all firm favourites, but no chocolate, so no place on the list.

This is my top ten

Mars Bar

Invented in 1937 in Slough, it’s hard not to include this as the first entry on the list, it feels like the ultimate indulgence. I have spent many hours refining the best way to devour one. First chill the bar for 30 minutes in the fridge. Cut off the ends of the bar with a sharp knife, then lay the unwrapped bar on it’s top and make two incisions, where the sides meet the bottom layer of chocolate, along the length of the bar. Carefully chisel out the nougat section, so you’re left with the top, caramel and sides in a U-shape. Eat the nougat, fold in the sides and enjoy.

Fry’s Chocolate Cream

It’s the confectionery equivalent to a PG Wodehouse story. Each of its seven sections of fondant filling are enrobed in a crisp dark chocolate, reminiscent of when sartorial elegance was part of everyday life. It actually feels like you’re waiting with your Man at the railway station, ready for a spot of shooting in the country. It’s one of the few chocolate bars which carries in its taste, the heritage the brand has.

Galaxy Ripple

The brouhaha that went with the launch of Cadbury’s Twirl was simply a waste of time. There was already an incumbent on the coated rippled chocolate throne. It cost more than a Flake and tasted so much more like luxury, despite being made of Galaxy chocolate – which some have described as waxy, oily and cheap.

Double Decker

Overly sweet without any feelings of decadence, this nougat-biscuit combination has unique properties. If you feel like a Double Decker, there is nothing similar with which to replace it, should you not have one to hand. There are memories of raisins lurking in the biscuit base, but I’m not sure whether they were meant to be there.


Whilst other pocket money treats came in flimsy paper wrapper, Smarties lived in a sturdy cardboard tube. With its alphabet-embossed coloured plastic lid and beautiful smooth rounded edges, it was the perfect diameter for little hands. Now in a flimsier hexagonal tube, with more colours, the wonder of having that many sweets in one packet is undiminished.


Never has a snack item got the balance of chocolate to interior more correct than the Crunchie. From the golden wrapper to the rich golden interior – it’s a party in a bar. Due to its composition it’s impossible to eat without chipping the chocolate from the honeycomb for at least a part of the experience. There is something pleasingly gender neutral about the Crunchie.

Cadbury s Caramel

Recently bought into the Dairy Milk stable, this was always sold as a seductive luxury item. Sensuous and seductive, from the gentle curves of the bar (which, for some reason, always reminded me of a Ford Sierra) to the unctuous caramel interior. Like all good treats, the Caramel shares the feeling that even though you’ve finished, there should be another piece left


Targeted at women and sold as a lighter option to the more substantial bars on the market, this is a mistake. Although these crisp malt and chocolate spheres are lightweight, it’s the sheer quantity that give them their gravitas. With so many in a bag, a good rhythm can be established. I did go through a phase – which lasted about 10 years – of counting the amount in every bag I ate, 13 was a bad day, 20 a very good one, normally it was 16-17.

Surprisingly high in calories and remarkably bland in chocolate satisfaction. None the less there is something very alluring about the twin bars of a Twix, least of all the ways in which to eat them. Do you bite off the caramel first, or the biscuit? Nibble or bite? It is always more satisfying than you think and whilst a lot of confectionary doesn’t quite live up to there billing, the Twix does.


Munchies are what Rolos want to be when they grow up. Carrying a premium price, each gold-tipped tube contains chocolate cubes filled with caramel AND biscuit! I always feel a touch nauseous after eating a whole pack, but take this as a sign of value for money.

What is the answer to life

Math Riddles: Try to answer these brain teasers and math riddles, what

Math Riddles

Logic Games And Riddles

    Other Math Brain Teasers:
  • Math Puzzles
  • Monty Hall Simulation
  • Cheryl Math Problem
  • Math Jokes
  • Math Horror Stories from Real world
Riddle 1

How can you add eight 8’s to get the number 1,000? (only use addition)

What is the answer to this math question

The key to this math riddle is realizing that the one place must be zero. 888 + 88 + 8 + 8 + 8 = 1,000

Riddle 2

Two fathers and two sons sat down to eat eggs for breakfast. They ate exactly three eggs, each person had an egg. The riddle is for you to explain how

How to Explain the Riddle

One of the ‘fathers’ is also a grandfather. Therefore the other father is both a son and a father to the grandson.

In other words, the one father is both a son and a father.

Riddle 3

Part I. What digit is the most frequent between the numbers 1 and 1,000 (inclusive)? To solve this riddle you don’t want to manually do all of the math but rather try to figure out a pattern.

Answer to Riddle

The most common digit is ‘1.’ Can you figure out why? No hints until you try the next riddle because the next riddle is closely tied to this one.

Part II. What digit is the least frequent between the numbers 1 and 1,000?

0 is the least common digit even though 1,000 has three zero’s !

Explanations for both riddles

The digits 0 through 9 all follow the same pattern there is exactly 1 occurrence of each digit for every ten numbers.

  • For instance the digit 2 appears once between 10 and 19, at 12. And 2 appears once between, 30 and 39 at 32.
  • However, each of the digits 1 through 9 also appear in other numbers in the tens and hundreds place

Again, let’s look at 2 which appears in 20,21,22, 23, etc.. as well as 200,201, 202,203..

So to figure out how to answer the first riddle you had to see what distinguishes the number 1? Only that we are including 1,000 which would be the first ‘1’ in a new series of ten! In other words, the digit 1 only has a single extra occurrence (301 occurrences) compared to 2 or 3 or 9 which each have exactly 300 occurrences.

The reason that zero has the least (BY FAR at only 192 occurrences) is because zero does not have any equivalents to 22, 33, 44, 222, 3333 etc..

Riddle 4

Three guys rent a hotel room for the night. When they get to the hotel they pay the $$\$30 $$ fee, then go up to their room. Soon the bellhop brings up their bags and gives the lawyers back $5 because the hotel was having a special discount that weekend. So the three lawyers decide to each keep one of the $5 dollars and to give the bellhop a $2 tip. However, when they sat down to tally up their expenses for the weekend the could not explain the following details:

Each one of them had originally paid $10 (towards the initial $30), then each got back $1 which meant that they each paid $9. Then they gave the bellhop a $2 tip. HOWEVER, 3 • $9 + $2 = $29

The guys couldn’t figure out what happened to the other dollar. After all, the three paid out $30 but could only account for $29.

Can you determine what happened?

Answer to Riddle

There are many ways of explaining/thinking about this truly brain bending riddle! It all boils down to the fact that the lawyers’s math is incorrect.

They did NOT spend $9 3 + $2.

They spent exactly $27 dollars. $25 for the room and $2 for the tip. Remember they got exactly $3, in total back.

Another way to think about the answer to this riddle is to just pretend that the bellhop refunded $3 to the lawyers (rather than giving them $5 and receiving $2 back).

If the lawyers get $3 back and each takes $1. They they spent exactly $27 dollars.

Riddle 5

In a certain country of 5 = 3. If the same proportion holds, what is the value of 1/3 of 10 ?

Answer to Riddle

The answer is 4

What is the answer to this math question

Riddle 6

A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?

11 cartons total

7 large boxes (7 * 8 = 56 boxes)

4 small boxes (4 10 = 40 boxes

11 total cartons and 96 boxes

Riddle 7

A farmer is trying to cross a river. He is taking with him a rabbit, carrots and a fox, and he has a small raft. He can only bring 1 item a time across the river because his raft can only fit either the rabbit, the carrots or the fox. How does he cross the river. (You can assume that the fox does not eat the rabbit if the man is present, you can also assume that the fox and the rabbit are not trying to escape and run away)

The key to solving this riddle is realizing that you have to take the rabbit over first and the switch the fox with the rabbit. See step 2.

Take the rabbit to the other side

Go back and get the Fox and switch it with the Rabbit

**The key here is that the carrots and the rabbit are not being left alone.

Take the carrots across

Go back and get the rabbit

Riddle 8

Three brothers live in a farm. They agreed to buy new seeds: Adam and Ben would go and Charlie stayed to protect fields. Ben bought 75 sacks of wheat in the market whereas Adam bought 45 sacks. At home, they split the sacks equally. Charlie had paid 1400 dollars for the wheat. How much dollars did Ben and Adam get of the sum, considering equal split of the sacks?

Every farmer’s part is 1/3(45+75) = 40 sacks.

Charlie paid $1400 for 40 sacks, then 1 sack costs $1400/40 = $35/sack.

Adam got $35*(45-40)=35*5 = $175.

Ben got $35*(75-40)=35*35 = $1225.

Riddle 9

An insurance salesman walk up to house and knocks on the door. A woman answers, and he asks her how many children she has and how old they are. She says I will give you a hint. If you multiply the 3 children’s ages, you get 36. He says this is not enough information. So she gives a him 2 nd hint. If you add up the children’s ages, the sum is the number on the house next door. He goes next door and looks at the house number and says this is still not enough information. So she says she’ll give him one last hint which is that her oldest of the 3 plays piano.

Why would he need to go back to get the last hint after seeing the number on the house next door?

Because the sum of their ages ( the number on the house) is ambiguous and could refer to more than 1 trio of factors.

If you list out the trio of factors that multiply to 36 and their sums, you get :

  • 1 1 36 = 38
  • 1 2 18 = 21
  • 1 3 12 = 16
  • 1 4 9 = 14
  • 6 6 1 = 13
  • 2 2 9 = 13
  • 2 3 6 = 11
  • 3 3 4 = 10

Since the number on the house next door is not enough information there must be more than 1 factor trio that sums up to it, leaving two possibilities: < 6, 6, 1>, <2, 2, 9>. When she says her ‘oldest’ you know it can not be <6,6,1>since she would have two ‘older’ sons not an ‘oldest’.

Riddle 10

This is a famous one. The classic Monty hall riddle!

The Situation: What is the answer to this math question Your First Choice

You are confronted by 3 doors. Behind one of them is a car, behind the two others, you will only see a goat. Now, if you correctly pick the car, you win the car ! Otherwise, if you get one of the 2 goats, you don’t get the car.

So, pick any door. It doesn’t matter which one, but we will suppose that you picked door #2, as an example.

What is the answer to this math question Should You switch?

Now, after you have picked a door and before finding out what is actually behind it, you are shown a goat behind one of the other doors.(Remember there has to be a goat in 1 of the doors that you have not picked. )

Let’s say you choose door #2, as shown above. For example’s sake, let’s say there’s a goat in door 1. The question and the riddle is : should you switch the door that you picked? In other words, in this example, should you now choose door 3? Or, should you stick with your first choice (door #2)?

There actually is a mathematically correct answer to this riddle: You should indeed change your choice. If you don’t believe me, just try out our free online Monty hall simulation.

The Human Difference: How Humans are Unique Compared to All Other Animals,

The Human Difference: How Humans are Unique Compared to All Other Animals

Are Humans Unique?

Evolutionary biology proposes that humans evolved from ape-like ancestors. If this is true then we are nothing more than glorified apes. However, compared to our closest relatives , scientific research indicates that humans are unique on many fronts, including creativity, personality, abstract thinking, and moral judgment.

The Bible makes the claim that humans alone are created in the image of God. 1 What exactly does this mean? Some have equated the image of God as being the physical characteristics of our bodies that make up the way we look. In fact, the Mormons have taken this interpretation to extreme by saying that God is just an exalted man, who has a body of flesh and bones. 1 However, the Bible says that both males and females are created in the image of God. 2 Unless God were a hermaphrodite (having both male and female sexual organs), this phrase could not refer to just physical characteristics. In addition, there are various verses in the Bible that describe God as having non-human physical characteristics, such as feathers and wings. 3 Should we think of God as being an overgrown chicken? Certainly not! God is so unlike humans physically, that the Bible often paints word pictures to give us a glimpse of what God is like.


So if the image of God does not refer to physical characteristics, what does it refer to? It is certainly likely that part of the image of God refers to the ability of humans to be creative. Anthropology tells us that sophisticated works of art first appeared in the fossil record about 40,000-50,000 years ago, 4 at the time that moderns humans first appeared. No other species of animal, including the apes, are able to create and understand images of art and drawing.


Human consciousness is a mystery that has evaded decades of intensive research by neurophysiologists. According to a recent article:

When an organism s neural pathways grow sufficiently complex, materialists insist, their firings are somehow accompanied by consciousness. But despite decades of effort by philosophers and neurophysiologists, no one has been able to come up with a remotely plausible explanation of how this happens–how the hunk of gray meat in our skull gives rise to private Technicolor experience. One distinguished commentator on the mind-body problem, Daniel Dennett, author of Consciousness Explained, has been driven to declare that there is really no such thing as consciousness–we are all zombies, though we re unaware of it. 5


Another thing that makes humans unique is personality. According to Joseph LeDoux, a neuroscientist at New York University:

We have no idea how our brains make us who we are. There is as yet no neuroscience of personality. We have little understanding of how art and history are experienced by the brain. The meltdown of mental life in psychosis is still a mystery. In short, we have yet to come up with a theory that can pull all this together. 6

Abstract thinking

Is the human brain that much different from that of our closest relatives, the chimpanzees? According to Daniel J. Povinelli, from the University of Louisiana s New Iberia Research Center

Humans constantly invoke unobservable phenomena and variables to explain why certain things are happening. Chimps operate in the world of concrete, tangible things that can be seen. The content of their minds is about the observable world. 7

What is the answer to lifeInsight into how chimpanzees really think can be seen in some recent experiments performed by Dr. Povinelli. In these experiments, the researchers used the chimps natural begging gesture to examine how they really think about their world. They confronted the chimps with two familiar experimenters, one offering a piece of food and the other holding out an undesirable block of wood. As expected, the chimps had no trouble distinguishing between the block and the food and immediately gestured to the experimenter offering the food. Next, the researchers wanted to see if the chimps would be able to choose between a person who could see them and a person who could not. If the chimpanzees understood how other animals see, they would gesture only to the person who could see them. The researchers achieved the seeing/not-seeing contrast by having the two experimenters adopt different postures. In one test, one experimenter wore a blindfold over her eyes while the other wore a blindfold over her mouth. In the other tests, one of the experimenters wore a bucket over her head, placed her hands over her eyes or sat with her back turned to the chimpanzee. All these postures were modeled after the behaviors that had been observed during the chimpanzees spontaneous play. The results of the experiments were astonishing. In the tests involving blindfolds, buckets and hands over the eyes–the apes entered the lab and paused but then were just as likely to gesture to the person who could not see them as to the person who could. In several cases, the chimps gestured to the person who could not see them and then, when nothing happened, gestured again, as if puzzled by the fact that the experimenter did not respond. In the case of experimenters facing with their backs to the chimps, they performed as if they knew that those facing way from them could not see and offer them food. However, subsequent experiments proved that the chimps had merely responded to conditioning from the initial experiments, since they had only received food from those experimenters who faced them. This was proven by having experimenters facing away from the chimps, but then turning to look over their shoulders. The chimps were just as likely to gesture to the experimenters facing away as the one who turned to look at them. Chimpanzees have no clue that humans must face them in order to see. It is obvious from these experiments that chimpanzees lack even a simple understanding of how their world works, but merely react to conditioning from directly observable events. 8

Other researchers have noted that chimpanzees do not understand the cause and effect of their actions. Apes will climb onto a box to reach fruit, but if the box is absent, will place on the ground beneath the fruit a sheet of paper and stand upon it. 9

A more recent study examined the ability of human infants and young chimpanzees to help human adults. 10 18-month-old human infants and young chimpanzees were presented with four categories of problems: out-of-reach objects, access thwarted by a physical obstacle, achieving a wrong (correctable) result, and using a wrong (correctable) means. While human infants could perform all four tasks, chimpanzees could only perform the first task. As in previous studies, chimpanzees were unable to discern when an individual failed at a simple task and how he could help. The researchers concluded:

A number of theorists have claimed that human beings cooperate with one another and help one another (especially non-kin) in ways not found in other animal species (26 28). This is almost certainly so, and the current results demonstrate that even very young children have a natural tendency to help other persons solve their problems, even when the other is a stranger and they receive no benefit at all. 10

Body, soul, spirit

Besides the rather obvious differences in the way animals process information in their brains, the Bible (and science) confirm that there are major differences in the ways humans make moral judgments (animals don t make such judgments, as we shall see). Part of what is meant by the term in the image of God can be found in chapters immediately following its first usage (Genesis 1) in the Bible. Both Adam and Eve had a personal relationship with God in the Garden of Eden. Such a personal relationship is not described, nor seen, for any other animal species. It is the presence of a spirit that was instilled into humans 11 that separates us from the animals. There are three kinds of life that God has created in this universe:

This math question meant for 7-year-olds has everyone stumped, what is the



What is the answer to this math question

UPDATE: May 18, 2017, 5:06 p.m. SGT Updated with the Ministry of Education’s new statement.

A math question apparently meant for 7-year-olds has left adults befuddled.

The bonus math question — which was first said to have originated on a first-grade level exam paper in Singapore — has been making the rounds on social media.

Singapore’s Ministry of Education (MOE) later told Mashable that there were in fact no examinations for Primary 1 students.

The question shows a circular puzzle with five numbers in it. There are four corresponding blanks that are meant to be filled in, but no further information is given on how to solve it.

What is the answer to this math question

Adults have been unable to solve it.

“Now that I can’t solve this, I feel super uncomfortable,” said user Kenny Eng on Facebook.

“Maybe Sheldon from the Big Bang Theory could have done this when he was seven,” said Facebook user Mingli Lin.

“I just finished my course on advanced applied math and I can’t solve this. Whoever set this is sick,” said user Jacky Wu.

Where did the math question originally come from?

The question first surfaced on an online forum, posted by a user who claims that it was a bonus question taken from a Primary One, or first grade, examination paper.

But Singapore’s Ministry of Education (MOE) initially couldn’t confirm this. “From the image, we are unable to ascertain if the question was from a school’s Primary 1 examination paper,” an MOE spokesperson said in a statement.

The MOE later told Mashable on Thursday that there were in fact “no examinations at Primary 1.”

However, the question bears a striking resemblance to one that has previously appeared on a math blog by Gordon Burgin, who calls himself an author of Maths Puzzles. (Mashable has reached out to Burgin for comment).

The two questions are almost identical, with only one difference. The bottom-left number in Mr Burgin’s puzzle is 20 instead of 2.

What is the answer to this math question

Image: gordon burgin

According to Burgin, the way to solve his puzzle is this:

What is the answer to this math question

Image: gordon burgin

It’s not the first time an exam question has left people stumped

In 2015, people in Singapore were similarly unable to solve a math question nicknamed “Cheryl’s birthday.”

The question was first reported to be a fifth-grade level question, but was later revealed to be a ninth-grade Maths Olympiad question.

So what is the answer to the original math question you ask?

Your guess is as good as mine.

WATCH: Someone drilled a hole in an iPhone to make a fidget spinner because. the internet

What is the answer to this math question

Life Insurance Rates: Compare Life Insurance Quotes, what is the answer to

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Question-Answer Relationship (QAR), Classroon Strategies, Reading Rockets, what is the answer to

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What is the answer to this math questionThe question–answer relationship (QAR) strategy helps students understand the different types of questions. By learning that the answers to some questions are “Right There” in the text, that some answers require a reader to “Think and Search,” and that some answers can only be answered “On My Own,” students recognize that they must first consider the question before developing an answer.

Why use question–answer relationship?

How to use question–answer relationship

What is the answer to this math question

1. Explain to students that there are four types of questions they will encounter. Define each type of question and give an example.

Four types of questions are examined in the QAR:

  • Right There Questions: Literal questions whose answers can be found in the text. Often the words used in the question are the same words found in the text.
  • Think and Search Questions: Answers are gathered from several parts of the text and put together to make meaning.
  • Author and You: These questions are based on information provided in the text but the student is required to relate it to their own experience. Although the answer does not lie directly in the text, the student must have read it in order to answer the question.
  • On My Own: These questions do not require the student to have read the passage but he/she must use their background or prior knowledge to answer the question.

2. Read a short passage aloud to your students.

3. Have predetermined questions you will ask after you stop reading. When you have finished reading, read the questions aloud to students and model how you decide which type of question you have been asked to answer.

4. Show students how find information to answer the question (i.e., in the text, from your own experiences, etc.).

Watch: Question-Answer Relationship

An elementary teacher demonstrates the QAR strategy in this video from the Virginia Department of Education. Watch question-answer relationship in action


In this lesson, students apply the question–answer relationship strategy to word problems that refer to data displayed in a table.

Differentiated instruction

for second language learners, students of varying reading skill, and younger learners

  • Have students work together to form questions about the text, find the answers and share with the whole class.
  • Ask students to write down questions and answers.

See the research that supports this strategy

Raphael, T.E., Au, K.H. (2005). QAR: Enhancing comprehension and test taking across grades and content areas. The Reading Teacher, 59, 206-221.

Children’s books to use with this strategy

What is the answer to this math question

One Hen: How One Small Loan Made a Big Difference by Kate Smith Milway , illustrated by Eugenie Fernandes (Kids Can)

This fictionalized story of Kojo, a boy from Ghana, who changes his world with a small loan and one hen, is based on a real person. Kwabena Darko lives in West Africa and started a system of micro-loans in villages that would not otherwise have access. Additional resources and sources for further information allow readers to find out more.

What is the answer to this math question

How to Heal a Broken Wing by Bob Graham (Candlewick 2008)

Children often see what adults miss, and so it is when Will finds a pigeon with a broken wing on the sidewalk of a busy city. Will and his parents, help the bird recover over time then release it. Limited text and well paced and placed illustrations tell the affecting story.

What is the answer to this math question

Pale Male: Citizen Hawk of New York City by Janet Schulman , illustrated by Meilo So (Knopf)

Stunning watercolors evoke the height and breadth of New York City while a dramatic text relates the true story of a now-famous feathered resident, a hawk named Pale Male. The tension between the lifestyle of Pale Male and human residents as well as the fate of Pale Male’s mates and offspring create riveting reading.

Selected Answer 3 Correct Answer 3 Question 14 5 out of 5

Selected answer 3 correct answer 3 question 14 5 out

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JSC All Subject MCQ Suggestion Question With Answer 2018, what is the

JSC All Subject MCQ Suggestion Question With Answer 2018

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What is the answer to this math question

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Applied Math Problems: Using Question-Answer Relationships (QARs) to Interpret Math Graphics, Intervention

Applied Math Problems: Using Question-Answer Relationships (QARs) to Interpret Math Graphics

Students must be able to correctly interpret math graphics in order to correctly answer many applied math problems. Struggling learners in math often misread or misinterpret math graphics. For example, students may:

  • overlook important details of the math graphic.
  • treat irrelevant data on the math graphic as ‘relevant’.
  • fail to pay close attention to the question before turning to the math graphic to find the answer.
  • not engage their prior knowledge both to extend the information on the math graphic and to act as a possible ‘reality check’ on the data that it presents.
  • expect the answer to be displayed in plain sight on the math graphic, when in fact the graphic may require that readers first to interpret the data, then to plug the data into an equation to solve the problem.

Teachers need an instructional strategy to encourage students to be more savvy interpreters of graphics in applied math problems. One idea is to have them apply a reading comprehension strategy, Question-Answer Relationships (QARs) as a tool for analyzing math graphics. The four QAR question types (Raphael, 1982, 1986) are as follows:

  • RIGHT THERE questions are fact-based and can be found in a single sentence, often accompanied by ‘clue’ words that also appear in the question.
  • THINK AND SEARCH questions can be answered by information in the text–but require the scanning of text and the making of connections between disparate pieces of factual information found in different sections of the reading.
  • AUTHOR AND YOU questions require that students take information or opinions that appear in the text and combine them with the reader’s own experiences or opinions to formulate an answer.
  • ON MY OWN questions are based on the students’ own experiences and do not require knowledge of the text to answer.

Steps to Implementing This Intervention

Teachers use a 4-step instructional sequence to teach students to use Question-Answer Relationships (QARs) to better interpret math graphics:

1. Distinguishing Among Different Kinds of Graphics

Students are first taught to differentiate between five common types of math graphics: table (grid with information contained in cells), chart (boxes with possible connecting lines or arrows), picture (figure with labels), line graph, bar graph.

Students note significant differences between the various types of graphics, while the teacher records those observations on a wall chart. Next students are shown examples of graphics and directed to identify the general graphic type (table, chart, picture, line graph, bar graph) that each sample represents.

As homework, students are assigned to go on a ‘graphics hunt’, locating graphics in magazines and newspapers, labeling them, and bringing them to class to review.

2. Interpreting Information in Graphics

Over several instructional sessions, students learn to interpret information contained in various types of math graphics. For these activities, students are paired off, with stronger students matched with less strong ones.

The teacher sets aside a separate session to introduce each of the graphics categories. The presentation sequence is ordered so that students begin with examples of the most concrete graphics and move toward the more abstract. The graphics sequence in order of increasing difficulty is: Pictures tables bar graphs charts line graphs.

At each session, student pairs examine examples of graphics from the category being explored that day and discuss questions such as: “What information does this graphic present? What are strengths of this type of graphic for presenting data? What are possible weaknesses?” Student pairs record their findings and share them with the large group at the end of the session.

3. Linking the Use of Question-Answer Relations (QARs) to Graphics

In advance of this lesson, the teacher prepares a series of data questions and correct answers. Each question and answer is paired with a math graphic that contains information essential for finding the answer.

At the start of the lesson, students are each given a set of 4 index cards with titles and descriptions of each of the 4 QAR questions: RIGHT THERE, THINK AND SEARCH, AUTHOR AND YOU, ON MY OWN. (TMESAVING TIP: Students can create their own copies of these QAR review cards as an in-class activity.)

Working first in small groups and then individually, students read each teacher-prepared question, study the matching graphic, and ‘verify’ the provided answer as correct. They then identify the type of question being posed in that applied problem, using their QAR index cards as a reference.

4. Using Question-Answer Relationships (QARs) Independently to Interpret Math Graphics

Students are now ready to use the QAR strategy independently to interpret graphics. They are given a laminated card as a reference with 6 steps to follow whenever they attempt to solve an applied problem that includes a math graphic:

  • Read the question,
  • Review the graphic,
  • Reread the question,
  • Choose the appropriate QAR,
  • Answer the question, and
  • Locate the answer derived from the graphic in the answer choices offered.

Students are strongly encouraged NOT to read the answer choices offered on a multiple-choice item until they have first derived their own answer-to prevent those choices from short-circuiting their inquiry.