efficient subtraction problem solving

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Course: 3rd grade   >   Unit 3

• Subtraction by breaking apart
• Break apart 3-digit subtraction problems
• Adding and subtracting on number line
• Subtract on a number line
• Methods for subtracting 3-digit numbers

Select strategies for subtracting within 1000

• (Choice A)   Yes, 563 − 192 = ( 563 − 200 ) + 8 ‍   . A Yes, 563 − 192 = ( 563 − 200 ) + 8 ‍   .
• (Choice B)   No, 563 − 192 > ( 563 − 200 ) + 8 ‍   . B No, 563 − 192 > ( 563 − 200 ) + 8 ‍   .
• (Choice C)   No, 563 − 192 < ( 563 − 200 ) + 8 ‍   . C No, 563 − 192 < ( 563 − 200 ) + 8 ‍   .

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4.4: Subtraction

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• Page ID 82998

• Julie Harland
• MiraCosta College

You will need: A Calculator, Base Blocks (Material Cards 4-15) C-Strips (Material Cards 16A-16L)

How would you use manipulative to explain how to do subtraction to a young child?

There are two distinct approaches to subtraction. The one most of us are familiar with is the Take-Away Method . A typical way someone might introduce the idea of subtraction is by saying "If I put five apples in the bowl and then take away two of the apples, how many are left in the bowl?" The illustration below shows this as a subtraction problem where after two apples are removed from the bowl, there are three apples remaining.

The above problem illustrates the Take-Away Approach to Subtraction.

Subtraction Vocabulary: For x – y = z , x is called the minuend , y is called the subtrahend , and z (the answer) is called the difference .

For the subtraction problem 7 – 3, State the

Definition: Subtraction of Whole Numbers using Set Theory

If B is a subset of A, then n(A) – n(B) = n(A – B)

In your own words, explain how to use the definition of subtraction. What are the steps involved?

Examples of how to do subtraction using the Set Theory Definition:

Use the set theory definition of subtraction to show that 5 – 2 = 3.

Let A = {v, w, x, y, z} and B = {w, z}. Since n(A) = 5, n(B) = 2 and B \(\subseteq\) A,

\[\begin{aligned} 5 – 2 &= n(A) – n(B) && \text{ by substituting } n(A) \text{ for 5 and } n(B) \text{ for 2} \\ &= n(A – B) && \text{ by the set theory definition of subtraction} \\ &= n(\{v,x,y\}) && \text{ by computing }A – B \\ &= 3 && \text{ by counting the elements in } A – B \end{aligned} \nonumber \]

Therefore, 5 – 2 = 3.

Use the set theory definition of subtraction to show that 6 – 1 = 5.

Let A {1, 2, 3, 4, 5, 6} and B = {4}. Since n(A) = 6, n(B) = 1 and B \(\subseteq\) A, \[\begin{aligned} 6 – 1 &= n(A) – n(B) && \text{ by substituting } n(A) \text{ for 6 and } n(B) \text{ for 1} \\ &= n(A – B) && \text{ by the set theory definition of subtraction} \\ &= n(\{1, 2, \mathbf{3}, 5, 6\}) && \text{ by computing }A – B \\ &= 5 && \text{ by counting the elements in } A – B \end{aligned} \nonumber \]

Therefore, 6– 1 = 5.

Use the set theory definition of subtraction to show that 3 – 0 = 3.

Let A = {x,y, z} and B= {}. Since n(A)=3, n(B)=0 and B \(\subseteq\) A,

\[\begin{aligned} 3 – 0 &= n(A) – n(B) && \text{ by substituting } n(A) \text{ for 3 and } n(B) \text{ for 0} \\ &= n(A – B) && \text{ by the set theory definition of subtraction} \\ &= n(\{x,y,z\}) && \text{ by computing }A – B \\ &= 3 && \text{ by counting the elements in } A – B \end{aligned} \nonumber \]

Therefore, 3 – 0 = 3.

For each subtraction problem below, provide two sets that allow you to use the definition of subtraction to find the answer. Then, compute the answer using this definition.

Parts b and c of Exercise 4 illustrate two familiar properties of subtraction.

The first property states that for any whole number \(m\), \(m – 0 = m\). Using our knowledge of Set Theory, choose the first set A to have m elements and then choose a second set B that has zero elements – there is only one set you can choose and that is the null or empty set, { }. Then, A – { } = A. Therefore, it is a fact that m – 0 = 0.

The second property states that for any whole number m, m – m = 0. This must be true because for any set A, whether it has m elements or any other number of elements, we know from Set Theory that A – A = { }.

We will use the Take-Away approach to perform subtraction problems in Egyptian now.

You are reminded of the symbols and their Hindu-Arabic equivalents below:

To use the Take-Away approach, we want to see the subtrahend as a subset of the minuend and then remove the subtrahend from the minuend. The symbols that remain in the minuend is the difference. In this first example, notice how the following subtraction is performed. In this case, you can see the subtrahend as a subset of the minuend. A box is put around what is to be taken away and the final answer is clear.

Sometimes, exchanges have to be made in the minuend before the subtraction can be done. For instance, consider the following subtraction:

The first step would be to make some exchanges in the minuend. One lotus flower must be exchanged for ten scrolls and one heel bone must be exchanged for ten staffs. After doing that, the subtraction can be performed as shown below:

In the above example, put a box around the subset that is being removed from the minuend.

The next subtraction will be

. This time the subtraction will be shown as a vertical problem with the minuend and subtrahend shown enclosed in a box. In order to do the subtraction, first the pointed finger in the minuend must be exchanged for ten lotus flowers. Then, one lotus flower must be exchanged for ten scrolls and one heel bone must be exchanged for ten strokes. Finally, the subset (the subtrahend) is taken away from the minuend. I've traced out what is being removed. The symbols remaining in the minuend is the answer (

) as shown in the illustration below.

Perform the following subtraction problems in Egyptian, showing all steps. You can model the problem however you like as long as the steps are clear.

Let's use the take-away approach to subtract Mayan numerals. It's similar to addition in that you remove a subset at each level – exchanges or trades might have to be done before being able to take away at any given level. Pay close attention to which level you are on when making exchanges. A dot at one level can be traded in for a group of 20 at the next level down except from level three to level two – one dot at the third level is replaced by a group of 18 at the second level . Study the following examples. See if you can figure out which exchanges are being made. I will indicate exchanges which are being made from one level to the other with a downward arrow.

In Examples 1 and 2, note that as exchanges are being made in the minuend (so that you can use the take-away approach), the subtrahend just keeps getting repeated. Alternately, you can first show the exchanges being made for the minuend, make a break (like a dotted line as shown below) and then write the subtraction problem out and subtract. Here is another way, you might show the steps for Example 2.

Perform the following subtraction problem in Mayan and show all of the steps.

Here are some more examples.

It takes a lot of concentration and effort to work these correctly. Perform each step carefully because it is easy to make mistakes. Each of the previous four examples can be checked by adding the answer to the subtrahend and seeing if the sum is the minuend. The other way to check is convert the minuend and subtrahend to Hindu-Arabic, subtract in Hindu-Arabic, then convert the difference to Mayan, making sure the answer is the same as the one you came up with when you did it in Mayan. Here is the check for Example 4: 46,084 –25,396 = 20,688. I made mistakes on this problem the first time through, but found my mistakes by checking and starting over. You should definitely check your answers. Try doing examples 3 and 4 above on your own before going on to the next exercise.

Perform the following subtraction problems in Mayan. Show all steps and check!

Take out a set of Base Four blocks. We are going to do the subtraction problem 17 – 7 in Base Four. \(101_{\text{four}}\) is the Base Four numeral for 17 and \(13_{\text{four}}\) is the Base Four numeral for 7. We will make a pile, called Pile A, using the Base Four blocks to represent 17 and another pile, called Pile B, to represent 7. Your piles should look something like what you see to the right.

Below is an illustration of the subtraction problem being performed. In order to use the take-away approach, Pile B must be a subset of Pile A. That exact subset must be removed from Pile A. First, the flat in Pile A must be exchanged for 3 longs and 4 units so you can actually see Pile B inside Pile A. There is a box around the subset (Pile B) to be removed from Pile A note how it matches Pile B. After taking those blocks away, 2 longs and 2 units remain. Therefore, the completed subtraction problem is \(101_{\text{four}} – 13_{\text{four}} = 22_{\text{four}}\).

Get out and use your base blocks to do the following exercises! Follow directions.

Count out 17 unit blocks and make exchanges with base five blocks. Put them in a pile, called Pile A, and SAVE THIS PILE. Since you've made exchanges in base five, write 17 as a base five numeral on the space provided for Pile A below. Now, count out 9 more units and make exchanges with base five blocks. Put them in a pile, called Pile B. Since you've made exchanges in base five, write 9 as a base five numeral on the space provided for Pile B below. If necessary, make exchanges within Pile A so that an exact subset of Pile B is seen in Pile A. Take away those blocks in Pile A which represent the blocks in Pile B. The blocks left in Pile A are those that are left after subtracting the blocks that were in Pile B. If necessary, make any exchanges with base five blocks and then write this number as a base five numeral on the third blank provided below.

Below is the subtraction problem you have just performed in Base Five :

____________ + _____________ = _____________________

Pile A Pile B Difference of Pile A and B

Convert the difference (answer) to Base Ten. It should be 8 since 17 – 9 = 8. Is it?

Illustrate the subtraction problem using blocks below. Show the steps.

Count out 17 unit blocks and make exchanges with base eight blocks. Put them in a pile, called Pile A, and SAVE THIS PILE. Since you've made exchanges in base eight , write 17 as a base eight numeral on the space provided for Pile A below. Now, count out 7 more units and make exchanges with base eight blocks. Put them in a pile, called Pile B. Since you've made exchanges in base eight , write 7 as a base eight numeral on the space provided for Pile B below. If necessary, make exchanges within Pile A so that an exact subset of Pile B is seen in Pile A. Take away those blocks in Pile A which represent the blocks in Pile B. The blocks left in Pile A are those that are left after subtracting the blocks that were in Pile B. If necessary, make any exchanges with base eight blocks and then write this number as a base eight numeral on the third blank provided below.

Below is the subtraction problem you have just performed in Base Eight:

Convert the difference (answer) to Base Ten. It should be 10 since 17 – 7 = 10. Is it? Illustrate the subtraction problem using blocks below. Show the steps.

Exercise 10

Count out 21 unit blocks and make exchanges with base three blocks. Put them in a pile, called Pile A, and SAVE THIS PILE. Since you've made exchanges in base three , write 21 as a base three numeral on the space provided for Pile A below. Now, count out 7 more units and make exchanges with base three blocks. Put them in a pile, called Pile B. Since you've made exchanges in base three , write 7 as a base three numeral on the space provided for Pile B below. If necessary, make exchanges within Pile A so that an exact subset of Pile B is seen in Pile A. Take away those blocks in Pile A which represent the blocks in Pile B. The blocks left in Pile A are those that are left after subtracting the blocks that were in Pile B. If necessary, make any exchanges with base three blocks and then write this number as a base three numeral on the third blank provided below.

Below is the subtraction problem you have just performed in Base Three :

Convert the difference (answer) to Base Ten. It should be 14 since 21 –7 = 14. Is it? Illustrate the subtraction problem using blocks below. Show the steps.

Exercise 11

Write the three subtraction problems from exercises 8, 9 and 10 in a vertical format like the one in Base Four (my example) shown to the right. Study this Base Four problem as well as the three problems you write down. Try to figure out a way to do the subtraction problems using paper and pencil instead of by using the Base Blocks. In other words, try to come up with your own algorithm (method) for doing subtraction in other bases. Explain your method and show a few examples. Later, you will be learning algorithms for subtraction.

\[ \begin{aligned} 101_{\text{ four}} \\ \underline{ - 13_{\text{ four}}} \\ 22_{\text{ four}} \end{aligned} \nonumber \]

Exercise 12

Using your C-Strips, make two trains as indicated. Let B + N be the first train, \(t_{1}\), and let H + R be the second train, \(t_{2}\). Place \(t_{1}\) adjacent to t 2 as shown below. Find a train (write it as a single C-strip) that, when added to t 2 , will form a train equal in length to \(t_{1}\). This train is called the difference of the two trains, \(t_{1}\) and \(t_{2}\) and is denoted by \(t_{1} –t_{2}\). What is \(t_{1} –t_{2}\) ?

Exercise 13

Use C-Strips to find the following differences. Draw a diagram of your work.

Exercise 14

Use the C-Strips to verify and illustrate each of the following statements:

In Exercise 12, a new approach was used to defining difference. There are two distinct ways of defining subtraction – the take-away approach and the missing addend approach . We can use the model for how difference was defined using trains and now apply it to the definition of subtraction for whole numbers. Below is a definition of subtraction using the model for how difference was defined using trains in Exercise 12.

Definition of Subtraction (Missing Addend Approach) : Let a and b be any two whole numbers. a – b is the whole number c such that a = b + c . In other words, if c is added to the subtrahend, b , the sum is the minuend, a . The answer, c , is called the missing addend.

Exercise 15

Is there a whole-number answer for every whole-number subtraction problem? In other words, is subtraction of whole numbers closed? Explain your answer and provide a counterexample if it is not closed

Exercise 16

Determine which sets, if any, are closed under subtraction. Provide a counterexample if a set is not closed.

If you think of subtraction in terms of the missing addend approach, then we say that the statements a – b = c and a = b + c are equivalent to each other. Consider the statement, 8 – 2 = 6. It is equivalent to the statement 8 = 2 + 6. We also know that 2 + 6 = 6 + 2 because of the commutative property of addition. Therefore, 8 = 6 + 2, which in turn is equivalent to the statement 8 – 6 = 2. This gives us four facts about how to relate the numbers 2, 6 and 8 using addition and subtraction

Some teachers relate subtraction and addition by using the idea of "fact families" such as the four facts above, which is one fact family.

It is important to note that each addition statement gives us two subtraction statements, which is how many people learn their subtraction facts. Because of this relationship between addition and subtraction, once a child learns basic addition facts, the subtraction facts naturally follow.

Exercise 17

Write down two subtraction statements that are equivalent to each addition statement.

You may wonder why I wrote the addition statements in Exercise 14 with the plus sign on the left of the equals sign, unlike the way I happened to write the two addition facts in the fact family relating 2, 6 and 8 at the top of the page. It's because 8 + 4 = 12 is the same fact as 12 = 8 + 4 due to the Symmetric Property of Equality which is defined below.

The Symmetric Property of Equality states that for any equation, if a = b, then it is also true that b = a

Therefore, it is perfectly okay to write the four facts above as

Use the symmetric property of equality to rewrite each equation.

Exercise 18

Exercise 19.

Is there a symmetric property of inequality? Explain.

Note: Inequality refers to less than ( < ) and/or greater than ( > ).

Let's do a subtraction problem using the missing addend approach in Egyptian. The set-up is exactly the same as when employing the take-away approach, but the way in which you go about finding the answer is different. The first example we looked at in Egyptian was

We ask ourselves "What must be added to

?" Another way to express this is to write:

. We begin by converting in the minuend until it contains the subtrahend. We did these exact steps when using the take-away approach. But to get the final answer, we note what must be added to the subtrahend to get the minuend. The answer is

. The illustration is shown below.

To check, see if the missing addend (the answer) + the subtrahend = the minuend. In other words, is the following addition statement true?

Another way to check is to convert to Hindu-Arabic.

The same approach could be used to subtract in Mayan. The steps used to get ready to find the missing addend are exactly the same as when employing the take-away approach. But to compute the answer, at each level you decide which symbols must be added to the subtrahend to get what is in the minuend.

Although it may be hard to distinguish between the two approaches to subtraction, it's the way that you think about the problem that makes it different. For instance, one child learning about subtraction might think about the problem 8 – 3 by thinking "If I have 8 pennies in one hand and take away 3 of them to put in my pocket, how many are left in my hand?" This is the take-away approach. The child might compute the answer by counting backwards –7, 6, 5 or by actually using pennies or manipulatives where 8 pennies are put in one hand, 3 are taken away and what's left is counted to get the answer. Another child might think of the same subtraction problem in this way –"If I have 3 pennies, how many more pennies do I need so that I'll have 8 pennies?" This is the missing addend approach.

Exercise 20

Make up two word problems that would require the subtraction problem 8 – 3 to be computed. The first should use the take-away approach and the second should use the missing addend approach. Explain and show how you would solve each word problem using the given approach.

Without using manipulatives, each subtraction problem can be worded as a missing addend addition problem. In other words, to find the answer to 8 – 3, you figure out what goes in the blank for 3 + ____ = 8. Since 3 + 5 = 8, then 8 – 3 = 5 .

Exercise 21

Perform the following subtraction problems by employing the missing addend approach. Fill in the blanks

Use Base Blocks to compute the following subtraction problems using the missing addend approach. Begin by forming two piles, one for the minuend (Pile A) and one for the subtrahend (Pile B). Then figure out what must go in a third pile (Pile X) so that B + X = A. Show how you found the answer.

Exercise 22

\(231_{\text{five}} – 140_{\text{five}}\)

Exercise 23

\(100_{\text{two}} – 11_{\text{two}}\)

Exercise 24

\(135_{\text{twelve}} – T6_{\text{twelve}}\)

The missing addend approach is sometimes called the Additive (or Austrian) Algorithm.

This approach is very useful for doing subtraction on the number line.

Let's review the definition of subtraction using the missing addend approach. It says the answer to a – b = c where c is the number that must be added to b to get c, or b + c = a.

Think about this using a number line. How would we find the answer to 7 – 3? We need to find a number to add on to 3 that gives us an answer of 7. In other words, what would go in the blank 3 + ____ = 7? I know you know the answer, but how could we get the answer by using a number line?

First, we have to define a new term: vector . A vector is a directed line segment. Basically, a directed vector looks like an arrow. It has a certain length and points in a certain direction. Since we'll be using horizontal number lines, we'll be using horizontal vectors. An arrow pointing to the right will denote a positive number and an arrow pointing to the left will denote a negative number.

Below is a number line, with some vectors shown above. Vector a is 6 units long and the arrow points to the right. Therefore, it represents the number +6. Vector b is also 6 units long, but it points to the left. Therefore, it represents the number -6.

Exercise 25

a. What number does vector c represent? _________

b. What number does vector d represent? _________

Now, we're ready to use vectors in conjunction with the missing addend approach to compute a subtraction problem. Let's go back to the problem 7 – 3. The missing addend approach states the answer to the subtraction problem is the number that when added to the number after the subtraction sign gives the number that is before the subtraction sign. Since 3 is the number after the subtraction sign, we have to find a number to add to 3 that will give an answer of 7. Using a number line, this means if you start at 3, how can you get to 7? In other words, draw a vector that starts at 3 and ends up at 7. Make sure the arrow points to 7. The number that the vector represents is the answer to the problem. The illustration is shown below. The vector has length 4 and points to the right, so the answer is 4, which is written above the vector to indicate the answer.

Let's try the problem 2 - 9. Then, 9 + ____ = 2. On the number line, draw a vector that starts at 9 and ends at 2. Then, see what number the vector represents to find the answer. The vector shown below gives the answer of -7.

Exercise 26

Find the answer to the following subtraction problems by using directed vectors on the number line in conjunction with the missing addend approach. Draw the vectors.

Exercise 27

Looking at the vectors a – d below, figure out what subtraction problem was being performed, and then state the answer. For instance, vector b came from doing the problem -1 – 5. So, -1 – 5 = -6 (since vector b is 6 units long and goes left).

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Making Subtraction Efficient – Just Think Addition!

Students who are efficient with the count-on , use-doubles,  and make-ten  strategies for addition have all they need to be proficient with subtraction number facts!

Subtraction is the inverse, or opposite action, of addition. Both operations involve a part-part-total structure. In the example below, 1 and 3 are two parts that make up the number 4.

Parts of Subtraction

With addition, the parts are known, but not the total; with subtraction, the total and one of the parts are known, but not the other part. Because of this relationship between the two operations, using addition is the most effective thinking strategy for helping students learn the basic subtraction facts. Watch this ORIGO One video  to learn more!

Fact Families

Addition facts and subtraction facts that involve the same parts and total form fact families . Clusters of subtraction facts are named according to the strategy used for the related addition facts. For example, 8 – 3 = 5 is part of the count-on subtraction fact cluster because its related addition fact 5 + 3 = 8 involves counting on three. Students need to understand the connections between the number facts within a family and the related strategy.

Subtraction Games: Teach Subtraction Using Addition

“Think addition to subtract” is one of the most effective strategies for subtracting mentally. This game reinforces the connection between addition and subtraction. The students are encouraged to use their knowledge of addition to make a true subtraction number sentence.

Materials needed:

• Take or Tally game board (access this subtraction game board file here )
• Write 1, 2, 3, 1, 2, 3 on one cube
• Write 4-9 on the other.

Game Directions: The aim is to complete twelve true number sentences.

• The first player rolls the two number cubes.
• The player then writes the two numbers in one of the number sentences on his or her game board. The completed number sentence must be true.

Example: Sue rolls 4 and 3. She completes the number sentence 7 – 4 = 3.

• If a true number sentence cannot be made, the player makes a tally in the space provided at the bottom of his or her game board.
• The first player to complete twelve number sentences before making a total of ten tallies is the winner.

Strategy Tip: Ask, How did you know to place your numbers in that sentence?

Extending the game:

• Change the rules so two players share the one game board. Each player has his or her own column of number sentences to complete. The remaining rules can stay unchanged.
• Use the Take or Tally Again game board for greater numbers. Make a new number cube by writing numerals 6-11 and replace the cube with 4-9 from the original game.

Encourage children to apply the think-addition strategy for subtraction to numbers beyond the basic facts. For example, the strategy can be extended to solve 106 – 89. This is specifically highlighted in the ORIGO One video referenced earlier in this blog!

Download the subtraction game board referenced in this article and let us know if we can help!

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• 07 April 2021

Adding is favoured over subtracting in problem solving

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Tom Meyvis is in the Leonard N. Stern School of Business, New York University, New York, New York 10012, USA.

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Heeyoung Yoon is in the Leonard N. Stern School of Business, New York University, New York, New York 10012, USA.

Consider the Lego structure depicted in Figure 1, in which a figurine is placed under a roof supported by a single pillar at one corner. How would you change this structure so that you could put a masonry brick on top of it without crushing the figurine, bearing in mind that each block added costs 10 cents? If you are like most participants in a study reported by Adams et al. 1 in Nature , you would add pillars to better support the roof. But a simpler (and cheaper) solution would be to remove the existing pillar, and let the roof simply rest on the base. Across a series of similar experiments, the authors observe that people consistently consider changes that add components over those that subtract them — a tendency that has broad implications for everyday decision-making.

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Adams, G. S., Converse, B. A., Hales, A. H. & Klotz, L. E. Nature 592 , 258–261 (2021).

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Tully, S. M., Hershfield, H. E. & Meyvis, T. J. Consumer Res. 42 , 59–75 (2015).

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Year 4 Maths Efficient Subtraction Lesson - Autumn Block 2 - by Classroom Secrets

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

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This Year 4 Efficient Subtraction lesson covers the prior learning of looking at different methods of subtraction including counting on using a number line, before moving onto the main skill of identifying the most efficient method of subtraction.

The lesson starts with a prior learning worksheet to check pupils’ understanding. The interactive lesson slides recap the prior learning before moving on to the main skill. Children can then practise further by completing the activities and can extend their learning by completing an engaging extension task.

This pack includes:

Main Activity Worksheet Discussion Problems Homework Extension PowerPoint Lesson Slides Reasoning and Problem Solving Varied Fluency Practical Activities Prior Learning

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Subtraction Calculator

Subtraction calculator by newtum: making math subtracting easy and fun.

Welcome to our Subtraction Calculator page! This tool is designed to simplify the process of subtracting numbers, making it accessible to everyone. Whether you're a student, a teacher, or just someone who wants to make subtraction easier, our tool is here to help. Curious? Let's explore more about this amazing tool!

Discovering the Mathematics Tool

The Subtraction Calculator is an online tool that simplifies subtracting numbers. Whether you're dealing with large numbers or fractions, this Subtraction Calculator is here to help. It eliminates the hassle and time-consuming process of manual subtraction, providing you with accurate results instantly.

Demystifying the Formula in Subtraction Calculator

The formula used in our Subtraction Calculator is straightforward and efficient. It is the same traditional subtraction method that we use in our daily life but made more efficient and error-free. Understanding this formula can enhance your mathematical skills and increase your confidence in dealing with numbers.

• Enter the numbers you want to subtract in the given fields.
• Click on the 'Calculate' button.
• The Subtraction Calculator will instantly provide you with the result.

Step-by-Step Guide: Using the Subtraction Calculator

Using our Subtraction Calculator is as easy as 1-2-3. You simply need to input the numbers you want to subtract and hit the calculate button. The results will appear in no time. Follow the instructions below for a smooth and efficient calculation experience.

• Locate the input fields on the Subtraction Calculator tool.
• Enter the numbers you want to subtract.
• View the result displayed by the tool.

Features and Benefits: Why Our Subtraction Calculator Stands Out

• User-Friendly Interface
• Instant Results
• Data Security
• Accessibility Across Devices
• No Installation Needed
• Examples for Clarity
• Versatile Usage
• Transparent Process
• Educational Resource
• Responsive Customer Support
• Regular Updates
• Privacy Assurance
• Efficient Calculation
• Language Accessibility
• Engaging and Informative Content
• Fun and Interactive Learning
• Shareable Results
• Responsive Design
• Educational Platform Integration
• Comprehensive Documentation

Applications and Usages of Subtraction Calculator

• Academic Learning: Helps students understand subtraction better.
• Teaching: Assists teachers in explaining subtraction in an interactive way.
• Everyday Calculations: Useful for quick calculations in daily life.
• Professional Use: Can be used by professionals for complex calculations.

Understanding Subtraction Calculator with Examples

Example 1: Suppose you want to subtract 5 from 10. Simply enter these numbers in the Subtraction Calculator and click 'Calculate'. The result will be '5'.

Example 2: Suppose you want to subtract 3.5 from 7.6. Enter these numbers in the tool and click 'Calculate'. The result will be '4.1'.

Secure and Reliable Subtraction with Our Calculator

Our Subtraction Calculator isn't just about simplifying subtraction, it's about providing a secure and reliable platform for your calculations. We've designed this tool with the utmost respect for your privacy. All calculations happen right on your device without the data ever leaving it. This tool is purely client-side, meaning no data is ever transmitted to any server. This ensures that your calculations remain confidential and protected. Additionally, the Subtraction Calculator can be accessed across various devices, making it easy for you to subtract numbers anytime, anywhere. Let's make subtraction easy and secure, together.

Frequently Asked Questions (FAQs)

• What is the Subtraction Calculator? The Subtraction Calculator is an online tool that simplifies the process of subtracting numbers.
• How does the Subtraction Calculator work? Simply enter the numbers you want to subtract and the calculator will do the rest.
• Is the Subtraction Calculator free to use? Yes, it is completely free to use.
• Is my data secure with the Subtraction Calculator? Yes, all calculations are done on your device and no data is shared with any server.
• Can I use the Subtraction Calculator on different devices? Yes, the Subtraction Calculator can be used across various devices.

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Roll the dice, make four-digit numbers, and round them to the nearest 10.

4. Use lots of different methods

Encourage your child to explore a range of methods for solving addition and subtraction problems.

Methods could include partitioning numbers into parts to add or subtract. For example:

2143 + 625 = ?   To solve this, you could partition 2143 into 2000, 100, 40, and 3, and then partition 625 into 600, 20, and 5.   The next step is to add the numbers together. First, add the ones: 5 + 3 = 8. Then, add the tens: 40 + 20 = 60. Then, add the hundreds: 600 + 100 = 700. And you also have the 2000.   Then, you can add all of these together: 8 + 60 + 700 + 2000 = 2768.

Your child may also draw pictures to represent how they have added or subtracted numbers. Number lines and number grids are useful for solving problems, as are formal written methods like column addition and subtraction.

Your child will understand subtraction as ‘difference’ as well as ‘taking away’. A good method that sees subtraction as difference is placing groups of objects into two rows to compare them and find the difference. This is particularly good for more tactile learners.

Your child may also find the difference between two numbers by counting up or counting back. For example, 27 – 18 could be interpreted as, ‘What is the difference between 27 and 18?’ Your child may count back from 27 to 18 to find the difference of 9 or count up from 18 to 27 to find the difference of 9.

Practising lots of methods not only means your child can more easily check their work – it means they can always pick the best method for any particular question. When your child has solved a problem, encourage them to use a different strategy to check their answer, and ask why they have chosen that particular method.

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Efficient Subtraction Year 4 Addition and Subtraction Resource Pack

Step 8: Efficient Subtraction Year 4 Resources

Efficient Subtraction Year 4 Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Autumn Block 2.

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This pack includes:

• Efficient Subtraction Year 4 Teaching PowerPoint.
• Efficient Subtraction Year 4 Varied Fluency with answers.
• Efficient Subtraction Year 4 Reasoning and Problem Solving with answers.

National Curriculum Objectives

Mathematics Year 4: (4C2)  Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate Mathematics Year 4: (4C3)  Estimate and use inverse operations to check answers to a calculation Mathematics Year 4: (4C4)  Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

Differentiation for Year 4 Efficient Subtraction:

Varied Fluency Developing Questions to support comparing two methods of subtraction. Two 3-digit numbers with no exchanging. Expected Questions to support comparing methods of subtraction. Includes two 4-digit numbers, with exchanges. Greater Depth Questions to support comparing methods of subtraction. Includes 3-digit numbers from a 4-digit number or two 4-digit numbers, with exchanges. Includes some multi-step subtractions.

Reasoning and Problem Solving Questions 1, 4 and 7 (Problem Solving) Developing Check a method of subtraction and create a further calculation for the method. Involves subtracting two 3-digit numbers (no exchanges). Expected Check a method of subtraction and identify how it could be done more efficiently. Involves subtracting two 4-digit numbers (with exchanges). Greater Depth Check a method of subtraction and identify how it could be done more efficiently. Involves subtracting 3-digit numbers from a 4-digit number (with exchanges).

Questions 2, 5 and 8 (Reasoning) Developing Explain whether a suggested method is efficient. Includes subtracting two 3-digit numbers, with no exchanging. Expected Explain why a statement regarding subtracting two 4-digit numbers (with exchanges) is always, sometimes or never true. Greater Depth Explain why a statement regarding subtracting 3-digit numbers from a 4-digit number or a 4-digit numbers from a 5-digit number (with exchanges) is always, sometimes or never true.

Questions 3, 6 and 9 (Reasoning) Developing Use and compare two methods of subtracting two 3-digit numbers (no exchanges). Expected Use and compare two methods of subtracting two 4-digit numbers (with exchanges). Greater Depth Compare two methods of subtracting a 3-digit number from a 4-digit number (with exchanges).

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Increasing Efficiency in Mathematics: Teaching Subitizing to Students with Moderate Intellectual Disability

• ORIGINAL ARTICLE
• Published: 08 August 2018
• Volume 31 , pages 23–37, ( 2019 )

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• Bree Jimenez 1 &
• Alicia Saunders   ORCID: orcid.org/0000-0002-1313-5719 2  

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Subitizing is an early numeracy mathematical skill where students are able to state the quantity of something without counting. This mathematical skill is more efficient than counting with one-to-one correspondence and leads to increased addition speed and accuracy. As more research emerges showing students with moderate and severe intellectual disability can learn mathematical concepts, there is a need for addressing efficiency. A single-case, multiple probe across participants design was used to investigate the effects of simultaneous prompting on subitizing and addition problem solving speed on three students with moderate intellectual disability. Visual analysis of baseline, intervention, and maintenance phase data indicated a functional relationship between simultaneous prompting and subitizing, and statistical analysis (Tau-U) further supported this with a large effect. This also led to increasing the speed with which addition problems were solved. In accordance with previous research on the use of systematic instruction (i.e., simultaneous prompting), students with intellectual disability can benefit from learning mathematical strategies to support their conceptual understanding and mathematical fluency. Future research and implications for practices are discussed.

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Jimenez, B., Saunders, A. Increasing Efficiency in Mathematics: Teaching Subitizing to Students with Moderate Intellectual Disability. J Dev Phys Disabil 31 , 23–37 (2019). https://doi.org/10.1007/s10882-018-9624-y

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Intervention based on science of reading and math boosts comprehension and word problem-solving skills

by University of Kansas

New research from the University of Kansas has found that an intervention based on the science of reading and math effectively helped English learners boost their comprehension, visualize and synthesize information, and make connections that significantly improved their math performance.

The intervention , performed for 30 minutes twice a week for 10 weeks with 66 third-grade English language learners who displayed math learning difficulties, improved students' performance when compared to students who received general instruction. This indicates that emphasizing cognitive concepts involved in the science of reading and math are key to helping students improve, according to researchers.

"Word problem-solving is influenced by both the science of reading and the science of math. Key components include number sense, decoding, language comprehension and working memory. Utilizing direct and explicit teaching methods enhances understanding and enables students to effectively connect these skills to solve math problems . This integrated approach ensures that students are equipped with necessary tools to navigate both the linguistic and numerical demands of word problems," said Michael Orosco, professor of educational psychology at KU and lead author of the study.

The intervention incorporates comprehension strategy instruction in both reading and math, focusing and decoding, phonological awareness, vocabulary development, inferential thinking, contextualized learning and numeracy.

"It is proving to be one of the most effective evidence-based practices available for this growing population," Orosco said.

The study, co-written with Deborah Reed of the University of Tennessee, was published in the journal Learning Disabilities Research and Practice .

For the research, trained tutors implemented the intervention, developed by Orosco and colleagues based on cognitive and culturally responsive research conducted over a span of 20 years. One example of an intervention session tested in the study included a script in which a tutor examined a word problem explaining that a person made a quesadilla for his friend Mario and gave him one-fourth of it, then asked students to determine how much remained.

The tutor first asked students if they remembered a class session in which they made quesadillas and what shape they were, and demonstrated concepts by drawing a circle on the board, dividing it into four equal pieces, having students repeat terms like numerator and denominator. The tutor explains that when a question asks how much is left, subtraction is required. The students also collaborated with peers to practice using important vocabulary in sentences. The approach both helps students learn and understand mathematical concepts while being culturally responsive.

"Word problems are complex because they require translating words into mathematical equations, and this involves integrating the science of reading and math through language concepts and differentiated instruction," Orosco said. "We have not extensively tested these approaches with this group of children. However, we are establishing an evidence-based framework that aids them in developing background knowledge and connecting it to their cultural contexts."

Orosco, director of KU's Center for Culturally Responsive Educational Neuroscience, emphasized the critical role of language in word problems, highlighting the importance of using culturally familiar terms. For instance, substituting "pastry" for "quesadilla" could significantly affect comprehension for students from diverse backgrounds. Failure to grasp the initial scenario could impede subsequent problem-solving efforts.

The study proved effective in improving students' problem-solving abilities, despite covariates including an individual's basic calculation skills, fluid intelligence and reading comprehension scores. That finding is key, as while ideally all students would begin on equal footing and there would be few variations in a classroom, in reality, covariates exist and are commonplace.

The study had trained tutors deliver the intervention, and its effectiveness should be further tested with working teachers, the authors wrote. Orosco said professional development to help teachers gain the skills is necessary, and it is vital for teacher preparation programs to train future teachers with such skills as well. And helping students at the elementary level is necessary to help ensure success in future higher-level math classes such as algebra.

The research builds on Orosco and colleagues' work in understanding and improving math instruction for English learners. Future work will continue to examine the role of cognitive functions such as working memory and brain science, as well as potential integration of artificial intelligence in teaching math.

"Comprehension strategy instruction helps students make connections, ask questions, visualize, synthesize and monitor their thinking about word problems," Orosco and Reed wrote. "Finally, applying comprehension strategy instruction supports ELs in integrating their reading, language and math cognition…. Focusing on relevant language in word problems and providing collaborative support significantly improved students' solution accuracy."

Provided by University of Kansas

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Intervention based on science of reading, math boosts comprehension, word problem-solving skills

English learners with math difficulty showed improvement following culturally-responsive training.

New research from the University of Kansas has found an intervention based on the science of reading and math effectively helped English learners boost their comprehension, visualize and synthesize information, and make connections that significantly improved their math performance.

The intervention, performed for 30 minutes twice a week for 10 weeks with 66 third-grade English language learners who displayed math learning difficulties, improved students' performance when compared to students who received general instruction. That indicates emphasizing cognitive concepts involved in the science of reading and math are key to helping students improve, according to researchers.

"Word problem-solving is influenced by both the science of reading and the science of math. Key components include number sense, decoding, language comprehension and working memory. Utilizing direct and explicit teaching methods enhances understanding and enables students to effectively connect these skills to solve math problems. This integrated approach ensures that students are equipped with necessary tools to navigate both the linguistic and numerical demands of word problems," said Michael Orosco, professor of educational psychology at KU and lead author of the study.

The intervention incorporates comprehension strategy instruction in both reading and math, focusing and decoding, phonological awareness, vocabulary development, inferential thinking, contextualized learning and numeracy.

"It is proving to be one of the most effective evidence-based practices available for this growing population," Orosco said.

The study, co-written with Deborah Reed of the University of Tennessee, was published in the journal Learning Disabilities Research and Practice .

For the research, trained tutors developed the intervention, developed by Orosco and colleagues based on cognitive and culturally responsive research conducted over a span of 20 years. One example of an intervention session tested in the study included a script in which a tutor examined a word problem that explained a person made a quesadilla for his friend Mario, giving him one-fourth of it, then needed to students to determine how much remained.

The tutor first asked students if they remembered a class session in which they made quesadillas, what shape they were and demonstrated concepts by drawing a circle on the board, dividing it into four equal pieces, having students repeat terms like numerator and denominator, and explaining that when a question asks how much is left, subtraction is required. The students also collaborated with peers to practice using important vocabulary in sentences. The approach both helps students learn and understand mathematical concepts while being culturally responsive.

"Word problems are complex because they require translating words into mathematical equations, and this involves integrating the science of reading and math through language concepts and differentiated instruction," Orosco said. "We have not extensively tested these approaches with this group of children. However, we are establishing an evidence-based framework that aids them in developing background knowledge and connecting it to their cultural contexts."

Orosco, director of KU's Center for Culturally Responsive Educational Neuroscience, emphasized the critical role of language in word problems, highlighting the importance of using culturally familiar terms. For instance, substituting "pastry" for "quesadilla" could significantly affect comprehension for students from diverse backgrounds. Failure to grasp the initial scenario can impede subsequent problem-solving efforts.

The study proved effective in improving students' problem-solving abilities, despite covariates including an individual's basic calculation skills, fluid intelligence and reading comprehension scores. That finding is key as, while ideally all students would begin on equal footing and there were little variations in a classroom, in reality, covariates exist and are commonplace.

The study had trained tutors deliver the intervention, and its effectiveness should be further tested with working teachers, the authors wrote. Orosco said professional development to help teachers gain the skills is necessary, and it is vital for teacher preparation programs to train future teachers with such skills as well. And helping students at the elementary level is necessary to help ensure success in future higher-level math classes such as algebra.

The research builds on Orosco and colleagues' work in understanding and improving math instruction for English learners. Future work will continue to examine the role of cognitive functions such as working memory and brain science, as well as potential integration of artificial intelligence in teaching math.

"Comprehension strategy instruction helps students make connections, ask questions, visualize, synthesize and monitor their thinking about word problems," Orosco and Reed wrote. "Finally, applying comprehension strategy instruction supports ELs in integrating their reading, language and math cognition… Focusing on relevant language in word problems and providing collaborative support significantly improved students' solution accuracy."

• Learning Disorders
• K-12 Education
• Educational Psychology
• Intelligence
• Special education
• Problem solving
• Developmental psychology
• Child prodigy
• Intellectual giftedness
• Lateral thinking

Story Source:

Materials provided by University of Kansas . Original written by Mike Krings. Note: Content may be edited for style and length.

Journal Reference :

• Michael J. Orosco, Deborah K. Reed. Supplemental intervention for third-grade English learners with significant problem-solving challenges . Learning Disabilities Research & Practice , 2024; 39 (2): 60 DOI: 10.1177/09388982241229407

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