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Subtracting fractions with like denominators is an inevitable part of mathematics. It is an essential concept that needs to be understood by students as it plays a crucial role in advancing to higher mathematical operations. It is essential for teachers to devise activities to help students grasp the concept of subtracting fractions with like denominators easily. Here are a few activities that can help teachers teach students how to subtract fractions with like denominators quickly and with ease.

Fraction War Game

To engage students in subtracting fractions with like denominators, teachers can play the fraction war game. For this game, students will need a deck of cards with fractions on each. Students will have to deal with two cards each and apply the process of subtraction on both. They can then compare their results. Whoever gets the highest value will win the game.

Fraction Dominoes

Another fun way to teach students to subtract fractions with like denominators is to use fraction dominoes. The teacher can prepare the dominoes with fractions on each, and then students will have to subtract the fractional values. They can also compete with each other and form a chain of correct answers while subtracting fractions with like denominators.

Fraction Subtraction Puzzle

Teachers can prepare fraction subtraction puzzles for students. The puzzles can be in the form of a crossword or jigsaw puzzle. The students can solve the puzzle and write the correct answer to the subtraction problem on each puzzle piece. They can then stick the pieces together to form a beautiful picture.

Fraction Board Games

Fraction board games can be an enjoyable and interactive way to teach students to subtract fractions with like denominators. The games can be made with varying levels of difficulty to cater to different student levels. Students can play in pairs or groups, and they will have different scenarios to work with while subtracting fractions with like denominators.

Fraction Subtraction Worksheets

Teachers can prepare worksheets that have subtraction problems involving fractions with like denominators. They can give the students enough space to work out the problem and write the corresponding answer. Teachers can then check the answers and provide feedback on the marked worksheets.

Conclusion

In summary, subtraction of fractions with like denominators is an essential concept in mathematics, and it is essential for students to grasp it thoroughly. Teachers can use fun activities such as the fraction war game, fraction dominoes, fraction subtraction puzzles, fraction board games, and fraction subtraction worksheets to engage students while teaching them the necessary skills. Through these activities, students will be able to learn how to subtract fractions with like denominators easily and with confidence.

As students progress in their studies of mathematics, they must learn to work with fractions. One essential skill is the ability to subtract fractions with like denominators. With a firm grasp of this concept, learners can tackle more complex mathematical problems.

Using number lines is a helpful tool for teaching this concept. With a visual representation, students can better grasp the idea of subtraction and see how the numbers relate to one another. Here are some fun and engaging activities to teach students to subtract fractions with like denominators using number lines.

1. Fraction Splat – This game is a hands-on way to reinforce the concept of subtraction. Draw a large number line on the board or use a long strip of paper. Divide the line into equal parts and label fractions with like denominators.

Then, pass out fly swatters or small squares of paper to represent “splat.” Call out a subtraction problem and have students race to “splat” the correct answer on the number line using the appropriate fraction. For example, if the problem is 4/7 – 2/7, students would splat the difference of 2/7 between the corresponding fractions on the number line.

2. Shape Creations – Print out shape templates that are divided into equal parts on colorful paper. Cut the shapes into parts and distribute them to your students. Then, have them use the pieces to create their own number lines.

Students can label the fractions on the line and use them to answer subtraction problems. This activity emphasizes the hands-on nature of math, as students can physically move the fractions to solve problems.

3. Fraction Hop – Create a giant number line with chalk on the playground or use tape on the classroom floor to represent the number line. Then, have students stand at one end and give them subtraction problems to solve for each hop. For example, if they start on zero and the problem is 5/8 – 1/8, they will take five hops forward and then one back. This activity gets your students up and moving while reinforcing the concept of subtraction.

4. Story Problems – Present students with real-life examples of subtraction with like denominators in the form of story problems. For example, you could describe a pizza that was divided into eight slices and how four have been eaten, leaving four slices. Then ask students to determine the answer by drawing out the problem on a number line.

These story problems make the concept more relatable to students and can keep students engaged in the lesson.

In conclusion, teaching students to subtract fractions with like denominators using number lines can be an exciting and engaging experience. By incorporating games, hands-on activities, and real-world examples, students can better grasp the concept and apply it to future endeavors. When students understand the basics of math, they will be more prepared for the challenges to come.

If you’re a teacher looking for activities to improve your students’ subtraction skills, teaching them how to subtract doubles is a great way to start. This foundational skill helps build understanding of subtraction principles, as well as mental math skills and fluency. Here are some fun and engaging activities to help your students master double subtraction:

1. Double Subtraction Flashcards

One classic way to practice double subtraction is to use flashcards. Print out a set of double subtraction cards for each student, as well as an answer key. Have students take turns flipping up a card and answering the equation without looking at the answer key. For each correct answer, they can tally a point. This game can be played in teams or individually.

2. Double Subtraction Bingo:

Another fun way to practice double subtraction is with a bingo game. Create bingo cards with double subtraction equations, and then call out the answers. Students can then search for the equation on their card and mark it off. The first to fill their card wins!

3. Double Subtraction War:

This classic card game can be used to reinforce double subtraction skills. Have students deal out a deck of cards, excluding face cards. Students then turn over two cards at a time and subtract them. The person with the lowest answer wins the cards. Whoever has the most cards at the end of the game wins!

4. Double Subtraction Challenge:

Create a worksheet of double subtraction equations from 10-20. Give students a set amount of time to complete the worksheet, and have them record their time on the bottom of the page. Repeat this challenge once a week, tracking students’ progress. Students enjoy trying to beat their personal best time!

5. Double Subtraction Balloon Pop:

Write double subtraction equations on small slips of paper, and stuff them into balloons. Blow up the balloons and have students take turns popping a balloon and solving the equation. This game works well with teams or individuals.

These activities are a great way to help your students develop mastery of double subtraction. With consistent practice and a range of engaging activities, your students will soon be solving double subtraction equations with ease!

Subtracting decimal numbers is an important math skill for students to develop. This skill can be particularly challenging for students who struggle with math concepts. To overcome this challenge, teachers should employ a variety of engaging, hands-on activities that help students master the basics of decimal subtraction. Below are some activities to teach students to subtract decimal numbers.

1. Combine Like Terms

One effective way to teach students to subtract decimal numbers is to begin with combining like terms. Start by writing simple decimal equations on the board, such as 2.3 – 1.7. Before getting into the mechanics of the subtraction process, ask students to identify the like terms in the equation. In this case, the like terms are 0.3 and 0.7. Ask students to add these terms together to come up with the answer. Once they understand that subtracting decimal numbers is the same as adding like terms together, they will be able to apply this concept to more complex problems.

2. Play Decimal War

Decimal War is a fun way for students to practice subtracting decimal numbers. To play, give each student a deck of cards that only contains digits 0-9 and decimal points. Students should draw two cards from their decks and arrange them to make the largest possible decimal number. Once all students have done this, they should subtract their decimal number from another student’s decimal number. The student with the smallest difference wins the round. Play multiple rounds to give students plenty of practice with this skill.

3. Use Real-Life Examples

Using real-world examples can be an effective way to teach students to subtract decimal numbers. You could give students a grocery list that includes items with decimal prices, such as $1.99 for a pound of grapes. Ask them to subtract the price of one item from another item to determine the total cost of their grocery shopping trip. This activity helps students see the practical importance of decimal subtraction and helps them apply their skills to real-world situations.

4. Use Anchor Charts

Anchor charts are visual aids that can help students understand complex ideas. To create an anchor chart for decimal subtraction, write down each step of the process in a clear, easy-to-read format. Include pictures or diagrams to help students better understand what is happening at each step. Display this chart in your classroom so students can refer back to it as they work through different problems.

5. Use Online Resources

Online resources can provide students with an interactive way to practice decimal subtraction. Many educational websites offer fun games that challenge students to subtract decimal numbers in various contexts. For example, students may have to subtract decimal numbers in order to run a lemonade stand or bake cookies. These games can be played alone or with a partner and are designed to engage students with the material in a fun and enjoyable way.

In conclusion, teaching students to subtract decimal numbers can be challenging, but it doesn’t have to be boring. By using a variety of hands-on activities, real-world examples, and online resources, teachers can help their students master this important math skill. With practice and patience, students can gain confidence in their abilities to subtract decimal numbers and tackle more complex math concepts in the future.

Subtracting decimals can be a complex concept for students to understand. However, using blocks can make this process easier and more engaging. Blocks are a powerful tool for visual learners, allowing students to see the relationship between decimal numbers and their value. Here are some activities to teach students how to subtract decimals using blocks.

1. Building Blocks

To begin, give each student a set of blocks that represent tenths and hundredths. Students should build different decimal numbers using the blocks, such as 1.23 or 0.45. Next, give students a subtraction problem to solve using the blocks. For example, 1.23 – 0.45. Students should use blocks to represent each number and then visually subtract the blocks to find the answer. This allows students to see how the decimals are being subtracted.

2. Picture It

Another fun activity to teach subtraction of decimals with blocks is to have students create a picture using the blocks. Give them a set of decimal values and ask them to build a picture out of the blocks with a certain value. Next, ask students to subtract another decimal value from that picture to create a new picture with a different value. This allows students to use their imagination and creativity to visualize and solve subtraction problems.

3. Number Line

Use block pieces and ask the students to put them in order of increasing or decreasing value. Then, on a number line, have the student plot each of the decimal values represented by the block pieces. Afterward, give the students some subtraction problems that they have to solve. They will be able to subtract the blocks to find out the answer. This activity will help in visually understanding how decimal numbers are ordered and related to each other.

4. Equation Blocks

This activity involves having the student work with decimal subtraction problems using blocks to represent the operands and difference. Instead of using numerals in the problem, utilize blocks that represent the various components of the equation. In this way, students will need to identify the right combination of blocks to get the answer and have a better understanding of how to subtract decimal numbers.

In conclusion, teaching subtraction of decimals might be tough, but providing students with a visual learning experience using blocks can make learning fun and easy. These activities will help students understand the concept of decimal subtraction and develop crucial skills that they can use for a lifetime. It’s essential to provide students with opportunities for hands-on, engaging activities to help them learn new concepts while promoting creativity and critical thinking.

Subtraction of decimal numbers can be a little tricky for students, but with the help of manipulatives, they can easily grasp the concept of subtracting decimals. Using blocks or base ten blocks is a great way to teach students how to subtract decimal numbers.

Here are some important activities to teach students how to subtract decimal numbers using blocks:

1. Show and Tell with Blocks: At first, it is important to introduce the blocks or base ten blocks to the students. You can start with a demonstration by using a few blocks and subtracting the numbers. Ask the students to participate in the demonstration by coming to the board and taking away blocks.

2. Practice subtraction with Blocks: After demonstrating, it is important to give students the opportunity to try it themselves. Distribute blocks to each student and ask them to create their own numbers using blocks. Once they have created their numbers, they can subtract them by taking away blocks.

3. Balancing Blocks: This activity will allow students to practice subtraction by balancing blocks. Give students a set of blocks and ask them to balance the blocks on a beam scale. After they have balanced the blocks, ask them to subtract one set of blocks from another set of blocks.

4. Roll and Subtract: In this activity, students will roll a dice with decimal numbers and subtract them using blocks. Provide students with a dice with decimal numbers from 0.1 to 0.9. Ask them to roll the dice twice and subtract the numbers using blocks.

5. Adding and Subtracting decimals with Blocks: This baking activity will showcase the use of adding and subtracting decimals. Provide students with baking ingredients with decimals (e.g. 0.25 cups of flour, 0.5 cups of sugar, etc.) and ask them to add or subtract the ingredients using blocks. Once they have added or subtracted the ingredients, they can create a recipe.

With these activities, students will have a better understanding of subtraction with decimals. Using manipulatives like blocks, is an effective way to teach math concepts and makes learning enjoyable for students.

Subtraction is a math skill that is essential for children to learn. It is a basic concept that is used in a variety of situations in our everyday life. When children are just starting to learn subtraction, they often struggle with the concept of counting backwards. However, counting on can be a great alternative to solve subtraction problems. Here are some activities that can help teach children how to subtract by counting on, up to 20.

1. Use Counters or Objects

One of the easiest and most effective ways to teach subtraction using counting on is by using counters or objects. For example, if you ask a child to subtract 4 from 8, give them eight counters or objects and ask them to count on four times to find the answer. For instance, they could say “eight, nine, ten, eleven, twelve” which is equal to 8 – 4 = 4.

2. Use Number Lines

Number lines can be a great visual aid to teach subtraction. Start by drawing a number line and marking two numbers on each end of the line. For instance, if you want to teach subtraction of 7 – 4, mark 7 on one end and 4 on the other end. Then, tell the child to start counting at 4 and move three spaces to the right, which will lead them to 7. This will help them to understand that 7 – 4 = 3.

3. Use Worksheets

Worksheets can be an excellent tool to reinforce the concept of subtraction by counting on. You can find subtraction worksheets that include pictures or objects that kids can use to count on. For example, if there is a picture of eight apples and you need to subtract three apples, the child can count forward from three to find the answer.

4. Use Interactive Games

Games can often be a great way to engage children and make learning fun. There are several interactive games available online that can help children learn subtraction by counting on. For instance, “Penguins on Ice” is a game where kids subtract penguins from an ice block by counting on. This game is perfect for kids who can easily be distracted while learning.

5. Use Real-life Examples

Using real-life examples is an excellent way to teach children the practicality of subtraction. For instance, you can ask them to subtract the number of items that they have left from the number of items they started with. This can be applied to various situations such as counting money, counting toys, and so on.

In conclusion, subtraction by counting on is a crucial concept that children should learn during their primary education. These activities are designed to make learning subtraction more accessible and enjoyable for children. Be patient and give your child enough time to understand the concept and skills involved in subtraction by counting on. With consistent practice and patience, your child will grasp this skill and become more confident in their ability to do math problems.

Subtraction is an essential skill that students need to master as part of their elementary math curriculum. While traditional methods of subtraction involve borrowing or regrouping, there is another method that is equally effective, which is counting on.

Counting on is a simple and straightforward method that involves starting with the larger number and counting up to the smaller number. This method is particularly useful when teaching subtraction to young students, as it helps them visualize the number line and understand the concept of subtraction.

To help teachers introduce students to counting on, here are five engaging activities to teach students to subtract by counting on – up to 10.

1. Count and Cover Game

In this game, students start by covering ten pictures with counters or small objects, such as buttons or tokens. They are then asked to count how many counters they have covered, and then take away a few from the group. They can then count up from the remaining counters to find the difference. This game can be played in pairs or small groups, and is a great way to reinforce subtraction skills.

2. Number Line Race

The number line race is a fun and interactive game that helps students visualize the number line and understand the concept of subtraction. To play, students are given a number line from 1 to 10 and are asked to start at the larger number and count down to the smaller number. They can then move their marker on the number line to show the difference. The first student to reach the correct answer wins the game.

3. Subtraction Bingo

Subtraction Bingo is a fun and engaging way to reinforce subtraction skills. To play, students are given a bingo card with a variety of subtraction problems. The teacher or a designated caller reads out the subtraction problem, and students must find the answer on their bingo card and cover it with a counter. The first student to get a line or a full card wins the game.

4. Roll and Count Game

In this game, students roll a die and count up to the corresponding number on the number line. They then take away the number of objects rolled on the die, and count up to find the remainder. This game can be played in pairs or small groups, and is a great way to reinforce the concept of counting on.

5. Toss and Subtract Game

The toss and subtract game is a fun and interactive way to teach subtraction skills. To play, students are given a set of small objects, such as mini erasers or small toys. They are then asked to toss them onto a playing surface and count how many objects landed on each side. They can then take away the smaller number from the larger number to find the difference. This game can be played individually or in pairs, and is a great way to reinforce subtraction skills in a playful way.

In conclusion, teaching students to subtract by counting on is an effective way to help them understand the concept of subtraction and visualize the number line. These five activities are engaging and interactive ways to reinforce the concept of counting on and help students develop strong subtraction skills. By incorporating these activities into their lessons, teachers can help their students become confident and proficient in subtraction.

Teaching subtraction to young students who are just starting to explore the basics of math can be overwhelming. It is important to make sure that teachers are using a variety of teaching methods and out-of-the-box activities to help children understand this concept better. One such effective technique to teach subtraction is by counting back, which is a visual and interactive method that can help kids understand the idea, process, and significance of subtraction.

Activities to teach students to subtract by counting back can be both fun and exciting, making the experience memorable for children. Here are some exciting activities that teachers can use to help their students understand subtraction concepts by counting back up to 20.

1. Fish Bowl Activity

This activity is perfect for young students who are just starting to learn subtraction. It involves two bowls of fish, one bowl with, let’s say, ten fish and the second bowl with no fish.

The teacher will start by asking the students how many fish are in the first bowl, and the students will count the fish together. The teacher will then explain that they will remove some fish from the bowl and put them in the other bowl, and the students will count how many fish remain in the first bowl.

The teacher will continue this process, and the students will count back the number of fish that have been removed from the first bowl to calculate the remaining fish. This way, students will easily grasp the idea of counting back to subtract.

2. Number Line Activity

Young students enjoy interactive activities. To teach subtraction better, teachers can create a number line on the floor, and students will stand on it. The teacher will choose two numbers, let’s say 10 and 5.

The teacher will explain that they are going to jump back from ten to five and count how many jumps they need to take to reach five. Students will take a step back with each count, and when they land on five, they will count the number of steps taken to reach there. This activity allows children to learn and apply subtraction concepts by visualizing the number relationship and subtly subtracting.

3. Flower Garden Activity

This activity uses scenarios that engage students in a playful way while teaching them subtraction. Teachers can create a garden with different flowers that have a designated value, let’s say we choose daisies as the flower with the value of 5, and there are ten daisies in the garden, and we also have potted flowers as counters.

The teacher will begin with asking the students how many flowers are in the garden and pick up a pot, inviting the student to remove the number of flowers they wish to subtract. They will count the remaining daises after the subtraction, allowing students to understand that they counted back to subtract the flowers.

4. Pirate Subtraction Activity

Who doesn’t like pirates? This fun pirate thematic activity uses playful scenarios to teach subtraction. The teacher will tell the classroom a story of a pirate ship and how much treasure was lost or stolen, let’s say 6 gold coins.

Teachers can use manipulatives such as golden plastic coins or paper cutouts to visualize the gold coins. Then the teacher will ask the students how much treasure is left after the pirate took six coins and encourage the students to start counting from 20 to reach the answer of 14. By using a fun and playful story, students will engage with the lesson content and learn subtraction equations by counting back from a given number.

In conclusion, teaching young students subtraction can be made more accessible and effective if we use various techniques that focus on counting back. Activities, such as the fishbowl game, the number line activity, flower garden activity, and pirate subtraction activity, are interactive and playful ways to teach children how to subtract when counting back. By using these activities, students will learn and retain lesson information and develop a basis to move to more complex mathematical concepts like addition, multiplication, and division.

Subtraction is one of the foundational math skills that students learn in school. While there are a number of different methods to teach subtraction, one effective method is teaching students to count back from a given number. This approach can be particularly effective for young students who are just starting to learn the basics of math. Here are some activities to teach students to subtract by counting back up to 10.

1. Number Line Exercises

One of the easiest and most effective ways to teach students to subtract by counting back is through number line exercises. Simply draw a number line from one to ten on a sheet of paper or whiteboard. Then, ask students to count back from ten to find the answer to subtraction problems such as 5-2 or 8-6.

2. Counting Back with Blocks

Another great way to teach students to subtract by counting back is by using blocks or other manipulatives. For example, you could give students 10 blocks and ask them to count back to 7. They would then remove 3 blocks from the pile to represent the subtraction problem. You could also use a visual aid such as a ten-frame to help students visualize the concept of counting back.

3. Subtraction Memory Game

Students love games, and a subtraction memory game is a fun way to reinforce the concept of counting back. To play, print out pairs of number cards from 1-10 and arrange them face down in a grid. Players take turns flipping over two cards in an attempt to find a match. When a pair is found, the player must count back from the higher number to the lower number to find the answer to the subtraction problem.

4. Roll and Subtract

To play Roll and Subtract, students will need a pair of dice and a sheet of paper or whiteboard. One student rolls the dice and another student writes the numbers on the board. The first student then counts back from the highest number to the lowest number to find the answer to a subtraction problem. This game can be played individually or in small groups.

5. Subtraction Song

For auditory learners, a subtraction song can be an effective tool for learning to count back. There are many great subtraction songs available online that students can sing along to. For example, the popular song “10 Little Indians” can be adapted to teach subtraction up to 10.

In conclusion, there are many effective activities to teach students to subtract by counting back up to 10. No matter which approach you choose, it’s important to make learning fun and engaging for students. By using manipulatives, games, and other interactive exercises, you can help your students build a strong foundation in math that will serve them well for years to come.

Subtraction across zeros can seem like a daunting task for students, but with the right activities, it can become an enjoyable and engaging experience. Here are some activities to help teach students to subtract across zeros:

1. Place Value Mats

Using place value mats can be an excellent way to introduce subtraction across zeros. Place value mats allow students to visualize the numbers they are subtracting, which can help them understand the process better.

To use place value mats, simply draw a large square on a piece of paper or use a pre-made printable version. Write the numbers you are subtracting on the top and bottom of the square, and then work through the problem by subtracting each place value column. Students can place manipulatives like base ten blocks or counters on the mats to help reinforce the idea of zeros in the subtraction problem.

2. Number Lines

Number lines can be another excellent tool for teaching subtraction across zeros. To use number lines, draw a horizontal line and label the starting number at one end and the ending number at the other end. Then, identify the zeros in the problem and mark them on the number line.

Next, work through the problem by subtracting the non-zero digits, starting at the right-hand side of the number line and working left. When students get to a zero on the number line, they know that they need to borrow from the next place value column, just like in a traditional subtraction problem.

Students can also use number lines to check their answers by adding the difference back to the starting number and ensuring that they get the correct ending number.

3. Games

Games are a great way to make learning fun and engage students in the process of subtraction across zeros. One game to try is “Zero Out,” where students take turns rolling a dice and subtracting it from a starting number. The catch is that if they roll a zero, they need to subtract from the next place value column.

For example, if the starting number is 50 and a student rolls a two, they would subtract two from 50 and get 48. However, if they rolled a zero, they would need to subtract from the tens column and say “forty” instead of “fifty.” The first student to get to zero wins the game.

4. Real-Life Scenarios

Another way to help students understand subtraction across zeros is to provide them with real-life scenarios where this skill is necessary. For example, you could have students plan a party and subtract the cost of various items to stay within a budget.

You could also give students a recipe and ask them to subtract the amount of ingredients needed to make half of the recipe. This can help them understand the concept of the zeros being a place holder and the need to borrow from the next place value column in real-life situations.

In conclusion, teaching subtraction across zeros doesn’t have to be boring or difficult for students. By using place value mats, number lines, games, and real-life scenarios, students can grasp this concept with ease and have fun in the process.

Subtraction is a crucial mathematical skill that every student must master in their early years of learning. However, it can be challenging for some students, especially when they need to subtract a one-digit number from a two-digit number with regrouping. As a teacher, you need to find engaging activities that make learning fun and help your students understand the concept.

Here are some activities that can help you teach your students how to subtract a one-digit number from a two-digit number with regrouping:

1) Base-Ten Blocks: Using base-ten blocks is an excellent visual aid for students to understand regrouping. You can display the problem on the board and use the blocks to show the process of regrouping. For example, if you need to subtract 5 from 27, you can use two ten rods and seven units to represent the number 27. To subtract 5, you can take away five units, but since you can’t do that, you need to regroup one ten rod into ten units. You can then take away the five units to get the answer – 22.

2) Interactive Worksheets: Interactive worksheets can be a great way to engage students in their learning. You can create online worksheets that allow your students to drag and drop the digits to carry out the subtraction process. This will help students to visualise the process of regrouping, making it easier for them to comprehend.

3) Subtraction Games: Playing subtraction games can be a fun and engaging way to teach your students. You can create a subtraction game where students have to answer subtraction problems and move their game piece accordingly. The game can be made more challenging by adding problems with regrouping.

4) Real-life Scenarios: Incorporating real-life scenarios in your lessons can help students connect with the subject matter. You can use situations like buying groceries, calculating change, and measurement problems that require subtraction skills. This will make learning more practical and help students to see how subtraction can be used in their daily lives.

5) Peer Collaboration: Collaborating with peers is an effective way to learn because it allows students to share their thoughts and ideas. You can create partnerships, where students can work together to solve subtraction problems that involve regrouping. This will help them to learn from one another and develop team-building skills.

6) Online Resources: There are a variety of online resources available that can help you teach subtraction with regrouping. Websites like Math Playground and Math Games offer interactive games and activities that can help your students practice their subtraction skills.

In conclusion, mastering subtraction with regrouping can be a challenging task for some students. However, by using engaging activities such as base-ten blocks, interactive worksheets, games, and real-life scenarios, teachers can help their students learn this essential mathematical skill. Additionally, online resources and peer collaborations can further enhance students’ learning and understanding of subtraction with regrouping.