13 Simple Ways to Practice Addition and Subtraction
In my day, we just memorized math. I don’t know that I ever really truly understood much of what math was nor was I able to compute higher-level skills until I started teaching math and learned how to be flexible with numbers. Flexibility with numbers is a key foundational skill for young learners and those who don’t have it, struggle from early on. When it is hard to figure out what 7 + 4 =, a child will become easily frustrated, leading to the oh so often felt and heard, “I’m just no good at math.” It isn’t about memorization and speed (puuuhhhleeeease – stop with the timed tests!) with basic addition and subtraction – it is about developing strategies that lead to fluency, automaticity, and understanding.
There are a number of ways to accomplish this, but one thing I am passionate about is making sure instruction is developmentally appropriate. Research tells us that learning through play is most appropriate for early childhood students (and that designation goes through age 8 or 9 depending on where you look) and the kids are way more engaged when they’re playing games. To develop strategic thinking, use lots of concrete representations to start, then move to the more abstract (for example, start with dot dice and move on to numeral dice). So, here are 13 ways to practice simple addition and subtraction that are sure to please.
Way 1. Dice –
There are so many different kinds of dice you can get now and if you can’t find the ones you want, there’s DIY wood block dice! Place value blocks, ten frames, dots, numerals of any range with any number of sides, big and wooden dice, colorful dice, foam dice… Just search for dice online – but be prepared to get lost in that rabbit hole! Lots of work with making five and ten is required in K/1 and this can easily be done with addition (and frankly, subtraction, too – think fact families) and dice. Tenzi is a great way to have multiple players with a target number in a fast-paced, fun game.
Pull out the numbered cards and only use those. You can use them in a number of ways – simply flip two cards and add or subtract, play make five or make ten go fish, addition/subtraction war (flip two cards each, whoever has the most/least wins all four cards, repeat) or any of a number of other card games.
This low prep way to practice addition and subtraction involves simply giving students a bin of dominoes and having them pull one at a time. Then, they either add or subtract using the two sides of the domino. It is important, as with all of these ideas, to encourage strategy use. They should subitize the numbers, use counting on strategy, think about a rekenrek or a ten frame – playing these while simply counting all the dots won’t improve their skills at all.
Way 4. Hopscotch –
Need to get some wiggles out? Go out to the playground or make an indoor tape hopscotch board and give each square a number 0-10. The directions can vary based on your students’ abilities and be used to find the missing addend or subtrahend (“What goes with 6 to make 10?” and they hop to the 4) or to do more basic addition and subtraction (toss two small pebbles or sticks and add/subtract the two numbers). Ready to up the challenge factor? Have kids make the target number a different way after they give you the first way or make a target number with three addends.
5. Musical Chairs –
This is another movement activity for math where you simply put number models on index cards – one per chair. Then play musical chairs like you always would, but kids have to answer their problems correctly to stay in the game as well!
6. Sparkle –
This whole class game can be used to practice skip count adding by any number you choose. Select a number to stop at and whoever follows the person with that number says, “Sparkle,” with the next person being out. For example, count by 5’s to 40. The kids stand in a circle and have to count by 5’s going around the circle (“0, 5, 10, 15, 20, 25, 30, 35, 40, Sparkle, (student is out), 0,5, 10, etc.). This continues until there is one student left standing! My students love this game and it is so easy to play if you’re waiting for a specials class to start or have a few extra minutes!
Way 7. How Many Are Hiding? –
Using unifix cubes, have your paired students create one tower of 5 or 10 (depending on your target number – going to other numbers once they are solid in 5 and 10). One student from each pair takes the entire tower and puts it behind their back, breaking the tower into two parts. Then, they show their partner one of the towers, and the partner has to guess how many are hiding behind their partner’s back. This is another favorite in my classroom.
Get a cheap beach ball and put numbers 0-10 all over it with a permanent marker. Partners toss the ball back and forth, adding or subtracting whatever numbers their hands land closest to! Gross motor and math at the same time, while the kids are learning? That’s a winner!
Red and yellow counters placed in a cup are all you need to practice addition and subtraction with shake, spill, and add/subtract. Place your target number of counters into the cup, shake, spill onto the table and then add or subtract (just like it the name sounds!). I usually have my students record their answers by drawing or coloring in the circles on a recording sheet along with writing the number model. For subtraction, they just have to know to start with the larger number, then we stack the other counter on top to represent the ‘taking away. ’
There are plenty of color by number addition or subtraction pages out there for those days when you just need a few minutes of quiet. The best part? Students get a self-checking, fine-motor practicing math activity that they love so you both win!
11. Eyes Closed –
This game can be done as a small group game to start and then with partners once the kids know how to play. Grab whatever is close and easy and put out a certain amount of that object on the table. Have the students close their eyes and either add some more or take some away. Have the students open their eyes and they have to write on their whiteboard + or – and how many.
12. Guess My Way –
Using a bead rack/rekenrek and a target number of 10, screen your bead rack so students can’t see and make 10 in any way (0/10, 1/9/ 2/8, etc.). While you’re doing that, have students make 10 on their own bead rack. When you’re all ready, have students guess what way you made 10 by sharing their way. Keep guessing until there’s a winner (if students are ready, they can be the next ‘maker,’ taking turns each time there’s a new winner.
Way 13. Riddles –
Kids love to solve riddles, so make them math riddles! Create a set of task cards with four choices and three clues that can be either addition or subtraction practice, or both! For example, the answer options could be 10, 8, 7, 4 (you determine the level of difficulty in the number models). The clues might be, “The answer is not 5 + 5. The answer is not 3 + 4. The answer is not 4 + 0,” leaving them with the answer to the riddle (8).
Give your students lots of options for concrete representation practice before moving on to the more abstract. We do lots of practice with bead racks and ten frames, so I have these tools out for kids to use, but also large versions on my whiteboard. Kids can visualize the pieces moving without actually moving them after a while, and then eventually they just have that image in their mind and don’t need to look at the tool. Remember, it is about strategies and understanding – not memorization and speed!
Written by: Kristin Halverson
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Fun Ways to Learn Addition and Subtraction Math Facts
Math fact fluency is one of the key math goals in elementary school. If you’re teaching little ones in first or second grade, you’re likely spending a lot of time helping kids learn addition and subtraction math facts. Slowly you shift from teaching kids the basic concepts of combining and separating sets to emphasizing rapid recall of basic facts.
To be honest while these skills are very important, teaching them can sometimes rely too heavily on worksheets, and we know kids tend to zone out when that happens. In this article we’re outlining some of our favorite math fact games, addition and subtraction toys, and a few math fact workbooks to supplement your hands-on learning if you really need them.
These math fact activities are great to use in the classroom or at home.
Games to Practice Addition and Subtraction Math Facts
Games are by far the most fun way to help kids learn math facts. These are our top picks for teaching addition and subtraction math facts.
Snap it Up is our family favorite right now. It’s fast-paced and each round goes rather quickly, so you aren’t pulled into a game that never ends. We can easily play a few rounds before or after dinner, or whenever we have a couple of extra minutes. I love that it encourages kids to really think about different ways to make a number. They get excellent practice in figuring out how to add or subtract to reach a certain number. And it’s FUN! Because of the fast pace, it’s best for kids who already have a certain level of skill in addition add subtraction.
Math War is a better option for kids who are just started with math facts. They can take their time to solve each problem. We played this one a lot before transitioning to Snap it Up, but it’s still a go-to option for both of my kids. You play it exactly like traditional war, except you’re solving addition and subtraction facts along the way. This one requires more time than Snap it Up, but you get a lot of valuable math fact practice in the process.
Head Full of Numbers is a bit of a step beyond Snap it Up in my opinion. It’s a bit like a math version of Boggle. Kids make different addition, subtraction, multiplication, or divisions facts given a set of numbers. The goal is to see who can come up with the most correct equations. While I like that this one involves mixed operations, it does require that kids are on a relatively close skill level to keep interest high in playing the game. But if you do have a group of kids working on about the same skill level, it’s an excellent game to get them to stretch their mathematical thinking.
Sequence Numbers is another family favorite. Kids solve basic math problems to block a spot on the board. In a bit of a tic-tac-toe style they aim to get a certain number of spots in a row to win the game. Here again like in Math War there are numerous opportunities to practice different math facts with the added element of strategizing to win.
Prefer printable math game options? Playdough to Plato has full fact fluency sets for both addition and subtraction.
In the Addition Fact Fluency set, kids play-
–> Addition Race // Spin the fact and graph the sum.
–> Roll and Add // Roll a die, write the addend and solve the problem.
–> Connect Four // Challenge a partner to solve four facts in a row first.
In the Subtraction Fact Fluency set, kids play-
–> Subtraction Race // Spin the fact and graph the difference.
–> Roll and Solve // Roll a die and solve a problem from the matching column.
–> Tic Tac Toe // Challenge a partner to solve three facts across, down or diagonally first.
–> Subtraction Color Up // Roll a die and color the matching answer.
Toys for Hands-On Addition and Subtraction Activities
Giving kids a variety of options for exploring addition and subtraction can also help them learn math facts. These toys are great additions to independent play or math center options.
Make it yourself math fact games and activities
These hands-on activities are also great for helping kids practice math facts.
Practice adding with pom pom “apples” in this apple tree addition game.
Grab a deck of cards and this free printable game mat to practice making ten.
Use toy cars to practice ways to make ten.
Build your own math facts with this fun bird nest addition and subtraction activity.
Practice adding and subtracting on a number line with this grasshopper math game.
Grab some pipe cleaners and pony beads to build math facts.
Use subtraction flash cards and play dough for this fun subtraction game.
Use nuts and bolts to practice addition and subtraction.
Craft sticks for the win! Use them to make a math fact matching game.
Make a portable math box to practice addition or subtraction facts. Great for independent practice time!
Get moving with this math facts island gross motor math game.
Play tic-tac-toe math fact style with this free printable addition game.
Practice adding with this bee hive addition freebie.
Put those mini erasers to good use in this number bonds math activity.
Use paper cups and this free math fact printable for more hands-on practice.
Work those fine motor muscles as you practice math facts with this cardboard box math facts activity.
Find the missing addend with toy cards and triangles in this number bond activity.
Make math fact targets and use your Nerf gun to knock them over!
All of our roll and color math games have math fact activities in each set!
Cootie catchers are so fun! Use them to practice math facts, too.
During the spring try this free printable flower petal math fact activity.
Engaging Workbooks Options for Kids Who Still Need Extra Practice
Some kids do enjoy using a workbook, and some parents like to be able to follow along in a series of activities. Try these options if you’re looking for addition and subtraction workbooks.
Keep up with New Recommendations We Discover on Our Amazon Shop Page
As we discover new toys and teaching tools we’ll be adding them to or Amazon Shop Page. Bookmark this page to visit as you’re looking for new teaching resources for early childhood education.
With a little creative thinking and the right materials, you can definitely make learning math facts fun! We hope these resources come in handy.
Is there another way you love to teach math fact fluency, tell us about it in the comments. We’re always looking for new ways to teach math facts.
theory and practice with examples
Solving complex examples correctly is an impossible task for those who do not understand elementary rules and laws in mathematics. Addition and subtraction of mixed numbers can rightfully be classified as complex examples. However, with the correct parsing of the numbers themselves, you can easily carry out any action.
What is it?
A mixed number is a combination of an integer part and a fractional part. For example, there are 2 and 3, of which 2 is a prime number, but 3 is already mixed, where 3 is an integer part, and is a fractional one. The presented varieties are added and subtracted in different ways, but do not entail difficulties in independently solving examples.
Full analysis of the example
For a full presentation of the essence of mixed meaning, it is necessary to give an example of a task that will help to display the meaning of the narration conceived. So, Vasya cycled around the school in 1 minute and 30 seconds, and then walked another circle in 3 minutes and 30 seconds. How much time did Vasya spend on the whole walk around the school?
This example is aimed at adding mixed numbers, which in this case do not even have to be converted to seconds. It turns out that addition is carried out by separately adding minutes and seconds. As a result, we get the following result:
- Addition of minutes — 1+3=4.
- Addition of seconds = 30+30=60 seconds = 1 minute.
- Total value 4 minutes + 1 minute = 5 minutes.
Based on the mathematical display, then the presented actions can be distinguished in one expression:
From the above, it becomes clear that mixed numbers should be added separately in parts — first integer parts, and then fractional ones. If a fractional number still gives an integer value, it is also added to the integer value obtained earlier. The fractional part is added to the resulting integer value — a mixed number is obtained.
To reinforce what you have learned, you should give a rule for adding mixed numbers. Here you should use the following sequence:
- To begin with, separate the parts from the value — into integer and fractional.
- Now put together the whole parts.
- Next, add the fractions.
- If it is possible to extract an integer part from a fractional number — convert it to a mixed value — then a similar breakdown is carried out.
- The integer part obtained from the fractional value is added to the integer value previously obtained.
- The fractional part is added to the integer part.
For clarification, a few examples should be given:
Addition of mixed numbers occurs according to the same algorithm as subtraction, so the following action will be considered in detail below.
As in the first case, there is a rule for subtracting mixed values, but it is fundamentally different from the previous sequence. So, here you should follow the sequence:
- Subtraction example is presented as: minuend — subtrahend = difference.
- In connection with the above equation, you should first compare the fractional parts of the numbers presented.
- If the decrement has a larger fractional part, then the subtraction is carried out according to the same criterion as in addition — first integers are subtracted, and then fractional values. Both results add up.
- If the decrement has a smaller fractional value, then they are first converted to an improper fraction and a standard subtraction is performed.
- The integer part and the fractional part are determined from the obtained difference.
For clarification, the following examples should be given:
From the presented article, it became clear how to add and subtract mixed numbers. In the example described above, it is clear that it is not always necessary to modify numbers — to translate them from simple fractions to complex ones. Often it is enough to simply add or subtract whole and fractional values separately, which for a person with more experience can be easily carried out in the mind.
The article discusses in detail the examples, the solution of which is presented in full accordance with the mathematical rules and fundamentals. Separate situations are analyzed, for each an example of modifications that can be encountered in solving problems and complex examples is given.
rule, algorithm, examples with detailed solution
The same values in mathematics can be written in different expressions. The use of one or another entry depends on the specific example. Quite often you have to deal with mixed numbers. Their addition and subtraction is based on the rules of simple arithmetic operations with ordinary fractions having the same denominators. In other words, the integer part in the expression is represented as a fraction and the necessary action is performed.
- The concept of mixed numbers
- Actions on fractions
- Simple examples
- Hard level tasks
The concept of mixed numbers
A number represented as the sum of a natural number and a correct ratio is called a mixed number. In this case, a rational fraction will be proper if its dividend is less than the divisor. If the numerator of the expression is equal to or greater than its denominator, then the fraction is called improper. The correct notation of a fraction will always be less than one, and the wrong one will exceed it or be equal to it.
Any mixed fraction consists of two parts:
- integer — write on the left side of the expression;
- fractional — indicate after the integer part.
Do not put any mathematical signs between the integer and the fractional part. For example, an expression like 3 ½ is called mixed. In this case, the number three is an integer part, and ½ is a fractional part. It should be understood that the upper value in the fractional part indicates the number of parts available, and the lower one indicates how much they are divided.
It is very important to understand the mixed expression notation. For example, suppose you need to add the number five and the fraction ¼. Knowing how operations are performed on fractions, we can write the following solution chain: 5 + 1/5 = 5/1 + 1 / 5 = (5 * 5) / (1 * 5) + (1 * 1) / (5 * 1 ) = 25/5 + 1/5 = (25 + 1) / 5 = 26 / 5 = 5 1/5.
Paying attention to the beginning of the record and the end, you can see that the difference is only in the omitted plus sign in the second case: 5 + 1/5 = 5 1/5. That is, in fact, there is a folded and expanded form of recording. It follows that if it is necessary to add the integer part and the correct form of the expression, then you can remove the addition sign, and write the integer and fractional numbers together.
By analogy with addition, subtraction is also considered. For example, one-third must be subtracted from one. The integer part can always be written as a fraction, since in it the line separating the numerator and denominator indicates division: 1 — 1/3 = 3/3 — 1/3 = (3 — 1) / 3 = 2/3. That is, an integer is represented with a denominator equal to the fractional part: 1 — 2/19 = 19/19 — 2/19; 1 − 2/999 = 999/999 − 2/999.
When the integer part is not a unit, it is decomposed in such a way that it contains a single term, and then the notation of a mixed number is used in addition. For example, 3 — 1/3 = 2 + 1 — 1/3 = 2 + 3/3 — 1/3 = 2 + 2/3 = 2 2/3 .
The above operations must be understood so that they can be performed in the mind. In this case, problems with finding the difference of mixed numbers or their sum should not arise. With knowledge of the material, the answer for examples of the form (4 — 1 ½) is quickly calculated in the mind: (4 — 1 ½) = 4 — (1+ ½) = 4 — 1 — ½ = 3 — ½ = 2 + 1 — ½ = 2 + 2/2 − ½ = 2 + ½ = 2 ½.
Actions on fractions
In the fifth grade of a comprehensive school, before studying operations on mixed numbers, addition and subtraction of fractions with equal denominators are carried out. These are fundamental operations, and calculations are based on them both in mathematics and in algebra. The algorithm for calculating such examples is quite simple and consists of only three steps:
- entry in the response of the denominator, which is the total number for all added terms;
- calculation of the numerator by performing arithmetic operations on divisible members while preserving their signs;
- simplification of the received expression and, if necessary, reduction of the answer to a mixed fraction.
For example, ¾ + 7/4 = (3+7) / 4 = 10/4. This can be explained as follows. Let there be a cake that is divided into four equal pieces (parts). Three parts were taken away. Accordingly, in mathematical form, it looks like ¾. For the second fraction under consideration, it turns out that there are two such cakes, each of which is divided into four identical pieces. In the first, all parts will be taken away, and in the second, only three. In total, you will get three cakes cut into four parts each with ten pieces taken away, that is, 10 / 4.
From the resulting expression, you can extract the integer part — lead to a mixed fraction. To do this, the dividend is divided by the denominator with a “corner” and the remainder is transferred to the numerator. For this example, the correct answer would be 2 ½. Do the same with subtraction. The denominator is rewritten without change, and the numerator is represented as the result of subtracting divisible terms: 7/5 — 2/5 = 5/5 = 1. These rules are also valid for calculating expressions containing more than two members. For example, 17/19 + 1/19− 8 / 19 = (17 + 1 − 8) / 19 = 10 / 3 = 3 1/3.
When performing operations with different denominators, the calculation principle is to bring the example to the form when all terms are obtained with the same divisor. In some cases, the easiest way is to multiply the numerator and divisor of each fraction by the number in the denominator of another expression. For example, 8/9 + 17 /18 = (8*18 / 9*18) + (17 *9) / (18*9). But such a record is most often cumbersome and inconvenient. Therefore, should learn to find the lowest common denominator . It is calculated by factoring the given divisors.
For the example under consideration, the following solution chain will be valid: 8/9 + 17 /18 = (8 / (3*3)) + (17 / (3*3*2))= ((8 * 2) + (17 * 2)) / 9. That is, the same terms are multiplied and the result is written to the dividend, and the remaining ones are used as factors of the numerators.
It is important not only to understand the principle of mixed addition and subtraction by 5 points or 12, that is, “excellent” (depending on the grading system in the educational institution), but also to be able to apply the acquired skills in practice. There are a number of examples that allow you to practically master theoretical skills. With the ability to solve them, tasks of varying complexity will not cause difficulties in finding the right answer.
Here are some of them where you need to take the required action:
- Add: 12 8/11 + 9 3/11. When solving this example, it should be remembered that 12 8/11 is nothing more than the addition and subtraction of mixed numbers 3 + 8/11, and 9 3/11 is another expression for the expression 9 + 3/11. It follows that the given expression can be rewritten as (12 + 8/11) + (9+3/11). Then apply the rule that says that in order to sum the mixed parts, you must perform operations separately on the integer parts and fractional parts. That is, the following will be true: (12 + 8/11) + (9+3/11) = (12+9) + (8/11+ 3/11) = 21 + ((8+3)/11) = 21 + 11/11 = 21 + 1 = 22.
- Determine the difference of two numbers: 7 3/15 − 2 2/15. The solution is performed by analogy with the previous problem: 7 3/15 — 3=2 2/15 = (7 + 3/15) — (2 + 2/15) = (7 — 2) + (3/15 — 2/15 ) = 4 + ((3−2) /15) = 4+ 1/15 = 4 1/15.
- A slightly more complicated example, in which an improper fraction is obtained: 6 10/13 + 2 9/13. After summing the integer and fractional parts, the following answer will be obtained: 8 + 19/11. Divisor with remainder, so the answer is normalized: 8 + 19/13 = 8 + 1 6/13 = 9 3/13.
- In this task, you need to subtract the fractional part from the integer part: 2 − 6/7. Express the integer part as two numbers, one of which must be a unit: 2 — 6/7 = (2 + 7/7) — 6/7 = 2 1/7.
- The last type of task involves finding the result of calculating the addition or subtraction of an integer and a mixed number. For example, 10 − 5 4/23. Nine should be represented as 9 +1. This is necessary for further reduction of a prime number to a fraction. That is: 10 − 5 4/23 = 9+1 — 5 4/23 = 9 + 23/23 — 5 4/23 = 4 19/7 = 6 6/7.
Simple examples do not require detailed calculations. They should try to do orally, as if to collapse. When training, it is convenient to pronounce intermediate operations to yourself until the actions reach automatism.
Hard level tasks
When solving problems involving operations on mixed fractions, you must always use the rule for alternately adding or subtracting integer and fractional parts of an expression. Different tasks can contain the nth number of members, but the rule remains the same.
Let an expression like this be given: 5 15 / 21 + 9 20 / 21 − 6 7/1 3 + 9 5/12 − 6 11/12. Such examples are easier to solve by actions. For this example, there will be four of them:
- 5 15 / 21 + 9 20 / 21 = 15 2/3;
- 15 2/3 − 6 7/1 3 = 9 5/39;
- 9 5/39 + 9 5/12 = − 15/52;
- − 15/52 − 6 11/12 = − ((15*52 + 15)/52) − ((6*12 + 11)/12) = − 22 8/39.
The following problem requires not only knowledge of the rules, but also the practical skill of adding and subtracting numbers. 5 2/3 tons of apples were brought to the vegetable base, and pears were delivered 7/8 tons less, while the storage already had 1/8 tons more peaches than pears. The question is, how many tons of cargo are in the vegetable base.
It is necessary to solve it as follows. From the condition it is known that there are less pears than apples by 7/8 tons. Therefore, it will be correct to write down that there are 2 3/8 — 7/8 \u003d 1 + 8/8 + 3/8 — 7/8 \u003d 1 (8 + 3 — 7) / 8 \u003d 1 4/8 tons of pears. Using the second condition, you can find the previously imported number of peaches: 1 4/8 + 1/8 = 1 5/8. The last step is to calculate the total weight of vegetables on the base: 2 3/8 + 1 4/8 + 1 5/8 = 4 + 12/8 = 4 + 1 4/8 = 5 4/8 tons. Thus, it is correct to say that there are five point four eighth tons of vegetables at the base.
It should be noted that only an independent solution of several tasks will allow you to consolidate the acquired skills. To check the correctness of the solutions, you can use mathematical online calculators.
These are specialized sites that perform any actions on fractions in automatic mode.