Numbers are all around us, and they play a big part in our lives. You might think that math is just something you learn in school, but understanding numbers, also known as "number sense," is super important in real life too! Teaching our children to understand numbers helps them develop a strong and intuitive grasp of math concepts. So, let's explore what number sense is and how we can make math exciting in the classroom.
What is number sense?
Number sense is like having a superpower for numbers. It's not just about memorizing math facts but truly understanding how numbers work together. It covers counting, number relationships, estimation, identifying patterns, and understanding place value. It provides the tools to be able to handle every day situations that involve math confidently and comfortably.
Let's take a closer look at some of the concepts it covers and how we can help kids understand the concepts.
Children need to learn to count fluently, not by rote, but with an understanding of each number being a quantity. When they count objects, each number relates to an object being counted. Touching objects as they count them will help with this correlation. It is important to practice counting objects until they are able to correctly count them every time.
Do hands on activities so the math is tangible. Start with real-life objects. Let students count and group toys, buttons, or snacks. Count books, pencils, or even footsteps. Ask questions like, "Can you find five red objects?" or "How many shoes do we have?" This makes numbers real and relatable.
It is important for kids to see how numbers relate to one another. For example: 6 is one more than 5 or two less than 8. These relationships will help them understand the basic operations of addition and subtraction and later on multiplication and division. Math vocabulary for these relationships in also important. Terms like: more than, less than, equal to, and greater than are only a few examples that can be taught to help them understand these relationships.
Play games that involve looking for clues that use some addition and subtraction to solve them. Practice making groups that show the relationships between numbers. Play "Guess the missing number" by answering yes or no questions.
It is not always possible to count everything, so it is important to make educated guesses for quantities. For example: How many candies are in the jar? Children often have little idea about how to estimate and the responses are way off. It will take practice estimating and then counting for them to understand how to get closer in their approximations.
Turn estimation activities into challenges. Who can get the closest number? Can they get it without going over?
Practice using small amounts at first and gradually increase the number of objects being estimated as the results get closer.
Get kids to recognize patterns in numbers, like even numbers (2, 4, 6) or the way odd numbers always end in 1, 3, 5, 7, or 9.
Try skip counting games and look for patterns when counting. For example: when counting by 5 all numbers end in 5 or 0.
Reading books about math patterns is also fun to do and helps kids understand the patterns better. For example: Even Steven and Odd Todd shows the relationship between even and odd numbers. Amanda Bean's Amazing Dream shows how multiplication is just a faster way of adding.
There are many books that show math patterns and relationships. Find some that fit with the concepts that you are teaching to help enrich your students' understanding.
Understanding place value
It is important that students understand what the relationship is between multiple numbers grouped together and their placement or order. For example: 4 in 42 means forty, and 2 means two). We refer to these as digits that represent different values.
Play games that encourage kids to identify the mystery digit or build a number with the place values given.
Check out this blog post for more about place value and some activities and resources that might interest you.
Connecting number sense to the real world
Number sense is not just for math classes. It is a necessary skill for navigating in the real world. The more we focus on how it is used in practical settings, the more our students will see its purpose and begin to use it more confidently.
Being able to understand number sense and use it effectively will help with handling money, time, and measurements. It will also be used in many different settings, whether budgeting an allowance, planning a trip, or even cooking a favorite meal.
Remember, math is not just about numbers; it's about exploring, discovering, and making sense of the world around us.
Next time I will share ideas and activities that can bring number sense into everyday activities, and how we can encourage activities at home to help our students develop a solid understanding of how to use their number sense skills in their world.
Changing weather, cooler temperatures, and color changes are all signs of the arrival of fall. There's something magical about the colors, sounds, and smells of fall. Students often find themselves more engaged in learning when they are surrounded by the beauty of nature. Whether it's studying the changing colors of leaves, identifying different animals, or learning about the life cycle of a pumpkin, outdoor lessons are inherently captivating.
Fresh air and natural surroundings can help improve students' focus and stimulate their creativity. Studies have shown that spending time outdoors can boost cognitive function and problem-solving skills, making outdoor classrooms an ideal setting for critical thinking activities.
Spending time outdoors has been linked to improved mental health and reduced stress levels. Fall's cool, crisp air and the calming influence of nature can help students feel more relaxed and connected to the world around them.
The hands on experiences and fresh air also invigorate students and engage them in their learning.
Fall is the perfect time to encourage physical activity among students. Hiking, nature walks, and outdoor games not only promote exercise but also foster teamwork and social interaction. Getting students moving in a natural setting can help overcome the hours of sitting in classrooms and keep them engaged.
There are many different subjects that can be taught outdoors. Each of these add a real world element to the students' learning and experience. Integrating social studies and science activities into your fall outdoor learning adventures can provide a well-rounded educational experience. To further enrich your fall outdoor learning adventures, try incorporating some math and language activities into the mix.
Here are some suggestions for social studies, science, math, and language arts that might be of interest.
• visiting local historical landmarks
* learning about fall harvest and traditions
• using maps and doing a geography scavenger hunt
• leaf identification activities
• studying the pumpkin life cycle
• weather monitoring
• learning about weathering and erosion
* keeping a nature journal
• stream study
• learning about seed dispersements
• nature math scavenger hunt
• using measurement skills outdoors
• fall data collection
• outdoor poetry writing
• nature journaling with descriptive writing
• vocabulary scavenger hunt (looking for examples in nature)
• reading fall themed books
Here are some preparation tips that will help make your outdoor sessions successful.
Select an outdoor location that suits your curriculum and learning objectives. Local parks, forested areas, the seashore, or even your school's own outdoor spaces can be transformed into effective learning environments. Make sure students are dressed appropriately for the fall weather. Layers, hats, and gloves are essential to keep everyone comfortable during outdoor lessons.
Tailor your lessons to incorporate the unique features of fall. Explore topics like the changing colors of leaves, the science behind falling leaves, the life cycle of pumpkins, or even Halloween-themed literature.
Bring technology outdoors by using tablets or smartphones for nature observation apps or taking pictures to document findings. This can enhance the learning experience and provide opportunities for digital storytelling.
Make sure that your plans are flexible and adaptable as the weather can be unpredictable and you may need to make changes quickly.
With preparation ahead of time and some back up ideas in case of change, getting outside to learn is worth the effort and will benefit your students.
Embracing the great outdoors during the fall season is a fantastic way to enhance your students' learning experience. The benefits of outdoor education are numerous, from improved engagement and focus to enhanced physical and mental well-being. By incorporating nature into your curriculum, you can create unforgettable learning moments and inspire a lifelong love for the natural world in your students. So, this fall, take your class outside and let the wonders of the season become your classroom.
Happy outdoor learning!
It's that time of year again. Summer break is ending for some and nearing the halfway mark for others. Teachers are starting to gear up again and think about the new school year. School supplies are everywhere, back to school ads are appearing on the television and the teacher brain is going into overdrive.
As hard as it is, it's important to try and keep relaxing and recharging so that you don't burn out before the year even gets going.
Does this sound like you?
• can't turn off teacher brain
• wondering how you are going to do assessments
• not finding enough time for planning
• juggling setting up routines while keeping kids engaged
• differentiating for range of ability levels
• trying to make lessons fresh and engaging
So many questions and worries
How can I go on when I am so exhausted?
How will I manage to assess everyone while keeping others engaged?
What if the range in my class is too wide?
I've been there. It is exhausting and at times overwhelming. That's why I have collected some of the different resources and activities that have been successful with my students and I've created The Ultimate Primary Teachers Ready To Go Kit.
These resources and activities can make the beginning of the year enjoyable and less stressful for both you and your students.
Returning to school after summer break isn't always fun for kids. They've been free to do different things without the structure of the classroom routines. Now they have to fit into set schedules, rules, and routines of a new grade and a new teacher.
Engage your students from the very first day with dynamic activities and icebreakers. This kit features interactive games, team-building exercises, and activities that foster a positive classroom community. With the colorful posters and educational activities, you can set up an inspiring learning space that encourages curiosity and exploration.
This comprehensive kit is designed specifically for primary teachers. Packed with a wide range of resources and activities, this kit is your go-to solution for start-of-the-year preparation, emergency sub plans, and engaging substitute teacher activities. From day one to those unexpected absences, it's got you covered!
Check out what it includes
Classroom management resources and ice breakers and some active games
Posters and task cards as well as ice breaker tools and active games that will help you with your classroom routines and management to create a positive classroom environment.
Back To School resources full of activities for the first weeks back
These resources will give your students many different activities to do while you are trying to do assessments or trying to get to know your kids.
Literacy activities for reading, writing, language development
Reading for evidence, working with vocabulary and sounds, task cards for parts of speech and idioms, writing prompts are just a few of the activities here.
Math review for basic operations, graphing, and measurement
Basic math operations review, working with glyphs, and measurement games to get kids ready for more skills as they move on to more abstract concepts.
Science posters, graphic organizers, and experiments to get the year started off right
Positive self esteem activities and resources to create positive mindsets
Get ready to kick off the school year with confidence and ease and ensure a successful academic year for both you and your students. Get The Ultimate Primary Teachers Ready To Go Kit today and experience the peace of mind that comes with being well-prepared!
Not sure if you need the full kit? There are individual kits available as well. There is even a sampler kit for those who want to try just a few of the activities from each area. Check out my TPT store to find out more about the individual kits. If you are ready for a less stressful start to the year grab your ultimate kit now.
How many times have you heard an adult say they are no good at math or that they hate math? So many times, it isn't that they weren't capable, but that they were never really shown how to do it with real world applications or with understanding. They were just taught algorithms and formulas and didn't see why they needed them.
The way math is taught now is very different, or at least it should be. I am a strong believer in making sure that things make sense so that they can be applied to other situations. What might seem straight forward or clear to one person might make no sense at all to another person.
Just think about the different ways math is used. It isn't just adding, subtracting, multiplying and dividing numbers. It is also measurement, geometry, coordinates, graphing, statistics, just to mention a few. Some people are really good at numbers and calculations, while others have great spatial awareness, and some can solve puzzles while others struggle to see the relationships between shapes and designs.
Math has it own language as well. This can be confusing for some people. Word problems are very hard for some people to figure out.
Over the years, i discovered that it is necessary to go back to the basics and make sure that the building blocks are in place before attempting more complex or abstract concepts. When I was working with intermediate students in small groups, I found that many of them didn't know their basic facts and they struggled with addition and subtraction strategies. This made multiplication and division almost impossible for them to do well. I took them back to the basics and in time they were doing much of the work covered in class with some proficiency. They still needed extra support, but it was starting to make sense to them. They even started to enjoy math instead of dreading it.
You can find out more about ways to help kids improve in this blog post.
Practicing math skills during the summer will go a long way in helping to maintain skills for the new year. There are plenty of fun and engaging activities you can plan for kids during the summer that incorporate math and keep them learning. Here are some ideas:
Math themed scavenger hunt
Create a scavenger hunt where kids have to solve math problems or puzzles to find hidden objects or clues. You can design it around a specific math concept, like geometry or fractions, and hide clues or objects that reinforce those concepts.
Cooking and baking
Involve kids in cooking and baking activities that require them to use measurements, conversions, and fractions. Encourage them to follow recipes, measure ingredients, and calculate serving sizes. They can also explore the concept of ratios by experimenting with different ingredient proportions.
Outdoor measurement exploration
Take advantage of the outdoors to explore measurement concepts. Have kids measure the height of trees, the length of their shadows at different times of the day, or the circumference of various objects using a measuring tape or ruler. They can record their findings and compare measurements.
Math board games
Introduce kids to math-focused board games or card games that involve strategic thinking and problem-solving. Games like Monopoly, Set, or Sudoku can help improve their math skills while having fun.
Math art projects
Combine math and art by engaging kids in geometric art projects. They can create symmetrical designs, tessellations, or use grids to draw patterns. This allows them to explore concepts like symmetry, shapes, and angles while expressing their creativity.
Math related crafts
Encourage kids to engage in crafts that involve math concepts. For example, they can create paper origami shapes, construct 3D models using geometric shapes, or design and build structures using various materials. These activities promote spatial reasoning and critical thinking skills.
Math apps and online games
Utilize educational math apps and online games that provide interactive learning experiences. There are numerous apps and websites available that offer math games, puzzles, and quizzes suitable for different age groups.
Have kids maintain a math journal where they can record and explore math concepts they encounter in their daily lives. They can write about real-life applications of math, solve problems, or illustrate concepts. This encourages reflection and critical thinking.
By integrating math into summer activities, you can help children strengthen their math skills while having a great time.
The sunshine is here and kids are anxious to get outside, so why not take advantage of this and do some outdoor math activities and other lessons? Many different subjects can be done outside the classroom walls if you add in some creativity and movement. Here are 5 fun ideas for teaching math and social studies outdoors.
Taking Measurement Outdoors
Many classes study measurement in the spring. A culminating activity for this could be an outdoor event where teams practice linear measurement. Here is a resource that might help.
Outdoor Measurement Games Team Events
Working With Time And Racing
If you teach time in the spring, perhaps you could go one step further and introduce stopwatches. Timing different events can be fun and many different devices actually have stopwatches on them now.
You could have a fun day with different activities that need timing, such as running, filling different containers, wheelbarrow races, etc. You could also set a time to beat and have the kids do activities that have to beat the time. For older children, comparing times, looking at the data and maybe even figuring out elapsed time could also be included.
Because the kids are having fun and moving around, they won't realize that they are studying time, but they will be applying skills to real world situations.
Taking Mapping Skills Outdoors
Reading maps and understanding them is still an important skill in today's digital age. Many people rely on the maps feature in their vehicle or on their phone to get them from point A to point B, but they don't have a clear understanding of how to read maps on their own. Learning how to use mapping skills like directions and grids helps when using maps at places that don't have a digital option. For example, when you go to certain amusement parks, zoos, or other events that have activities and events spread out around the grounds, being able to follow a map is important. Just think of all the maps in malls, at parks, or even at visitor centers that have "You Are Here" indicated on them. Can you follow directions from there to get to where you want to go?
Teaching kids how to use these skills in practical settings requires practice. Here is a chance to get outside and actually try to use them to find things, locate different areas, and be able to help others to find them too. Creating maps of the neighborhood or school grounds can also work as practice using grids, directions, and even symbols and legends. Here is a resource that may help.
Mapping Skills Using Grids
Using Grids And Working With Scale
Understanding how scale works is an important skill when interpreting maps, blueprints, house plans, and other documents. A great way to practice doing this is using grid paper and measuring the perimeter or area of an object and then drawing it on the paper. It is important to indicate what the size of each square is so that the measurements match what is drawn on the paper. You could choose the school yard, playground, surrounding neighborhood or any other area or object for your topic.
Here is a resource that may help with understanding perimeter and area along with some activities to practice using both.
Perimeter And Area
Solving Math Word Problems
Word problems can be especially challenging for some kids, so taking them outdoors and actually doing some hands on work with them might help. I remember creating puzzles when I was geocaching that required people to solve math questions using objects in the park in order to find the coordinates. Something similar could be done in the school yard. For example, check out and find all the trash containers, swings, trees, signs, basketball hoops, hopscotch or foursquare marking, etc. Using these objects around the school yard, create math word problems that must be solved. You could work in pairs, individually, or even in teams to solve them.
The Sky's The Limit
These are only a few of the different activities that can be done outdoors to work on math and social studies skills. Depending on what you are studying and how creative you are, there are many others that can be done as well.
So get outside, have fun, and keep the learning going.
When babies take their first steps, they wobble and they often fall. With help and practice they begin to take steps by themselves. Before long they are running and they are able to hop, skip, and leap over things. Baby steps lead to bigger steps. That is true in all areas of life including Math.
The basic facts are the baby steps that lead to more complex and abstract skills. Once the basic steps are mastered, it is time to move on to more complex problems using double and triple digit numbers. Complex problems can be daunting, but the good news is that there are many strategies that can help.
Looking for tens
This strategy involves breaking down the big numbers into smaller, more manageable ones. We search for numbers that can easily be combined or subtracted in groups of ten. Finding pairs of numbers that add up to ten make calculations easier.
It's like a treasure hunt where we search for numbers that can make adding and subtracting easier and use that knowledge to solve more challenging problems.
Using A Number Line
Number lines are a great tool for addition and subtraction. They provide a visual representation to help with seeing how numbers relate to each other. Kids can see the steps needed to get from one number to another and it helps them to understand more complicated calculations as they hop to the answers.
Regrouping Using Base Ten Blocks And Money
Regrouping is another strategy used when working with larger numbers. Using base ten blocks as you practice this skill will help with visualizing why we regroup and what it really means. Regrouping is really just trading ones for tens or tens for ones which helps to make calculations easier.
Once the concept of regrouping is understood there are several other ways to help with remembering how it works. My favorite is banking. I teach my kids to take 10 pennies and trade them for a dime when adding. If they don't have enough pennies when doing subtracting, I tell them to go to the bank and trade a dime in for 10 pennies. As they move on to 3 digit addition and subtraction I tell them that 10 dimes makes one dollar so they can trade dimes for dollars or dollars for dimes when doing their calculations.
Working With Expanded Notation And Combining Parts
We also have expanding notation which allows us to break down numbers into their individual digits. This helps us to see the value of the individual digits and it also helps us to add similar values. We can also use expanding notation for figuring out subtraction.
See the image below for an explanation and example.
Standard Algorithm For Addition
Many of us grew up with an algorithm for addition. This is still valid today, but it is important to understand how it works and what we are actually doing when we use it.
Most often we stack the numbers one under the other and make sure that the digits line up. The ones would be added and then the tens would be added.
For regrouping, you would need to carry the extra tens and add them to the tens column. See the images below for an example.
Standard Algorithm For Subtraction
The standard algorithm for subtraction works the same way, but when regrouping we need to take from the tens column and add it to the ones column when we don't have enough ones to do the subtraction.
See the images below for some examples.
Anchor Charts For Addition And Subtraction
When learning the basic facts for addition and subtraction, many strategies are taught and practiced. Each person will have some strategies that work well for them and they can apply these strategies to more complex questions.
Get a free copy of these anchor charts by signing up for my newsletter. If you are interested in some practice worksheets to go along with the different strategies, check them out here.
I hope you find these tips helpful as you continue to guide your students through the complexities of math.
Life is a series of give and take and in math class, this is also true. We give and take when we work with addition and subtraction and it is important that we learn how to do this well in order to be able to apply skills to real life situations.
Last week I focused on addition strategies for basic facts. Today I would like to look at subtraction strategies. You may notice there are many similarities between the two.
As with addition, I recommend starting with manipulatives such as base ten blocks, number lines, ten frames. These visuals will help the strategies make sense for many children.
Deciding what strategy to use will be different for each person, but in order to be able to choose, it is important to be introduced to a variety of strategies and have opportunities to practice them. Here are 6 strategies you might find helpful.
Just like in addition, zero is a special number for subtraction. Zero can be subtracted from a number and leave the same number or it can be the answer when a number is subtracted from the same number. When kids see a zero they should be able to automatically recognize this fact. It will come in very handy when they start to use larger numbers.
If you have a ruler or a number line, you can use a counting back strategy to figure out the subtraction question for basic facts. It is possible to do it for larger numbers as well, but it is not a very efficient strategy for subtracting double digit numbers.
Place your finger on the first number and count back the number of spaces of the second number to get your answer. If you use a pencil and paper with a number line, you can actually draw the steps backward. This will help to avoid getting lost or miscounting.
Related facts help when you know one fact and need to figure out the other fact. When you look at the question, think about the related fact to figure out the answer. Sometimes it is easier for us to figure out the related fact and then solve the question. It's just the way our brain works sometimes.
If you are taking away an amount that doubles to equal the first number of the subtraction question, then the answer will be the same as the amount taken away. This strategy depends on how well one knows the doubles facts.
Looking For Tens
With basic facts, tens can be a useful strategy. For instance, if you know the different combinations of numbers that equal ten, you can use fact family triangles or number bonds to figure out the different subtraction questions. If you are subtracting using a ten frame, colored objects or circles help you to see how many are remaining. See the image below as an example. For larger numbers up to 20, you could use a couple of ten frames.
Change To Addition
Sometimes it's easier to think of the question in addition rather than subtraction. You can also apply addition strategies to this. For instance, in the example below you could use doubles plus one to figure it out, or you could count on to get the answer.
Once the basic subtraction facts are well practiced, moving on to double digit subtraction and more complex questions requiring regrouping will make more sense.
Next time I will talk more about double digit addition and subtraction and strategies that will help these make sense.
Do you know your basic facts? This may seem like a silly question, but there are many people who struggle with the basics and this is why math is so difficult for them. When I worked with intermediate students that were struggling, I discovered that they were missing the building blocks that would help them with more complex situations. They didn't have a solid foundation and they struggled to find strategies to help.
Math is all around us and it can be frustrating if we don't have a good understanding of how to use it well. As a primary teacher, I know just how important it is to start building strong foundations in math. Learning basic facts is like laying bricks for a sturdy house - without them, the structure can easily crumble.
Fortunately, it is never too late to master the basics and improve math skills. There are many different strategies and approaches available to accomplish this. I would like to focus on a few addition strategies today.
Basic Facts Addition Strategies
Moving from concrete to abstract is important, but first it is necessary to make sure that the foundation of basic facts is solid. Using manipulatives and simple strategies help to make sense of the different concepts, so don't be too quick to remove them as you try out the strategies shown here today.
Adding zero is a concept that can be demonstrated easily with concrete examples. When nothing is added to something, there is no change. As you can see in the example below, it doesn't matter if the zero comes at the beginning of the number sentence or the number of objects comes at the beginning of the sentence, the answer still stays the same.
Turn it around
It's funny how our brains work sometimes. We can figure things out faster when we see a question shown in a certain way. Both of the number sentences below have the same numbers in them, but for some reason it may be easier to recognize the answer faster looking at one of the sentences. That is the beauty of understanding that the cummutative principle of addition means we can turn the question around and still get the correct answer. We may not use the formal term when we teach this strategy, but the visual makes it clear.
Counting on is a strategy that is well used for addition. Think of the number of times you may have noticed a child using fingers to count on when figuring out how much more is added. Maybe you have used your fingers to figure things out as well.
Using a number line is another great visual for counting on. Place your pencil (or finger) on the first number in the sentence and count on the number of spaces of the second number to get your answer to the question.
Making tens is a great way to help with figuring out addition questions. Start with looking at different ways to make ten using dice, fact families, number bonds, and ten frames.
Making Tens And More
After becoming comfortable with tens you can add in some of the larger numbers to figure out other basic facts.
For example: If you know that 8 + 2 = !0, then for 8 + 9 , you can take 2 from the 9 to make 10 and that leaves 7, so 10 + 7 = 17
See the image below for a visual representation.
Learning doubles can be a very helpful strategy. Here are some pictures that can be used as reminders for the doubles for each of the numbers from 1 to 9. There can be other images substituted for these depending on what may work for your students. It will take practice to remember these hints. An anchor chart might also help.
eyes for 1 + 1 : easy to remember because we have 2 eyes
domino with 2 + 2 : counting by twos also works
using dice with 3 + 3 : shows the two rows of 3 dots
spider legs for 4 +4 : spiders have 8 legs
hands for 5+ 5 : counting by fives works as well
carton of eggs for 6 + 6: a dozen is 12
calendar for 7 + 7 : each week has 7 days
2 octopus for 8 + 8 : each one has 8 legs
18 wheeler for 9 + 9 : each side has 9 wheels
Sometimes it helps to use doubles and add one when you need to add two numbers that are close together. For a simple example, check out the image below.
Some facts are harder to remember than others. This strategy can work well for some of these situations. For instance, many struggle with 8 + 9. If they double the 8 and add one, it can help.
Here is an addition mandala that is fun to do and helps with practicing basic facts in addition. It comes in both English and French. Get a free copy by signing up for my newsletter.
There are other strategies that can be used as well, but I wanted to focus on a few tried and true strategies that my students have used.
Once the basic facts are solid, moving on to more complex addition will be easier. I will share ideas about more complex addition in a future post. For now, I hope that these ideas and strategies help your students to build a strong foundation in math.
Do your students struggle to make sense out of math? Do they grumble and get frustrated whenever it is time for math? Maybe they just need to have more practice manipulating things and visualizing concepts.
Using concrete materials and hands on activities is the best way, in my opinion, to help kids make sense out of the math concepts they are being taught. However, at some point they need to be able to move from the concrete to the abstract. Here are a few ideas that combine both as they move towards that transition.
When we talk about basic facts, we usually mean addition and subtraction facts of single digit numbers. These are the foundation for all other addition and subtraction problems and they are also the base for multiplication and division. If kids are to make sense and be successful with more complex situations, they need to have a good handle on their basic facts.
Start out by using objects and combining them for addition and removing some for subtraction. As these steps are practiced, try using words like adding and plus or taking away and minus so that when the number sentences are used, they will be familiar with the language.
When the number sentences are added, make sure to have an image of the objects there as well so the correlation between the concrete and abstract is visible.
Fact Families and Number Bonds
Fact family triangles help kids to see the relationship between addition and subtraction and the separate elements. Number bonds are another way of representing this. Try using objects and breaking them down into the different sets so that they can actually count and check to see that the addition and subtraction sentences work.
Here are some resources that I created to practice using fact family triangles and number bonds. Click on the images to check them out.
Representing Numbers And Place Value
Once kids are able to recognize numbers up to ten, it is time to start looking more closely at numbers with two or more digits. They may be able to count past ten and even up to one hundred, but do they really understand what the digits in the numbers mean when they look at them?
In most cases, they think of a number such as 324 to be a 3, a 2, and a 4. They hear three hundred twenty-four when they say the number out loud, but they don't really understand that it is 300 plus 20 plus 4. There are several ways to help them figure this out. Here are a couple of ways that I like to use.
Base Ten Blocks
Base ten blocks allow kids to manipulate objects to show different numbers. They can touch the hundreds, tens, and ones as they count them and move them around. Once they can accurately create numbers using the blocks, they can draw them using large squares for hundreds, rectangles for tens, and small squares for ones.
If you don't have access to base ten blocks, try these portable ones that I created.
Expanded notation stretches the number out so that each of the digits is represented with its value. For example: 523 is really 500+20+3. Start out using the base ten blocks to show what it looks like before moving to the abstract addition sentence.
Practice saying different numbers and then representing them with the base ten blocks. Once they can show the number correctly each time, add in the written component. Draw a picture of the number using base ten symbols and write the expanded addition sentence under it.
Once they get comfortable with recognizing the standard notation and representing it with base ten blocks and expanded notation, matching the 3 different formats can be added. Here is a resource I created that does that. It also has a bingo component. Click on the images to see more.
Check out the video below for an explanation about how to use this resource to help kids understand ways to represent numbers.
Another way to show numbers with their actual values is to make card stock strips with 100,200,300,400,500,600,700,800,900 on them, and shorter ones with 10,20,30,40,50,60,70,80,90 on them, and shorter ones with 1,2,3,4,5,6,7,8,9 on them. Hand out the strips to the kids and have them show the actual numbers by standing together with the correctly numbered strips. For example: 362 is the number. The kids with 300, 60, and 2 would stand together to show that they make the number 362. They could also overlap their strips to show the standard notation number.
if you would like some worksheets to practice representing numbers in a variety of ways, check out my place value category in my store. There you will find sets for different holidays and seasons.
I have also created a sample set that is free for signing up for my newsletter..
These are only a few ideas for using hands on activities to help make sense of math concepts. Moving to the abstract will be an easy transition for some, but will be difficult for others. If necessary, add in concrete activities along the way to help kids see the relationships and apply concepts to other activities.
Next time I will share some addition tips and strategies.
Watching kids "get it" is exciting. There is that confusion and frustration at the beginning that gradually changes as things begin to make sense. Suddenly the light bulb goes off and the smiles appear. There is a definite sense of "Aha". This is often the case in math when kids work with concrete materials.
Hands on activities and manipulatives made the difference. That is the magic of using hands on activities and manipulatives to teach basic concepts in math.
Here are some different types of games and activities as well as resources that may help as you venture into teaching with concrete examples.
Before kids can move forward in math, they have to understand what numbers are and be able to work with them. This includes recognizing what the numerals look like, counting objects, making one to one correlation with the number and the object, etc.
Counting by one, two, five, and ten can all be done with concrete objects. It's important to make sure that there is understanding of one concept before adding in the next one.
Counting by one:
Start with picking up objects one at a time and counting them sequentially. Try counting up to five, then ten, and then twenty. Practice this until they can do it without help. Pointing at objects as they are counted also works. Make sure to also work on counting objects that may not be lined up but are in random positions.
Counting by two:
Once they are able to count by one without prompting, start introducing counting two together. There are several ways to do this. It is important that they understand that they are counting two objects at a time. You could put the objects in pairs and have them count by saying the odd numbers quietly and the even numbers loudly at first, and then have them say the odd number inside their head and the even number out loud. With practice, they will be able to say only the even numbers and do the skip counting by two.
Counting by five and ten:
Counting by five and ten require a good understanding of larger numbers. Practice using number lines and hundreds charts to expand to larger numbers and do lots of activities to help kids see how these bigger quantities work. Then work on patterns and skip counting by five and ten. Use things like hands or coins for visually counting by five or ten as well.
Teach children that numbers have many representations, such as dots, fingers, counters, numerals, objects, ten frames, etc.
The goal is to help them to see patterns and relationships between the numbers and objects. The goal is to help them to start understanding how different concepts like more, less, equal to, greater than, less than, etc work. Basic facts for addition and subtraction followed by multiplication and division are also part of number sense.
Number sense is key to all aspects of math. It is important to make sure that kids have a solid understanding of how numbers work and the relationships between different operations happen in order to ensure that they will be successful with more abstract and complex concepts.
When we refer to basic facts, we usually mean adding and subtracting single digit numbers. It's important to have a good understanding of these facts and how they work in order to do more complex math questions. Games are a great way to work on these.
Start by working with numbers that add up to ten. Making tens is a key concept for many different other skills and concepts.
Using dice work well for teaching basic facts to ten. Check out the video below to see how I used dice for teaching how to make tens.
Using ten frames is another great visual for how to make ten. Working with ten frame cards or placing objects in containers that represent ten frames help kids to see when they have a ten and how many are needed if they have a number that is less than ten. The more they see these visuals, the easier it is for them to quickly recognize numbers up to ten and what numbers go together to make ten. Check out this video to learn more.
I loved using these ten frame cards to play games with my students. They had fun, and they became very good at recognizing similar numbers quickly. Playing "Snap" added an element of friendly competition.
Another fun activity was playing with teams using the large cards. One person from each team came forward and as the cards were shown, whoever got the answer correct first got the card. When the cards were all played, the person with the most cards got a point for the team. Then the next two players came up. The cool thing about this, was that all the others saw the cards at the same time and they could mentally practice recognizing the numbers while waiting for their turn.
Once kids have a good understanding of how to make ten, they will be more prepared for the rest of the numbers needed for basic facts. Knowing basic facts is important for working with the different math operations successfully.
There are many different strategies for working with addition and subtraction to practice basic facts. I will share more about this another time.
There is a danger in trying to move kids to abstract concepts too quickly. Take the time to have them work with concrete examples and you will find that the abstract situations will be much easier for them to understand and grasp.
When I worked with several students that struggled in early intermediate grades, I found that returning to the basics and using the concrete activities made a world of difference not only to their understanding, but also to their confidence and engagement. It was exciting to see them find light bulb moments and attempt more difficult concepts as a result.
Next time I will focus on more skills such as how to represent numbers using base ten models as well as fact families and number bonds. I will also show some other ways to represent numbers as we move from concrete to ablstract.
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About Me Charlene Sequeira
I am a wife, mother of 4, grandmother of 9, and a retired primary and music teacher. I love working with kids and continue to volunteer at school and teach ukulele.