Addition strategies are fantastic because they provide your students with tools to make computations easier and quicker. These strategies help develop fluency and a deeper number sense. This post covers the top tips and tricks for teaching the strategies 1st & 2nd-grade students learn to use when solving addition equations.
Addition Strategies: Kinder & 1st Grade
Let’s start with a quick overview of the addition strategies that are introduced in kindergarten and first grade. These first two strategies are concrete and manipulative heavy.
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1- Counters & Manipulatives
This is where most of our learners begin their math adventures. The best part of this strategy is ANYTHING can be a counter. Counting chips are easy to store and sanitize and they’re relatively cheap. Those cute counting bears are always a hit. However, don’t feel obligated to buy anything fancy. Beans, macaroni, pebbles, caps from used up glue sticks, or bottle caps can all be counters.
Teach your students to write down their equations and use their counters to represent each addend. Then, they count them all up to get the sum. Remember to introduce and use the terms addition, addend, sum, and equation as often as possible. Exposure to those tier 3 vocabulary words is so important for our students.
2- Addition Strategies: Tally Marks
Tally Marks are introduced in Kindergarten and the skill is perfected over the next few years. We’ve got a great post filled with videos you can use in your classroom to help teach tally marks. Manipulatives are a great way to teach tally marks. Anything that is straight can be used to practice tally marks. To teach this skill, practice converting standard form single-digit numbers into tally marks using all kinds of fun things you can find around you. Try out popsicle sticks, q-tips, sticks, pretzel sticks, or wax craft sticks. Paper and pencil work too, but it’s always fun to mix things up and it will keep your students engaged while learning this important skill. Don’t forget to model skip counting tally marks by 5s. Keep in mind, skip counting leads students right into multiplication.
3- Addition Strategies: Ten Frames
The reason we teach our students all of these addition strategies is the desire to develop a more robust number sense. Ten frames help your students visualize equations and give them an opportunity to practice subitizing. Ten frames are all about understanding the value of numbers. After introducing your class to what a ten frame is and how it can be used give each student their own ten frame to work with. As a whole group or in small groups practice representing equations using ten frames and counters. Modeling can be done by filling the ten frame in horizontally, to practice skip counting by 5s or filling it in vertically to practice skip counting by 2s.
Addition Strategies: 1st & 2nd Grade
4- Counting On
Number lines are a wonderful tool for your students. In first grade, labeled and closed number lines are a great place to start. Teach your students to start with the biggest number and count forward.
As student proficiency increases, in first and second grade, you can introduce open number lines. Teaching open number lines can be challenging but it is all about modeling and metacognition. Since open number lines are what many adults are already doing in their heads, talking out loud about what you’re doing and why helps students understand how to use open number lines. Students need to posses a strong base of place value knowledge to use open number lines successfully. If you find your students struggling with this skill, add some place value activities to your math block.
5- Zero Facts
In my classroom, we call zero “the mirror.” To introduce zero facts, I have an oval-shaped mirror in my classroom. When they look in a mirror, what do they see? Themselves! Anything plus zero is itself! Then, we practice with single-digit numbers and get sillier to show them that adding zero to anything is simple. My students LOVE it when I write a ridiculous equation like 3,452,872,965 + 0= ? and ask them to solve it.
6- Make 10
As adults, many of us automatically make 10s to create friendlier numbers to add in our heads. Making 10 is such a powerful strategy for our young learners, as well. Second grade is when addition really ramps up a level in difficulty when addition with regrouping is introduced. Practicing making 10 and eventually memorizing which pairs make ten is a skill that they will fall back on when learning how to add larger numbers together or when they are adding 3+ numbers together.
Teaching this skill is all about opportunities to practice. Ten frames are a fantastic way to work on making 10. Give your students counters in two colors. Ask them to find as many ways as they can to make ten using their counters. The 1st Grade Math Notebook: Addition has some great interactive pages for students to work on. Fun songs can help your students learn how to make ten, too! As students become more proficient, remember to model how to use this skill to solve more complex addition equations.
Before we get into the hows of doubles let’s understand the whys first. Rote memorization gets a bad rap sometimes. Research shows that when students develop automaticity with their basic math facts they free up space in their working memory. Simply said, when students don’t have to worry about basic computations they are better able to handle higher-level mathematics. Students only have so much working memory and using it on adding up 8+8 is a waste. Having their doubles memorized lightens your student’s cognitive load and that’s what we’re looking for! Also, once their doubles are memorized students can quickly use that knowledge to solve near doubles.
So how do we teach doubles? Just like making 10, lots of opportunities for practice. There are really fun interactive practice pages in the Addition Notebook. These include kid friendly images as visual aids. Again, songs are also a really effective method of teaching. There’s nothing more satisfying then hearing your kids singing their math facts to themselves for fun.
8- Near Doubles
Once your students have their double facts down move into near doubles. This means doubles plus one or two. Similar to making 10, teaching students to solve near doubles is all about modeling. When introducing the concept, write equations out for your students to see and say everything you are noticing and doing out loud.
For example, If you’re using the equation 6+5, this might sound like, “I notice that this almost a doubles equation. The number 6 is only one more than 5. I bet I could use my doubles facts to solve this.” Draw number bonds to show that 6 is the same as 5+1 then proceed with, “I notice that when I decompose 6, I get another 5! Oh look, 5+5 is 10 and then I just have this 1 leftover. I can add that up in my head! 10+1 is 11.” Walk your students through this step-by-step a few times then ask them to try with you. Drawing out number bonds is very helpful for many students to begin with.
If you have students who are still struggling, manipulatives like counters can be really helpful to add in a more physical element.
9- “Turn Around Facts” or The Commutative Property
The commutative property is introduced in early addition and then revisited when students learn multiplication. So, it’s a vocabulary term they will revisit frequently over their first few years of school. Calling it “turn around facts” is kid-friendly and helps students remember what it means but remember to frequently reference the actual name of the property. This will be helpful to them in third grade when they’re learning the properties of multiplication.
Getting creative when teaching turn around facts is a great way to up the engagement. The commutative property is all about helping your students understand the value of numbers and that in addition moving the addends doesn’t affect the sum. The easiest way to do this drawing out the outline of an addition equation for each student. Use empty boxes to represent the addends and leave a line for your students to write the sum.
Pass out counters of any variety- plastic counters, cereal, fruit snacks, legos, puffballs, whatever you have on hand. Start with an equation like 5 + 2. Ask students to model this equation by placing the appropriate number of manipulatives in the appropriate space. Then, write the sum. Now, write the turn around fact 2 + 5, ask students to model this new equation using their manipulatives, and write the sum. Does the sum change? Do this a few times using different numbers. Ask students what they notice. How does turning around the addends affect the sum?
Addition Strategies: 2nd Grade & 3rd Grade
10- Expanded Form
Students practice writing numbers in multiple forms- standard, expanded, written, and base ten all throughout their first few years in the classroom. The ability to decompose a number into its expanded form shows that students really understand the value of the numbers they’re working with.
We Are Teachers has an awesome write-up on why expanded form is so important. Before using expanded form as an addition strategy make sure your students really understand how to break up numbers into their values. This post from Teach Junkie has some good ideas for practicing. We’ve also got some great interactive notebook pages for additional review.
Your students have got expanded form down. How do they use it to solve addition equations? Once students begin adding two and three-digit numbers they can use expanded form to do mental math calculations. For example, let’s try 64 + 42. Model for students how to solve this problem using number bonds or base ten blocks. 64 becomes 60 + 4 and 42 becomes 40 + 2. Make sure to always model your thinking and say everything you’re doing out loud. This might sound like, “64 becomes 60+4 because 6 is in the tens place so its value is 60 and 4 is in the ones place so its value is 4.” Tie in other strategies like mentioning that 6 and 4 make 10 when you are mentally adding 60 and 40. For students who struggle with mental math, drawing or using physical base ten blocks are really good support.
11- Base 10 Blocks
Addition using base ten blocks begins in 1st grade and is used when students learn regrouping. It can also be used as a support for older students who are struggling with addition.
Students can use plastic/wooden or printed paper base ten blocks or they can draw them. In 1st and the beginning of 2nd grade having something concrete to use is really helpful but once they become more confident with base ten blocks drawing them is totally fine.
12- Skip Counting
The importance of skip counting cannot be understated. Sometimes it feels as if skip counting gets put to the wayside for other “more important” skills but it shouldn’t be! Skip counting is all about patterns and is used in so many ways. Students use it when they’re counting money or when they’re telling time and when they’re learning multiplication. Mr. Elementary Math has some great ideas for practicing skip counting.
When teaching students how to use skip counting as an addition strategy begin with open number lines. Take an equation like 25 + 32 and write the number 25 on an open number line. Remember to model all thinking out loud. It might sound like, “I notice 25 ends in a 5. When a number ends in a 5, I can easily skip count by 5s or 10s. Now, I’m looking at 32 and I know that 32 has 3 tens in it. I’m going jump forward by tens. Start at 25, jump 10, 35, jump 10, 45, jump 10, 55. Great! Now, I used up the 30 and I have 2 left. I’m going to hop forward by ones. Start at 55, hop 1, 56, hop 1, 57.” Model a few times with your students, then let your students try it with you, and then gradually release them as they begin to feel confident. For older students or students who are excelling, use 3-digit addends.
13- Rounding or “Friendly Numbers”
Students are introduced to rounding in 3rd grade. Some schools teach it right at the beginning of the year and some schools like to save it for the end. Check your curriculum map to see when it’s in your schedule. If your school teaches rounding at the beginning of the year it can be used as an addition strategy throughout the year.
You’ll hear this strategy referred to as “friendly numbers” because that’s exactly what we’re teaching our students to do. They are learning to create numbers that are easier (more friendly) to work with mentally. Adding 312+453 in your head can be difficult but rounding those numbers to 300 and 450 makes them much easier to deal with. The key to this skill is a strong base knowledge of rounding. Once your students have rounding mastered introduce the WHY of this strategy. A common comment students make when learning this strategy is, “but that’s not the right answer.” Technically, they’re correct. So helping them understand why and when estimations are used is necessary if you want your students to buy into this strategy.
Once students understand why they’re rounding before adding it’s time to practice! Start with two-digit numbers like 34+29 (becomes 30+30) and let them practice giving you approximate answers. Then, move on to 3-digit numbers and ask them to round to the nearest hundred 245+682 (becomes 200+700). After they’ve mastered those two skills you can begin adding in rounding 3-digit numbers to the nearest ten. For students who are really excelling you can increase the rigor by giving them an already friendly equation like 300+600 and asking them to give you examples of what might have been the original “unfriendly” numbers.
14- Standard Algorithm
In 2nd grade, regrouping is introduced and in 3rd grade, it’s reviewed and perfected. The standard algorithm or as many people call it, “old math.” Normally, the standard algorithm is taught after students have some of the other strategies under their belt. With the number sense gained in all the previous addition strategies, the standard algorithm becomes more about applying what they know and less about memorizing a routine. That’s what’s so great about filling up those mathematics toolboxes! By the time kids get to regrouping- borrowing and carrying as us old-timers know it- they understand WHY they’re moving those numbers into the next column.
When it comes to teaching the standard algorithm chants are an amazing way to help students remember the steps they need to follow! Try the two listed below with your students.
Remember to slowly scaffold your instruction. It’s easy for students to get confused and end up borrowing from and carrying to strange places. Start with double-digit numbers and move on to three-digit numbers, when students are feeling confident and ready for increased difficulty. For many students, subtracting across zeroes is difficult. Saving that skill for last can prevent frustration.
Resources for Teaching Addition Strategies
If you’re looking for an all-inclusive pack with a TON of printable and digital math resources for your students including ten frames, counters, number lines, part-part-whole mats check out the Lucky Little Toolkit. It’s loaded with incredible resources for you and your students.
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