There are many ways to help your students master mental math strategies for addition. Some strategies are simple, like the counting on strategy, while others are more difficult. In this post, we’ll go over different ways you can help your 1st graders use a mental strategy to solve addition facts.
Mental math is an important skill for students to have, especially in the early grades. Being able to quickly and accurately do basic math calculations in your head can save time and help students feel more confident in their math abilities. You’ll be surprised at how much difference these techniques can make!
Here are five easy mental math strategies and ideas on how to teach and practice them. The ideas are great for small groups, whole group, or partner games!
The counting on to add strategy is one of the first mental math strategies for addition that I teach my class. This is when you start with the bigger number and count on. For example, in the problem 3 + 8 you would start with 8 and count on 3 until you get to 11. This strategy does not require anything but the students’ fingers and they catch on really quick to this.
One issue with this strategy is that students tend to want to use it all the time. Once more efficient strategies have been taught, I find I have to require my students to use them throughout the year and not always fall back to counting on.
Make sure when you begin teaching this strategy that you allow students to use manipulatives to slide as they count on. Lots of times teachers will skip this step and go straight to having students solve with just paper and pencil. First graders need to go through the concrete stage to get started with a firm foundation with any math skill.
How To Teach Counting On
To teach this strategy, have students practice counting on from a variety of numbers. You can also play games that involve counting on, such as “Roll and Add” where students roll two dice and then count on from the larger number to find the sum.
Here are a few other easy ideas to use in your classroom.
Number Line Race
Draw a number line on the board or on a large piece of paper. Split the class into pairs and give each pair a marker. Call out an addition problem such as 8 + 6 and ask students to find the sum of the two numbers by counting on from the bigger number. The first pair to reach the correct answer and raise their hand gets to put a mark or their initials on the number line at the answer. Repeat the process with different starting numbers and different sums until all pairs have had a turn.
This activity helps students practice counting on along a number line and reinforces their understanding of addition. By making it a race, students are motivated to find the answer quickly and efficiently.
Addition Dice Game
For this game you’ll need two dice, a whiteboard and marker or paper and pencil.
Player one rolls two dice and adds the numbers together and says the sum out loud. The next player rolls one die and adds that number to the previous sum. Players take turns counting on from the previous sum and adding the next number rolled until they reach a target number.
For example, let’s say player 1 rolls a 4 and a 5, giving them a sum of 9. Player 2 rolls a 3 so they count on from 9 up to 12. Player 1 will now roll one die. If they roll a 5, they would start with 12 (the previous sum) and count up 5 to 17. Whoever reaches the target number set by the teacher wins.
This game helps students practice adding and counting on, and reinforces their understanding of number sequences.
One of the other common mental math strategies for addition are doubles facts. Doubles facts are basic addition facts that involve adding two of the same number together such as 6 + 6 or 8 + 8. To teach doubles facts, flash cards are the best way to start. Simply having students memorize their doubles facts will be extremely beneficial in helping them with basic math down the road.
Try any of these activities to have students review their doubles facts so they don’t forget them.
- Doubles Flashcards: Create flashcards with double facts written on them (e.g. 2 + 2 = 4) and have students practice finding the sum.
- Doubles Fact Bingo: Create bingo cards with double facts and have students play bingo, marking the sums as they are called. Use a bingo card generator to make this easy!
- Roll and Cover: Create a 10×10 grid and write numbers 1 to 10 along the top and also down the side. Give each student a game board and a die. Students take turns rolling the die and adding the number they rolled to its double (if they roll a 4, they find 4 + 4 = 8). Students locate where the sum would go on their game board grid by finding 4 along the side and 4 along the top and write it in that spot like when you play Battleship. The first student to cover all the sums on their game board is the winner.
- Memory Match: Make sets of cards with one half of a double fact on each card (2 on one card, 2 on another). Do this for all numbers 0-10. Lay the cards face down. Students will turn over two cards on their turn. When they turn over 2 of the same number they say the double fact and the answer. If they are correct they keep the cards as a point.
- Doubles Race: Divide students into teams and have them race to write as many double facts as they can within a set time limit. Using a large piece of butcher paper and makers makes this game fun for students!
Doubles Plus 1
This strategy involves adding one more to a doubles fact. For example 5 + 6, if I know 5 + 5 = 10 then 5 + 6 = 11. This strategy cannot be taught until students have mastered their doubles facts. Once they have, try these activities to practice doubles plus 1.
Have students work in pairs to take turns saying a double fact and the corresponding doubles plus one fact. For example, “2 + 2 = 4 so 2 + 3 = 5. It may be helpful to have doubles facts already written out on cards for students to pick from. Then they must say the doubles plus one fact that goes with the card they draw. This game is great for those times when you have a few extra minutes between lessons.
Doubles Plus One Grid Play
On a grid write all doubles plus one answers (3, 5, 7, 9, 11, 13, 15, 17, 19, 21). Use a 10-sided die or create a spinner with 1-10 on it. This would also be a great oppurtunity to differentiate by using a 6-sided die or a spinner with only 5 sections.
Students will roll or spin and then double that number. Then they will say the doubles plus one fact that goes with it. So if they roll 5 they will say 5 + 5 = 10 so 5 + 6 = 11. If they are correct, they get to cover the number 11 on the grid with their color marker. When all spots are covered the player with the most of their color is the winner.
Fact families are one of the best mental math strategies for addition for 1st graders. They help students understand the relationship between addition and subtraction. One common misconception teachers have when teaching fact families is to give students 3 numbers and have them create 2 addition and 2 subtraction facts that go with those numbers.
By doing this students are not taught the reasoning behind fact families. It is vital for students to understand the relationship between the numbers and why they are related.
To teach fact families, teachers can start by using manipulatives such as number bonds or cuisenaire rods to show the connections between numbers.
For example, using number bonds, the teacher can demonstrate how to add the two smaller numbers to find the larger number, and then how to subtract one of the smaller numbers from the larger number to find the other smaller number. This helps students see the relationship between the numbers in a fact family and understand that the same numbers can be used in different ways in addition and subtraction equations. Using manipulatives can make abstract concepts more concrete and engaging for students, particularly in the early grades.
Here are some ideas to use with your students!
Fact Family Building Blocks
For the “Fact Family Building Blocks” activity, teachers can give each student a set of building blocks in different colors. Students can use the blocks to build the numbers in a fact family, such as the fact family for 4, 2, and 6. To build 4, students can use four blue blocks, for 2 they can use two red blocks, and for 6 they can use two blue and four red blocks, showing the connection between the numbers. Students can then practice solving the addition and subtraction equations using their blocks, such as 2 + 4 = 6 and 6 – 4 = 2. This activity provides a hands-on way for students to understand the relationship between numbers in a fact family and strengthens their understanding of addition and subtraction.
Fact Family Silly Stories
Students can use the numbers in a fact family to create silly stories, reinforcing the connection between the numbers.
For example, using the fact family of 4, 2, and 6:
- A student could create a story about two aliens, each with 4 arms, who find two more arms and now have 6 arms total.
- Their partner could create a story about a cat who loses two of its whiskers, leaving it with 4 whiskers.
This might need to be modeled a few times by the teacher for students to catch on.
By using the numbers in a fact family in their silly stories, students can build their understanding of the relationships between the numbers and practice mental arithmetic.
Making a Ten
Making ten is a crucial mental math strategy for 1st graders to learn. Before students can be held accountable for making a ten to add, they need to know the number partners for ten.
Teachers can make this interactive and fun by using hands-on activities such as building with blocks or using a ten-frame. For example, teachers can ask students to place blocks in a ten-frame to show the number they are working with, then ask them to find another number that, when combined, makes ten.
Another fun activity is to play a game of “What’s missing?” where students are shown a number in the ten-frame and have to figure out what number is missing to make ten. If you want more ideas on teaching your students the partners of ten check out this blog post where I give you 9 Free and Engaging Ways to Make 10 for 1st Graders along with a freebie!
To reinforce this concept, teachers can create a “Ten Club” where students receive a special recognition for being able to quickly recall the partners of ten.
Once students have mastered the partners for ten take this strategy to the next step and have them make a ten while adding.
Making a ten refers to the strategy of manipulating numbers to get a ten which makes adding easier for students. For example, if a student is shown the problem 8 + 6, they can use mental math to make ten by giving 2 to the 8 to make it a 10. The two that was given to the 8 came from the 6 so the six is now a 4. This turns 8 + 6 into 10 + 4 which is so much easier for students to add. This strategy is important for 1st graders to learn as it lays a foundation for more advanced arithmetic skills.
Make a Ten With Students
Use your students to model this strategy. Write the problem 9 + 5 on the board and then have a group of 9 students and group of 5 come up to the front. Let students tell you how many more we need to get from 9 to 10. Students should tell you we need one and you can model moving one student from the group of 5 to the group of 9. Make sure students see that we did not take any students away or add any new students. The numbers 9 and 5 stayed the same but just moved around. Let them count how many are in each group now and decide what the new, easier, addition problem is (10 + 4).
In my experience it takes students lots of practice actually seeing the numbers be moved with manipulatives before they get a sold grasp on this skill. I like to start with only addition problems with a 9 as one addend and then 8.
I will do the activity explained above using different variations such as using toy cars and driving them to make a ten, using goldfish or cheerios, crayons, books from our classroom library. Anything that the students can touch and move.
Mental Math Strategies Conclusion
In conclusion, mental addition is a crucial skill for 1st graders to have and these five mental math strategies can help students achieve that. From counting on, to using a number line, to playing addition games, there are many ways to make mental addition an engaging and fun experience for students. With the right teaching methods, students will develop confidence in their mental math abilities and be able to solve basic math calculations quickly and accurately.
If you’re looking for even more activities to help your students master mental addition, consider using these differentiated lesson plans that include even more activities and strategies to help reinforce these skills plus many other addition and subtraction strategies that every 1st grader needs.