The common core standards for first graders cover a variety of math skills, everything from geometric shapes and partitions of circles to algebraic thinking and length measurement of an object. One significant part of the 1^{st}-grade standards is addition and subtraction strategies. These strategies use place value and are based on the relationship between addition and subtraction and the properties of operations. Whoa. That is the reaction many think or say when they see all the common core standards for addition and subtraction. It can be overwhelming but keep in mind that we are providing our students with tools to approach addition and subtraction, which hopefully helps make it more approachable for all!

Before Common Core State Standards, students solved a subtraction equation, addition problem, or story problem by memorizing addition or subtraction facts. Now, students can use strategies of all kinds for basic operations to approach addition and subtraction problems. This process helps young learners see different ways to solve a problem. As a child practice these strategies, they might find one that clicks for them to help make the problem more accessible and continue to build their number sense.

The Common Core math standard 1.OA.C.6 states that students will “add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).” All these strategies are based on place value, the relationship between addition and subtraction, and the properties of addition.

### Counting On/Counting Back Strategy

This strategy involves students moving along a number line to find the sum or difference. Based on place value, students break numbers into “friendlier numbers” on the number line and move along the number line to find the sum or difference. This strategy is not just based on place value but also on the relationship between addition and subtraction. Students can think of the inverse operation to find the unknown whole number. For example, if students try to find 15 – 12 = ____, they can think of the relationship between addition and subtraction and think 12 + ____ = 15 to help them solve. If fact families are helpful for students, thinking of subtraction fact families can also be helpful in solving these types of problems.

### Decomposing Numbers

Decomposing numbers is sometimes called partial sums and is related to expanded form and place value. When decomposing numbers, students will break apart numbers based on their place value and then add or subtract to find each place value’s answer. Once the individual place value sums or differences are found, the numbers are put back into expanded form and returned to standard form. This strategy works well with two-digit numbers.

### Compensation

In this strategy, students are using their knowledge of place value and changing the numbers to friendlier ones by adding more to them. A friendlier number in addition, is a multiple of 10. A friendlier number in subtraction ends with a 9. The students would adjust the numbers by borrowing from each other to make those friendlier numbers. For example, If the addition number sentence was 54 + 47, I would change 54 to 50 by taking four away and then adding those 4 to 47, so my new problem would be 50 + 51. This strategy is an easier way to get the sum because mental math can be used.

Many of these strategies are based on understanding the properties of addition and basic addition facts. The commutative property of addition is referenced a lot, as it helps students to understand that the order of addends does not change the sum. The associative property of addition is also important as this helps to remind students that the groupings of the addends does not change the sum either. Making sure students understand these properties well will allow them to know how and when to use all these strategies. It is not just about memorizing anymore but showing them that there is more than one way to solve a problem. This process will help them not just with their first-grade level standards but down the line in second grade, third grade, and even fourth grade, as these strategies and properties will help with more complex concepts.

With many of these strategies, offering math manipulatives for concrete models helps students with addition and subtraction math problems. Providing these scaffolds and strategies for young learners will hopefully make addition and subtraction more accessible, so when it comes to real-life problems or issues that involve these operations, they can successfully solve them with confidence!

Below are some ideas that teachers can use with young learners that will help them grasp the addition and subtraction concepts in a fun way!

### Anchor Charts

When learning a new concept, coming up with a chart together as a reference point of all the new strategies learned, assists students in organizing their thinking and seeing the variety of ways they can solve a problem. Creating the chart together gives students ownership and helps them recall the information more because they were part of creating the chart.

### Math Manipulatives

Counting on and counting back are usually the first strategies to start with because they are working with ones digits that are whole numbers. Young learners can use counters, base ten blocks, or their fingers as tools to help them count on or back. Fingers are sometimes the easiest tool because they always are with them! However, fingers may be more complicated when working with the digits of a two-digit number. This is where counting bears, counters, popsicle sticks, or base ten blocks are super helpful to represent the written numeral in an equation! This activity is also great for tactile learners who need to manipulate something to understand and solve the problem.

### Drawing Pictures

Even though it is math time, drawing simple, non-detailed sketches to solve problems is very helpful! This activity is effective for addition and subtraction word problems as some students can get lost with all the words in these types of questions. Go sentence by sentence to draw the number of objects for the information the sentence gives you. This process will allow visual learners to “see” the problem. Drawing pictures to solve a problem can also be helpful when trying to find an unknown number in an equation. Being able to “see” what the equation is showing you and physically crossing out what is being taken away or drawing more for things being added will help students be successful!

### Number line Hop

Number line hope is a fun game that involves movement, which is perfect for our little learners and provides a break from printable worksheets! Put a long piece of tape on the ground with number cards in counting order spaced evenly on the tape. The numbers do not have to be a one-digit number. It can be whatever your students are working on at the time. This is your human-size number line! The students are given cards with the directions: “Solve the following equations.” You can add whatever equations you are working on, whether they are basic addition facts or subtraction facts, to even an unknown-addend problem! When the students are solving the equation, they hop to count on or back to solve for the sum, difference, or missing number. This activity is a fun break from practice worksheets and can be done as a whole class, in small groups, or as a center activity!

### Commutative Property Memory

For this Memory game, students will find the matching equations using the commutative property instead of matching the same numbers. This game is more interactive and fun for students and gives them a break from first-grade math worksheets but still provides learning and practice of the concept of addition.

### Balance Time

Part of addition and subtraction is understanding the meaning of the equal sign. Sometimes on a 1^{st}-grade math worksheet, students will see “5+3=8 is the same as 8=5+3” and think it is wrong. One of the best ways to show them this is to use a balance scale. For the previous example, using colored counters, on one side of the balance scale, put eight counters to represent the sum. On the other side, place five red and three blue to represent the addends. The scale should be balanced because both sides have 8. Then switch the eight counters with the five red and three blue, so they are on opposite sides. The balance is still the same. This method is a great way to show students the meaning of the equal sign despite the order in which it is written. To show how equations are equal, students can use the scale to show how 4+1 = 3+2, 7+4 = 8+3, etc. They will learn how equal shares are on both sides, making the scale balanced, furthering their understanding of the equal sign. This activity can become a true/false game where students must decide whether the equations are equal or not using the scale and counters. In some special cases, students can use the written method of solving the equations instead of using the scale to see if they are equal.

First-grade math standards are filled with many new concepts, such as understanding equal parts of two-dimensional shapes, composite shapes, the length of an object, an understanding of whole number relationships, and three-dimensional shapes. However, addition and subtraction strategies are crucial in helping students grow their number sense and operational thinking.