By Mollie Moore

Teachers know to expect a range of skills and abilities from incoming students each year, but there are certain fundamentals that children must finish each given year having mastered. For first grade teachers, your co-workers next door will thank you when you send them a classroom full of confident adders next fall. Below are some of the most foundational skills your first graders ought to know by June, and suggested methods for teaching each of them.

Counting On

What Is It?:

• Mentally starting with the larger of two addends in an addition equation, and counting up by ones to find the sum (e.g. To find the sum of 3+6, think “6...7, 8, 9” rather than “3...4, 5, 6, 7, 8, 9” or beginning the count at 1).

Methods for Teaching It:

• Teach learners to always identify the larger number first, regardless of its place in the equation.
• First teach counting on using a number line that pupils can touch as they count aloud.
• The dot method: After students learn the basic skill of counting on, this method will help them to no longer rely on a tangible counting tool. This method assumes that each of numbers 1 through 5 has invisible dots that our eyes, rather than our fingers, can follow as we count on. Still beginning with the larger of the two addends, pupils will then count on hands-free as they follow said dots with their eyes on the remaining addend (assuming it is 1-5).
• Imagine these dots to be in the following locations:
• 1 – At the top of the vertical line forming the 1.
• 2 – At both ends of the 2.
• 3 – At each of the three ends (on the left side) of the 3.
• 4 – Assuming a 4 to be written as an angular upside down “h”) at each of the four points/ends of the 4.
• 5 – At each of the four points/ends, as well as one dot on the belly (curve) of the 5.

Doubles Facts

What Is It?:

• The sum of a pair of the same integer. It is standard to teach 0+0=0 through 10+10=20 for mastery, although you may choose to take doubles further.

Methods for Teaching It:

• Use real-life examples (e.g. 5 fingers on each hand makes 10 fingers; two rows of 6 eggs makes 12 eggs).
• Speed games, such as Around the World: One student walks around the classroom, stopping behind one classmate at a time. The teacher holds up a flashcard containing a doubles fact (omitting the sum). The first child to state the correct answer continues to travel around the classroom.
• Timed, written drills: Pupils race the clock to complete a page full of doubles facts. They try to beat their own personal best each time the exercise is repeated.
• Ultimately, drill these in whatever ways work best for you and your class until your little adders have memorized them the way they have memorized their names.

Doubles Plus One

What Is It?:

• The sum of two neighboring integers (e.g. 2+3=5).

Methods for Teaching It:

• This skill should be taught after learners have memorized doubles facts, as doubles plus one builds on that prior knowledge.
• Begin with training young eyes to recognize neighbors. Teach this with enough repetition for students to be able to identify neighbors quickly, in the same way that doubles have become familiar to them by this point.
• Once first graders can quickly identify neighbors, give them a series of doubles plus one equations to solve. Have them circle the lower addend in each equation and write above it its corresponding doubles fact (e.g. Above 2+3=5, they would write 2+2=4). Finally, instruct them to count on one in their heads from the sum of that doubles fact, and record their answer. From this, children can progress one step at a time to solving all of the doubles plus one equations mentally, without needing to circle the lower addend or write the relevant doubles fact.

Making Tens

What Is It?:

• The six pairs of addends whose sum is 10.

Methods for Teaching It:

• Like doubles facts, these simply need to be committed to memory. Consider creative ways to drill these six important pairs of numbers.
• Lay twelve note cards, each containing one of the numbers 0 through 10 (with two containing the number 5), in front of pairs of students. Each pair will race when you give the signal to make a given number of sets of ten.
• The game of memory: Using the same twelve note cards, pairs of young mathematicians turn the numbers face down in a grid and take turns flipping over two cards at a time, trying to make tens. To make this game more challenging, double the number of note cards used, or place the cards facedown in a less geometric shape (e.g. scattered instead of orderly).
• Around the World (Find the Missing Number): See a description of the game under “Doubles Facts.” Vary the game for making tens by having the cards each contain an incomplete equation, the sum always being 10. Pupils are to be the first to identify the missing addend.

Some Special Sums – Part 3

Thorough and thoughtful, this lesson will help young adders of all skill levels to master doubles facts and doubles plus one.

Fishing for Tens

Modeled after the classic game Go Fish, this card game is certain to be a favorite amongst first graders. Young mathematicians seek to make pairs of number cards that add to ten.

Frogs on a Log

This interactive three-day lesson series especially speaks to kinesthetic learners, but is guaranteed to provide a fun time for all young learners. The lessons include a counting frog song, physically moving "frogs" onto “logs,” and pupils writing their own number sentences to match the frogs on the log demonstrations.