Math Concepts vs. Skills Practice

Math concepts are the big ideas behind the math problems that kids do. For example, first graders are mastering addition. Memorizing math facts (4+3, 2+2, and so on) is a skill.

But for a skill to make sense, they need to understand some concepts: that putting two groups of things together gets you a bigger whole, that 4+3 and 3+4 will get the same result, and so on. Math concepts give context to skills.

When kids are learning new concepts, dice games give them a chance to use counters, money, or other math tools in a real-life situation.

Ideas for Using Math Counters

Counting.
Addition. Count out 5 of one color, and 9 of another color. Push them together and count your total as you say "5 plus 9 equals 14".
Subtraction: To subtract 12-8, count out 12 counters. Put 8 in a cup. Count how many are left. Or practice subtracting from 10 with two-color counters. Drop 10 counters on the table. Separate the red ones into a pile. Count the white ones, then figure out how many red counters are in your pile.
Practicing Place Value. Count, add or subtract large numbers with place value counters.
Comparing Numbers: Which is bigger: 12 or 21? Use counters to figure it out. Base Ten Blocks are a good choice for comparing big numbers.
Patterns: Arrange counters in red, blue, yellow, red, blue, yellow. Continue the pattern. Some bear counters come in 3 sizes as well as different colors.

Hundreds Chart

The hundreds chart (or 100s chart) is an extremely simple idea with huge possibilities for helping first graders with math.

It consists of a grid of numbers from 1 to 100, with each row containing a group of 10 numbers. As a result, children using this chart can count across rows by ones, and down columns by tens. The 100s chart can be used as a tool for helping learning a range of first grade skills, including:

subtraction and "counting back"
addition and "counting on"
visualizing patterns of skip counting by 2s, 5s, and 10s
developing number sense skills
learning odd and even numbers
identifying numbers
counting from 1-100

Here are just a few first grade activities and games that you can do with a 100s chart:

Hundreds Chart Puzzle: Cut a hundreds chart into puzzle pieces along the lines. Give the pieces to a child to piece back together.

Find the Number Game: To play this 2-person game, you'll need a hundreds chart and two color counters, or squares of paper in two different colors. The child 1 says the name of a number on the chart. Child 2 finds the number and covers it with his color counter. Then they switch roles, with child 2 calling a number for child 1 to find. As they go back and forth, calling and covering numbers, the chart will fill up with two colors of counters. The goal is to be the first to get three of your colored counters in a row. (Players have no control over their own numbers, but they can use strategy to try and keep the other player from getting 3 in a row.)

Color It In: Give kids a 100s chart and some crayons. Have kids color in all the even numbers, or skip count by 5s and circle these numbers in red. First graders will enjoy seeing the colored patterns emerge when exploring skip-counting, especially when patterns overlap (counting by 5s and counting by 10s, for example).

Penny Calculations: Show kids how to add and subtract with a penny. Give an addition problem such as 35+7. Have kids identify the larger number and put their penny on that number. Then have the child move the penny up as many times as the second number shows. Practice with problems such as 6+22, and 9+41, to give kids practice identifying the larger number first, then adding the smaller number. This is an important addition skill. For Penny Subtraction, start on the larger number and move backwards.

Big Addition: The hundreds chart can be used to start kids adding numbers that would normally be too big for them to handle in normal calculations. Give a problem like 31+25. Have kids put a counter on the first number. When adding a number bigger than 10, first add tens by moving the counter down that many places. From 31, kids would move down 2 rows, going from 31, to 41, to 51. Then look at the ones place (5) and move the counter to the right five times, counting: 52, 53, 54, 55, 56. 31+25=56.
Big Subtraction: This is done just like Big Addition, but kids learn to start on the bigger number, move up by tens, and then move to the left by ones to solve subtraction problems.

Number Line Games for First Grade

A number line is a wonderful math tool for first graders. As children learn to count higher numbers and develop a better sense of how numbers relate to one another, number lines give kids a visual reference to work from. They can be a big help with concepts such as:

working with greater than/less than

finding which number comes just before, or just after, another number

finding odd and even numbers

addition
subtraction

helping kids develop a mental line of numbers in their head for doing simple calculations

You may have heard of strategy-based fact instruction, but what exactly does it mean? It boils down to helping kids become flexible thinkers. Helping them to use what they know to figure out what they don’t know. It gives them a place to start. Here are some examples of strategies for basic addition facts.

Counting on. Yes, this is a strategy. It’s not the most efficient, but it’s better than counting all. For example, one way to find 8 + 4 is to count 1, 2, 3, 4, 5, 6, 7, 8 and then 9, 10, 11, 12. So counting on from 8 (8, 9, 10, 11, 12) is definitely more efficient. And it is a strategy to know that when solving 4 + 8, I can count on starting at the bigger number. Take my 5th grader in the introduction–it doesn’t take 10 seconds to count 8, 9, 10, 11, 12, so it seems like this student didn’t even have the most basic strategy.
Make a ten. This is a powerful strategy for students who understand composing and decomposing numbers. Basically, you split one addend to make a ten out of the other addend. For example, to solve 8 + 4, I would split the 4 into 2 + 2, use 2 to make a 10 with the 8, and then add the other two. So…

8 + 4 = 8 + 2 + 2
Use doubles. Kiddos learn their doubles (2 + 2, 3 + 3, 4 + 4, etc.) quite easily. Knowing their doubles can help with near-doubles facts, like 6 + 7. I’ve watched a student stumped by 6 + 7 and asked them: What’s 6 + 6? Almost automatically they will say 12. So what is 6 + 7? The light bulb goes off and they answer 13 with a smile. It’s like you just taught them a magic trick!
Think +10 for +9. Those 9s are such difficult facts! But, adding 10 to a number is easy. So when I see 9 + 6, I can think 10 + 6 and then just subtract 1.