## Math Games for Third Graders

It may seem obvious to most third grade teachers and parents of third graders that multiplication is THE big skill to be learned in third grade. There are many great multiplication games for third graders.

However, as an elementary mathematics specialist, I have noticed that a great many third graders struggle with regrouping (borrowing and carrying). Most of the time, this is because they have been taught place value with only pencil and paper activities, which are not an effective or concrete enough way to teach place value for real understanding.

Once children have developed a basic number sense for numbers up to ten, a strong “sense of ten” needs to be developed as a foundation for both place value and mental calculations.

Ten is, of course, the building block of our Base Ten numeration system. Young children can usually “read” two-digit numbers long before they understand the effect the placement of each digit has on its numerical value. For example, a five-year-old might be able to correctly read 62 as sixty-two and 26 as twenty-six, and even know which number is larger, without understanding why the numbers are of differing values.

Place value is vitally important to all later mathematics. Without it, keeping track of greater numbers rapidly becomes impossible. (Can you imagine trying to write 999 with only ones?) A thorough mastery of place value is essential to learning the operations with greater numbers. It is the foundation for regrouping in addition, subtraction, multiplication, and division.

The follow are two very effective math games for teaching and reinforcing place value:

What you need:
2 players
deck of cards – 10s and face cards removed
paper and pencil for each person

Shuffle deck and place cards in a pile face down. Players take turns taking a card until both players have 4 cards (for double –digit addition) or 6 cards (for triple-digit addition) and arrange them to make a two- or three-digit addition problem. The object is to make the greatest sum. When each player is done arranging their cards, they write their problem down and find their sum. Players exchange papers and check each other’s addition.

The player with the greatest sum scores a point. Each player takes four or 6 new cards and play continues. The first player with 10 points is the winner.

Variation #1: the player with the smallest sum wins.

Double- or Triple-Digit Subtraction

What you need:
2 players
deck of cards, 10s and face cards removed
paper and pencils

Shuffle cards well and stack them face down in a pile. Both players take four cards (for double-digit subtraction) or 6 cards (for triple-digit subtraction). Players arrange their cards to make a two-digit or three-digit subtraction problem. The object is to make the smallest difference (answer).

Players move their four or six cards around until they think they have the smallest difference (answer) possible. Each player then writes down his/her problem and solves it. Players trade papers and check each other’s computation for accuracy. Players compare answers. The player with the smallest difference (answer) scores one point.

Each player takes 4 or 6 more cards and play continues. The first player to score 10 points is the winner.

Variation: Player with the greatest difference wins.

## Math Games for First Graders

I think that every topic in mathematics is fun if you master it and understand it. Since fun has always been a part of my teaching philosophy, I have found that math games are an enormously engaging and effective way to help children on their way to understanding and mastery in math. The greatest benefits of math games are the way they improve students’ basic arithmetic and problem-solving skills.

By the end of first grade, students should know or be able to do the following:
• understand and use the concept of ones and tens in the place value number system
• add and subtract small numbers with ease
• measure with simple units
• locate objects in space.
• describe data
• analyze and solve simple problems.

I have taught first grade for many years. If I could pick one math skill that I think is the most important skill for first graders to master, it would be the ability to know (without counting on fingers) all the addition facts to 10. Counting on fingers is a good beginning strategy, but children need to have all the facts in long-term memory and be able to recall them automatically.

What are all the facts that add to 10? (10+0, 9+1, 8+2, 7+3, 6+4, 5+5, 4+6, 3+7, 2+8, 1+9, 0+10)
What are all the facts that add to 9? 8? 7? 6? 5? 4? 3? 2?

The following game is one of many that help children master these basic addition skills, while having fun:

What you need:
2 players
Add-em Up game board for each player – each player writes the numbers 2-12 horizontally at the bottom of their papers.
2 dice
Counters – paper clips, pennies, etc.

Players place a counter above each number.

Player #1 rolls the dice and adds the 2 numbers. He/she may then remove the counter over the sum from the game board or the counters over any 2 numbers that add up to that same sum.

Example: Player #1 rolls a 3 and a 4. He/she may remove the counter above the 7 or the counters above any combination for 7, such as 1 & 6, or 2 & 5, or 3 & 4.

Players take turns rolling the dice and removing counters. When a player cannot remove counters that match the sum rolled or a combination, he/she loses that turn.

Play continues until neither player can remove counters. The player with the most counters removed wins.

## Math Games Develop Strategic Thinking

Strategic thinking is one of the most important skills for children to develop. It requires the ability to observe, take in different pieces of information, analyze information, plan and analyze possible solutions, and choose the appropriate action.

Strategic thinking is a way to solve problems. Every day we have to solve the problems. Every day, we need solutions. Problem solving is an essential skill in our professional, family, and social lives.

Games like bridge, chess, and backgammon are ideal for teaching strategic thinking. But learning bridge is more than fun and games; students who play, practice math and reasoning skills and show improvements on standardized tests.

However, games such as bridge have complex rules that can take time to learn and master. Instead of using complicated games, there are many math games at every grade level that are much easier for children to learn and play. All of the math games are focused on providing engaging activities to entertain strategic mathematical thinking both inside and outside of the classroom.

If you are a teacher or parent, I encourage you to have a look at the assortment of games. You will find many that will pique your interest and and help you develop strategic thinking and problem solving abilities in your students/children while having fun!

## Math Games and the Last Few Weeks of School

The Big Test is over. Yeah! The long Memorial Day weekend is past, or soon will be. Sigh! You’re way beyond burned out and thinking mostly about summer. You can’t figure out how you’re going to get through the next few weeks.

I have a great idea! Give a math game a try! Games can help children learn important mathematical skills and processes with understanding.

Besides that they:

• support concept development in math
• meet math standards
• offer multiple assessment opportunities which will help with report cards
• are great for diverse learners such as English-language learners
• encourage mathematical reasoning
• are easy to prepare
• are easy to vary for extended use and differentiated instruction
• improve basic skills
• enhance basic number and operation sense
• encourage strategic thinking
• promote mathematical communication
• promote positive attitudes towards math

Pick a skill set you know your students need to practice, and then find the right game that will offer practice with that skill set. The students will be engaged and quite willing to involve themselves in the repetitive practice needed to hone their skills.

## The What and Why of Math Games

As a veteran elementary teacher and math specialist, I’m a big believer in using math games to teach math in the classroom.

What is a math game? The most effective math games are those in which the structure and rules of the games are based on mathematical ideas, and winning a game is directly related to understanding the mathematics.

Why play math games? I will classify the intrinsic advantages of math games under three categories:

Learning

Much of mathematics teaching revolves around giving students practice in newly acquired skills and reinforcing and revisiting already introduced skills. Games provide a way of taking the drudgery out of this practice of skills, and making that practice more effective. A game can generate much more practice than a workbook page, ditto, or flashcards. When playing a game, students don’t mind repeating certain facts or procedures over and over.

In terms of gains in test results, research indicates that games are an effective way to retrain and reinforce children’s skills with basic number facts.

Playing games demands involvement. Successful mathematics teaching depends on the active involvement of the learner. Piaget, Bruner, and Dienes suggest that games have a very important part to play in learning mathematics. Dienes even suggests that all mathematics teaching should begin with a game.

Ways of Working

Children need to talk about the math as they are learning it. Math games demand mathematical communication. This can be encouraged by having students work with a partner against two other students. Not only will there be meaningful conversation between the two partners, but between the four players.

To play effectively the partners must co-operate. Thus playing games provides opportunities for children to work co-operatively – an important life skill.

Games put pressure on students to work mentally. The ability to do math in your head is a skill that I don’t believe we spend enough time on with students. If you think about it, when presented with a mathematical situation, most people would first try to do it in their head. It takes awhile for students to gain confidence in their ability to do math in their head. You must show them a variety of ways to do math mentally, which will give them tools they can use, but it also builds their desire to think more creatively on their own.

Within the normal classroom situation there few opportunities and little incentive for students to check and justify their work. Games offer a strong incentive for players to check each other’s mathematics, challenging moves which they think are unjustified. I encourage children to ask their opponents to “convince me” or “prove it”.

Probability is one of the mathematics standards that is only slightly addressed. Games bring probability to the forefront. Students are offered many opportunities to think about probability through games.

Engagement

Probably the most powerful reason for introducting games into the mathematics classroom is the enthusiasm, excitement, and total involvement and enjoyment that children experience when playing math games. Students are highly motivated and totally immerse themselves in the games, and, in the end, their attitude toward math grows increasingly more positive. Games offer children the opportunity to experience success, satisfaction, enjoyment, excitement, enthusiasm, active involvement, and gain confidence in their mathematical abilities.

Games teach or reinforce many of the skills that a formal curriculum teaches, plus a skill that formal learning sometimes, mistakenly, leaves out – the skill of having fun with math, of thinking hard and enjoying it.

## Fun and (Math) Games!

Saturday School A Success At Lincoln Elementary reads the headline from Madison, Wisconsin. Even on a Saturday, and even on a day that felt like summer, dozens of students at one elementary school spent the morning in class.

Every Saturday since the end of January, about 100 students have gathered for about two hours a week to get a little extra work done and to do so while having a little bit of fun. It is easy to assume that kids would want to be anywhere but school on a weekend morning, but this program is proving to be different. Instead of traditional instruction, students learn through playing games.

It seems somehow sad to me that kids are allowed to have fun with math only on Saturdays. Why isn’t math engaging, challenging, and fun all the time? As a veteran elementary teacher, I do understand that teachers feel like they don’t have enough time to teach all of the content within the course of a school year. Why on earth would they ever want to add more material in the form of math games when they can’t seem to finish the assigned math textbook? Turns out that making time to incorporate math games in the classroom can lead to rich results. I’ve been using games to teach mathematics for many years, and here are some of the significant benefits of doing so:

Benefits of Using Math Games in the Classroom

• Meets Mathematics Standards
• Easily Linked to Any Mathematics Textbook
• Offers Multiple Assessment Opportunities
• Meets the Needs of Diverse Learners (UA)
• Supports Concept Development in Math
• Encourages Mathematical Reasoning
• Engaging (maintains interest)
• Repeatable (reuse often & sustain involvement
• Open-Ended (allows for multiple approaches & solutions)
• Easy to Prepare
• Easy to Vary for Extended Use & Differentiated Instruction
• Improves Basic Skills
• Enhances Number and Operation Sense
• Encourages Strategic Thinking
• Promotes Mathematical Communication
• Promotes Positive Attitudes Toward Math
• Encourages Parent Involvement

Pick a skill that your students need to practice. One of the big ones is subtraction at any level. Kindergarteners through 6th graders find subtraction to be a challenge. Here’s a great double-digit subtraction game:

500 Shakedown

What you need:
2 players
2 dice
paper and pencil for each

Each player starts with 500 points.

Player #1 rolls the dice and makes the biggest two-digit number he/she can. Now he/she subtracts this number from 500.

Example: Player #1 rolls a 2 and a 4 and makes 42. Now he/she subtracts 42 from 500.

Player #2 rolls the dice and does the same. Players continue to alternate turns. The first person to reach 0 wins.

There’s only one complication! When you throw a 1, the rules change. You don’t subtract. Instead you make the smallest two-digit number you can and add.

Example: If the player throws a 1 and a 5, the smallest two-digit number is 15. So he/she adds 15 to the total.

## Teachers, Students, and Math Games

An Indiana math project focuses on helping kindergarten through sixth-grade teachers learn new techniques for teaching math.

Neill, along with partner Tara Sparks, a first-grade teacher at Eastern Greene Elementary School, demonstrated at a concluding session how they have “excited kids through games created with playing cards and dice.”

“The kids in my class have been taking them out at recess to play with them,” Sparks said in the press release. “They don’t want to put them down.”

As a veteran elementary teacher, I have used math games for many years to engage children in math they do not want to stop doing – even if it means skipping recess!! Many times they begged to take the game out to the playground, and they were always excited to take it home and teach it to their families. When was the last time that happened to you with math or math homework?

Math games in the classroom have many benefits:

• meets mathematics standards
• easily linked to any mathematics textbook
• offers multiple assessment opportunities
• meets the needs of diverse learners (Universal Access)
• supports concept development in math
• encourages mathematical reasoning
• engaging (maintains interest)
• repeatable (reuse often & sustain involvement
• open-ended (allows for multiple approaches & solutions)
• easy to prepare
• easy to vary for extended use & differentiated instruction
• improves basic skills
• enhances number and operation sense
• encourages strategic thinking
• promotes mathematical communication
• Promotes Positive Attitudes Toward Math
• encourages parent involvement

Children throw themselves into playing games the way they never throw themselves into filling out workbook pages or dittos. And games can, if you select the right ones, help children learn almost everything they need to master in elementary math. Good, child-centered games are designed to take the boredom and frustration out of the repetitive practice necessary for children to master important math skills and concepts.

Games teach or reinforce many of the skills that a formal curriculum teaches, plus a skill that formal learning sometimes, mistakenly, leaves out – the skill of having fun with math, of thinking hard and enjoying it.

## In Terms of Decimals, Math Is the Best Game in Town!

Ask fourth, fifth, and sixth grade teachers about decimals and the question is followed by groans of dissatisfaction. Basically, the groans stem from the lack of success that teachers have in teaching this concept. As one student put it, a decimal is “a thing that makes numbers even more confusing”.

Teachers can get some help in this area by playing decimal math games with their students. A math game has advantages over the traditional approach. Playing a game increases the excitement of any mathematics lesson, and games are engaging and give students the chance to cooperate and communicate with their peers. The following decimal games are two student favorites:

Decimal Dice

What you need:
2 players
two dice
paper and pencil.

Player #1 rolls the dice one at a time. The first number rolled is the whole number and the second number rolled is the decimal.

Example: Player #1 rolls a two and then a 6 – the score is 2.6

Player #1 records this decimal at the top of his/her paper.

Player #2 rolls the dice, one at a time, and records his/her score.

Players continue to alternate turns until each player has 10 decimals.

Player #1 adds his/her 10 decimals together. Player #2 does the same. Players exchange papers and check each other’s addition.

For each double rolled (2.2, 3.3, 6.6, etc.) you add 10 bonus points to your final score.

The player with the highest sum wins the game.

Variation: This game can also be played with subtraction. Begin with a score of 100. Roll the dice in the same manner and subtract your decimal from your score. If you roll doubles, subtract 10 bonus points. The person with the LOWEST score wins!

Decimal Dice 2

What you need:
2 players
two dice
paper and pencils

In this game, each player will roll the two dice exactly three times. At the end of three rounds, the player closest to 10 wins the game.

Player #1 rolls both dice. Player #1 must decide which of the numbers is the whole number and which is the decimal.

Example: Player #1 rolls a two and a 6 – he/she decides whether to
make 2.6 or 6.2

Player #1 records this decimal on his/her recording sheet.

Player #2 rolls both dice. Player #2 must decide which of the numbers is the whole number and which is the decimal and record this on his/her recording sheet.

Players continue to alternate turns until each player has thrown the dice three times.

Players add their decimals. Players exchange papers and check each other’s addition.

The player with the sum closest to 10 wins the game.

Children are all the same in one way: they love to play games. Put the right game in front of a child, explain the rules, and that child will eagerly play, happy and alert.

Math, on the other hand, can be intimidating for kids. If we understand the nature of a child’s strengths and weaknesses, we can help any child to achieve and feel good in mathematics. It’s a matter of finding the best itinerary and the best route through the subject’s many possible pathways.

They need practical arithmetic experiences that are fun. Playing math games is an effective and engaging one of those possible pathways. Whether you’re a parent or teacher, your children will learn, without even realising they are learning.

One of the things we positively know about children (and adults) is that if pleasure is not a part of what you are doing, you will not be willing to do it very much or for very long.

Many parents regard play as rather trivial in the lives of their young children and would much rather see their kids get involved in “educational” activities. To parents, it often seems that all children do is play! They play until they are five or six, then they go off to school and start to learn. They play until they are big enough to really begin to do things.

The act of playing is an important tool that influences a child’s life. The primary goals of childhood are to grow, learn, and play. It is often through play that children learn to make sense of the world around them. It is a child’s “job” to play to develop physical coordination, emotional maturity, social skills to interact with others, and self-confidence to try new experiences and explore new environments.

Play to a child IS learning! They learn to play and play to learn. Play is terribly important to a child. It is not a distraction. It’s not something they do to take up time. It’s a child’s life.

So, begin to “play” with your child. Math games are a fantastic way to learn as you play.

## A Math Game for First, Second, and Third Graders

When working with first graders, second graders, and sometimes even third graders, I have found that when asked, “How much is your number + 10 (e.g., 23 + 10)”, they struggle to know the answer and end up counting on their fingers. Counting on fingers is a good beginning strategy, but as children gain in number sense, fingers should no longer be necessary. The same is true if I ask, “How much is your number -10?”

A major learning goal for students in the primary grades is to develop an understanding of properties of, and relationships among, numbers. Building on students’ intuitive understandings of patterns and number relationships, teachers can further the development of this one aspect of number concepts and logical reasoning by using a math game Tens and Ones.

Tens and Ones

What you need:
2 players
0-99 chart for each player (find one and download it from the internet or have your child make one using a 10×10 grid.
1 counter (button, paper clip, rock, etc.) for each player
1 regular die with instructions for rolling (following)

Roll 1 or 2 – +10
Roll 3 or 4 – +1
Roll a 5 – -1
Roll a 6 – -10

Each player places a counter on the zero on his/her own 1-99 chart. Players take turns rolling the die.

Player #1 rolls the die and moves his/her counter according to the roll on his/her 0-99 chart. Player #1 checks to make sure that player #2 agrees and then hands the die to player #2.

Player #2 follows the same steps as player #1 using his/her own 0-99 chart.

It may be visually helpful to have the child roll the die, leave the counter where it is and then count on using his finger. When he/she reaches +10, the player will then be able to see that he/she is exactly one row down from where he/she started. Then the counter can be moved to the new spot.

The winner is the first player to move his/her counter to 99. To win a player must land on 99 exactly. For example, if a player lands on 90 and rolls a +10 on the next turn, the player must pass, as there are only nine boxes from 90 to 99. Players may not move their counters past 99 and off the chart.