Activities to Practice Addition and SubtractionOne of the best ways to work on computational fluency is through problem solving. Cognitively Guided Instruction has identified 11 different problem structures for addition and subtraction. Please see article about Cognitively Guided Instruction for a listing of these problem structures. In addition to solving problems, students should also participate in activities that will foster their fluency with adding and subtracting numbers. Since many students do not see the strategies that apply to related classes of facts, it is helpful to work on them explicitly until fluency is achieved. The fact tables have been broken up into pieces based on strategies to help make this process systematic and manageable for the student. Basic Fact Activities:
These activities taken from Student Centered Learning by John Van de Walle and LouAnn Lovin 1. One, Two, and Zero more and less Student draws a digit card and rolls a dice that is labeled +1, +2, +0, -1, -2, and -0. They say the resulting fact. Example- draw a 7 roll +2, say, “7 + 2 = 9.” 2. Doubles and Near Doubles Student draws a digit card and says the double fact. Example- draw a 7, say “7 + 7 = 14.” For near doubles follow the same procedure, but say the number on the card and the number one more than that number. Example- draw a 7, say “7 + 8 = 15.” 3. Facts up to 6 Students usually learn these number combinations fairly easily. One of the ways we drill is by playing a game called What’s Hidden?” The student takes the number of objects they are working on, for instance if they are working on number 5, they would take 5 objects. They then put the objects in something they cannot see through like a paper bag or under a bowl. They then grab some of the objects and based on what they see, they figure out what is hidden.
4. Make Ten The ten frame is a very useful tool for this activity. Student can play “What’s Hidden?” with 10 objects or they can draw a digit card and say the fact that will get them to 10. Example- if they draw a 7, say “7 + 3 = 10.”
This is a really important activity because 10 is such and important number in our place value system. Another similar activity is “Make the Next Ten.” Instead of drawing a single digit number, the student draws a double digit number tile and says the fact that gets them to the next ten. Example- draw number 53, say “53 + 7 = 60.” This is a really good activity because it builds number sense and really fosters mental math strategies.
5. Up to Ten (facts with a sum of 7, 8 and 9) Students play the What’s Hidden game for these upper digits. For some reason, these facts are really hard for kids to become automatic with, so they usually need lots of time to become automatic. 6. Facts Greater than 10 If a student has become automatic with the first 5 strategies there is only a few facts left to become automatic with. The basic strategy we try to teach is building up through ten or building down through ten. For instance for the fact 4 + 9 we would teach the students to think 4 = 1 + 3 so 4 + 9 = 1 + 3 + 9 which allows us to make a ten and some extras (1 + 9) + 3 = 14
Through repetition students will become automatic with these facts · Drill Facts through families.
Click here to download your fact triangles Activities that work all the facts: These activities can be used to work the basic facts or multi-digit computation. The Hundreds Chart and Open Number Line are two very useful tools as students transition from using manipulatives to count out the answer to solving either mentally or using a paper and pencil procedure.
How Many In All? Student either rolls two dice or draws two digit cards (can use number tiles numbered 1 to 100 if you want to work multi-digit problems). They figure out what the two numbers equal when added together. Depending on the student’s level they will figure out how many there is in one of three ways: 1. Take objects and count. 2. Draw a diagram to represent the numbers. 3. Solve mentally or use a paper and pencil procedure to figure out the answer.
Coin Toss – (Addition) Student takes a handful of coins (can substitute two sided counters) and tosses them on the table. The child counts how many heads and how many tails (or how many of each color). Then they figure out many there is in all. Good to use the ten frame as this fosters the idea of groups of tens.
Mathematical War (or Battle) - This can be a competition game if two players are playing. They roll the dice or flip the cards and the player who gets the total correctly fastest wins the point (takes those two cards).
Race to $1.00 For this activity you will need a bag of dimes and pennies and a deck of cards or two dice. The object is to get to $1.00. On their turn, the child picks a card or rolls the dice. They take the amount of money indicated in cents. If they can, they can make a trade of ten pennies for a dime. The player that gets to $1.00 first is the winner. A challenge can be to get to exactly $1.00 without going over. Students must decide whether to take the money on each turn before they total. If they go over $1.00 they get bumped back to a set amount (usually $0.50).
The 5 Tower Game- Can be played with two, three, four or five towers (addends). Students pick a digit card and take that many counters. Unifix cubes work well for this activity. They then pick another card and take that many counters or cubes. The idea is to put the cubes together to find the total. As more addends are used, there is more choice for how students can combine the blocks. The goal is to look for ways to combine the towers that are easy to do in your head. For example: if the numbers were 4 + 5 + 3 + 6 + 7 the student might notice the addends that made ten (4 + 6) + (3 + 7) + 5 = 25. Another student might group them like this taking advantage of double sevens since most people find doubles easy (3 + 4) + 7 = 14; (14 + 6) + 5 = 25. This activity can be done as a daily routine with the whole class or as an individual or small group activity.
Subtraction: Many students will solve subtraction problems by thinking of the related addition fact. For example to solve the fact 10 – 4 = ¨ the student thinks 4 + ¨ = 10. Piaget wrote that this is what always happens in our brain but that over time we can become so adept at it that it happens on an unconscious level. So even though these activities are listed as subtraction activities do not be surprised if the students figure out the answers using addition.
What’s the Difference? This is essentially the same game as How Many In All? Except the children figure out the difference between the two dice/cards. Child either rolls two dice or picks two cards out of a deck of cards. Depending on the student’s level they will figure out how many more in one of three ways: 1. Take objects and count. 2. Draw a picture to represent the objects. 3. Count dots or symbols on the dice/cards or solve mentally.
Mathematical War (or Battle) - This can be a competition game if two players are playing. They roll the dice or flip the cards and the player who figures out the difference correctly fastest wins the point.
Coin Toss – (Subtraction) Another way to practice subtraction is to take a handful of coins (can substitute two sided counters) and toss them on the table. The child counts how many heads and how many tails. Then they figure out which is more and by how many.
The other part of 100 This game is very valuable because it fosters getting to landmark numbers like the next ten or 25 or 75, which are useful in mental math. Student takes a number tile (or draws two digit cards and makes a two digit number) and then figures out how much more they need to get to 100. Example- student draws 27. They then figure out 100 – 27 or 27 + ¨ = 100. This could be done using counters, paper and pencil algorithms or mentally. One mental math method might be: + 3 gets me to 30, +70 gets me to 100 so the other part is 73.
What’s Hidden? Take a handful of objects (anything would do – Base 10 Blocks, coins, cereal, M&Ms, etc.). Child counts the objects and records how many there is. Take some of the objects and hide them from view. Child records how many are left in view and tries to figure out how many are hidden. This game is good for practicing Missing Addends and Subtraction because the children usually use one of those two ways of thinking to solve.
Guess and Check- This is a good game for building estimation skills. Student takes a handful of counters and guesses about how many? They record this in the first column of the chart (Guess or Estimate). They then count how many there actually are using the Ten Frame and record this in the middle column of the chart (Actual Amount). The student then calculates the difference between the estimate and the actual amount and records this in the third column of the chart (How far away?) This can be made into a competitive game by having two or more players play and player with lowest score at end of game is the winner. Play for set time or certain number of rounds.
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The benefit of Fact Triangles is that they cluster facts into fact families. Reducing the number of facts you need to master. Facts may be mastered through the use of triangle fact cards. A triangle fact is pictured to the left. Fact triangles are a more effective device for memorizing the facts than ordinary flashcards because of their emphasis on fact families. The three numbers involved in an addition fact are placed on the corners of a fact triangle. The sum (answer) is at the top, under the asterisk (*). You cover one of the corners of the triangle. Then your child gives an addition/subtraction fact that has the number you are concealing as its answer. For example, in the fact triangle pictured, your child would say either “3+4=7” or “7-3=4.”