Instructional Strategy Mathematics

Transcription

1 Instructional Strategy Mathematics Symbols of Comparison Three of the most important symbols in math are =, >, and <. They represent equal to, greater than, and less than which are the three expressions used in comparison. They are found on the basic keyboard of every computer. They are important because they can be used with objects and concepts to indicate degree of difference for any quantity or characteristics. For example: A carton holds a dozen eggs. The word dozen represents the quantity of 12. (a dozen = 12). Half a carton is less than a full carton. (Half a carton is < 12). Two cartons is more than a dozen. (2 cartons > 12). These skills align with Common Core for: Use addition and subtraction to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Order three objects by length; compare the lengths of two objects indirectly by using a third object. The symbols can be used to make a statement that two items or concepts are equal or different. For equal, this does not mean the items are the same. A dozen eggs is not the same as a dozen roses, but when measuring the concept of quantity, the amount of each is the same which makes them equal. For > and <, the statement is of comparison. One item has more or less of a specific characteristic when compared to another. It is best to use the same object or very similar objects for these so attention is on the aspect being compared and not on the specific items. Instructional strategies: 1. Use toothpicks to demonstrate the use of =,>, and < with pictures or items. Provide 2 toothpicks and 2 pictures for each math statement. Ask the student to make the toothpicks show the relationship of the 2 pictures. Place the toothpicks horizontal and parallel between the 2 pictures. Ask the student show greater than or less than by squeezing the ends together to form a point in the direction of the smaller quantity or to show equal to by leaving them alone.

2 2. Convert number expressions into sentences using different characteristics and the ending er. Chart words and phrases that represent equal, less, and more. Characteristic: equal Less than More than weight weight the same lighter than heavier than height are the same height shorter than taller than Using the same pictures as in the toothpick activity, create sentences that express the relationship. 1. There are as many birds as there are chairs. 1. The number of birds and chairs is the same. 2. There are fewer flowers in the first picture than in the second picture. 2. The first number of flowers is less. The symbols can also represent a request to solve a problem as when used in an equation. In the equation 12 x = 4, the equal symbol is asking for a value of X that will make the statement true. In this example, there is only one possible answer to solve the equation ( X=8 ). The symbols of comparison (< and >) can be used to solve a problem as in X + 7 < 10. There may be more than one answer. The emphasis is on whether the solution for x is correct or incorrect. The use of these symbols is especially important in solving word problems. It is essential to establish the comparison, or What is equal? as the first step in order to set up the equation. The symbol becomes the midpoint or fulcrum of the equation in which the sides must balance in order to be correct. Instructional strategies: 1. Create equations using objects and a visual map of the formula. + = 4 x 10 Use a Venn diagram to illustrate the equation. Have the student solve for x by drawing in the correct number of objects or write the number in the circle. 2. For older students emphasis the importance of these symbols in identifying properties by having them fill in the correct symbols. For example, the Transitive Property of Equality the Associative Property of Multiplication X O 6 and 6 O Y, thus X O Y 4(3X) O 12X The symbol = can also represent a definition. In algebra, a function can be defined as f(x) = x 2 + 4x 4. In geometry, the equal symbol can define specific points on a graph such as A = (1, 5) while B = (-3, 7). This corresponds to the language statement If ---, then ---- or the use of are to describe characteristics and qualities within a comparison. For example, If all birds have 2 feet, then a seagull has 2 feet.

3 Daily Weather Report Use weather information from the newspaper or internet to complete the weather chart. Compare the days using =, >, and <. Write a weather report. ************************************************************************************************************************************* Example: Day of the week Next day =, >, or < Language Weather fact: Monday s Tuesday s High temperature > higher than yesterday Low temperature > higher than yesterday Chance of precipitation (%) 60% 60% = the same Amount of precipitation 0.05 inches 0.00 inches < less than Amount of sun 70% 50% < less than Amount of clouds 30% 50% < more than Wind speed 12 miles per hour 15 miles per hour > greater than, increase UV index 9 9 = the same Weather report: Tuesday s weather was similar to Monday s. The high and low temperatures were slightly higher. There was less sun and more clouds on Tuesday. The chance of precipitation remained the same while the wind speeds increased slightly. The UV index remained high. ************************************************************************************************************************************* Weather Report Chart Weather fact: High temperature Low temperature Chance of precipitation Amount of precipitation Amount of sun Amount of clouds Wind speed UV index Day 1 Next day =, >, or < language Weather report - Based on the report, what outside activities can you do?

4 Compared to What? Using < and > to compare each item, then arrange from least to greatest. Example: length - airplane, car, bus airplane > car, airplane > bus car < bus car < bus < airplane 1. size elephant, mouse, lion elephant ( ) mouse, elephant ( ) lion, mouse ( ) lion 2. size chair, bed, foot stool chair ( ) bed, chair ( ) foot stool, bed ( ) footstool 3. length car, bus, tractor trailer car ( ) bus, car ( ) tractor trailer, bus ( ) tractor trailer 4. length dolphin, whale, seal dolphin ( ) whale, dolphin ( ) seal, whale ( ) seal 5. weight watermelon, apple, cherry watermelon ( ) apple, watermelon ( ) cherry, apple ( ) cherry 6. weight stone, pebble, boulder stone ( ) pebble, stone ( ) boulder, pebble ( ) boulder 7. height 2 story house, tent, skyscraper, cabin, castle < < 8. size basketball, golf ball, tennis ball, soccer ball, beach ball < < 9. length tortoise, snake, alligator, lizard, sea turtle < < 10. size stove, refrigerator, microwave oven, dishwasher, toaster < <

5 Word Problems Use <, >, or = to create the equations. equation 1. Mary and Tom each have a bike. Mary rode the same as Tom. Mary ( = ) Tom 1 = 1 2. Mary rode five miles on her bike. Tom rode ten miles on his bike. Mary rode less than Tom. Mary ( ) Tom ( ) 3. Mary has a bag of 20 potato chips. Tom has a handful of 15 chips. Mary has more than Tom. Mary ( ) Tom ( ) 4. Mary rode her bike seven days this week. Tom rode his everyday this week. Mary rode Tom. Mary ( ) Tom ( ) 5. John and Sue like to play archery. John shot seven bullseyes while Sue shot five. John shot ( ) Sue shot ( ) 6. Josh practiced for the Frisbee tournament. On Monday, he threw the Frisbee 35 feet. On Tuesday, he threw it 50 feet. On Wednesday, it rained and he did not practice. On Thursday, he threw the Frisbee 45 feet. Mon. ( ) Tues. Mon. ( ) Wed. Mon. ( ) Thurs. Tues. ( ) Wed. Tues. ( ) Thurs. > > > 7. Bob is learning to scuba dive. His first dive was to 10 feet below the surface. On his second dive, he dove 20 feet. On his third dive, he dove with his friend, Jo. They dove 30 feet. 1 st dive ( ) 2 nd dive 1 st dive ( ) 3 rd dive 2 nd dive ( ) 3 rd dive ( ) ( ) ( ) Bob s dive ( ) Jo s dive ( ) 8. The West High School basketball played the East High School team for the conference championship. In the first half of the game, West scored 35 points including 5 three point plays. East scored 35 points with 7 three point plays. The cheerleaders performed during halftime. In the second half, East pulled ahead and won with 64 to 60. 1st half - West ( ) East 2 nd half - West ( ) East ( ) ( )