1. Math Strategies “Did you try it this way?” Mrs. Fischer’s Academic Support

2. Multi-step Problems You may need to use more than one operation to solve some problems. These are called multiple-step problems. The blacksmith could forge 6 swords in two days. How many swords could he forge in 9 days?  First, divide 2 into 6 swords to see how many swords he could make in one day.  6  2 = 3  Then multiply your answer by 9 to see how many swords he could make in 9 days.  3 x 9 = 27

3. Extra Information  Sometimes a problem has extra information that you do not need to solve the problem.  At the tavern, Ralph bought a mug of mead for 1 shilling, bread for 2 shillings, meat for 2 shillings, and a souvenir for his children 5 shillings. How much did Ralph spend on food?  First, find the information you need to solve the problem. Some information is extra. The extra information is:  Ralph bought a souvenir toy for his children for 5 shillings.  I'll solve the problem using only the information I need.  1 + 2 + 2 = 5  Ralph spent 5 shillings on food.

4. Logical Reasoning – Use of Venn Diagrams To solve some problems a helpful strategy is LOGICAL REASONING. The Canterbury Dance Festival presented dances from many different countries. 32 children joined in the dances. 19 danced the Welsh Dance and 15 danced the Scottish Dance. How many children danced in both dances? I'll draw a Venn diagram. I'll put 19 counters inside the Welsh circle. I'll put 15 counters inside the Scottish circle. To do this with only 32 counters, I must place 2 counters so that they are inside both circles. 2 children danced both dances.

5. Problems with More than One Answer Some problems have more than one answer. When you find an answer to a problem, don't stop there. Ask yourself if there might be other answers. The villagers were building a bridge. While working under the bridge Rodney could see only the legs of those walking by. He counted 10 legs in one group. What combination of sheep and children could have been in that group? PeopleLegsSheepLegsTotal 122810 ok 242812 not ok 361410 ok 481412 not ok 3 people and 2 sheep. 6Try legs + 8 legs = 14 legs I can use guess and check. That's too many legs. Try 3 people and 1 sheep 6 legs + 4 legs = 10 legs Correct! Rodney saw 10 legs. I can check for other answers. I'll organize my work in a table. There are two possible answers: 1 person and 2 sheep, or 3 people and 1 sheep

6. Deciding When to Estimate In some problems you only need an answer that is close to correct. You can estimate. In other cases, you need an exact answer. Decide which method to use by what you are going to do with the answer. 1. Gerald is on duty in the watchtower. It is 10:37 PM. He wants to stop at an inn on the way home. At what time shall he tell his friends he will arrive at the inn? Gerald does not need to arrive at the inn at an exact time. He can estimate the time needed. 2. Joan is practicing for a rowing competition. She wants to know how much greater her trial time is than the course record time of 23 minutes, 9 seconds. Joan needs to know exactly how many seconds faster she must go to beat the record. Joan needs to know her exact trial time.

7. Data from a Chart To solve some problems, you need to sort through numbers in a chart to find the data you need. How much taller is the tallest knight than the shortest knight? Knight Statistics I'll find the data in the chart. Hector is 5 ' 4" tall. Galahad is 4' 11" tall. Now I’ll solve the problem 5' 4" = 64" 4' 11" = 59" 64 - 59 = 5 Hector is 5" is taller than Galahad. NameHeightWeight Galahad4' 11"110 pounds Gawain5' 1"103 pounds Lancelot5' 3"107 pounds Hector5' 4"118 pounds

8. Work Backwards To solve some problems, you may need to undo the key actions in the problem. This strategy is called Work Backward. The castle kitchen servants brought in 4 pies left over from the feast. 12 pies were eaten at the feast. Queen Mab took 2 home with her. How many pies did the servants bring into the feast at the beginning? First, I'll account for all the pies that were eaten or taken home. 12 + 2 = 14 Then I'll add the 4 pies that were left over. 14 + 4 + 18 Therefore, there must have been 18 pies at the start of the feast.

9. Guess and Check Some problems cannot be solved directly. You need to use a strategy called Guess and Check. Prince Carl divided 15 stone games into two piles: games he owns and games his brother owns. He owns 3 more games than his brother. How many games does his brother own?  I'll guess his brother owns 8 games.  That means Prince Carl owns 11 games. That's a total of 19 games.  My guess is too high.  I'll guess again. This time I'll guess his brother owns 6 games.  That means Prince Carl owns 9 games. That's a total of 15 games.  My guess is right.  His brother owns 6 games.

10. Look for a Pattern Some problems can be solved by recognizing a pattern. Make a table to help you. Daniel arranged loaves of bread on 6 shelves in the bakery. He put 1 loaf on the top shelf, 3 loaves on the second shelf, and 5 loaves on the third shelf. If he continues this pattern, how many loaves did Daniel put on the 6th shelf?  I'll make a table and look for a pattern.  I see the pattern. There are 2 more loaves on each shelf. I've completed the table to shelf 6.  Daniel put 11 loaves on shelf 6. Shelf123456 Loaves1357911

11. Draw a Picture Draw a picture to help you solve some problems. Four pages were in line. Daniel was behind Timothy. James was between Daniel and Timothy. Daniel was in front of Colin. A mud puddle was near the page who was in the back of the line. Who was in the back of the line?  First, I'll draw the line.  Daniel is in back of Timothy.  James is between Daniel and Timothy.  Colin is behind Daniel.  Colin is in the back of the line!

12. Remember…

13. Need more resources…  Solving Math Problems Solving Math Problems  Examples of Math Strategies Examples of Math Strategies