1 Dot: Can you make 6 out of either 6 and 11 or 3 and 9?
2 Dots: Can you make 8 out of either 9/14/12 or 5/2/1?
3 Dots: Can you make 24 out of either 5/17/14 or 18/3/9?
1 Dot: How can you make 24 using 9, 1, 8, and 6?
2Dots: How can you make 24 using 2, 7, 7, and 5?
3 Dots: How can you make 24 using 2, 9, 4, and 7?
Comment on this post telling us how you made the target number using all of the numbers once and only once.
1) If a class of children is separated into groups of 5 children, 2 children will be left over. If the class is separated into groups of 6 children, 3 children will be left over. What is the smallest number of children the class could have?
2) There is an even number between 200 and 300 that is divisible by 5 and also by 9. What is the number?
3) A book has 500 pages numbered 1, 2, 3, and so on. How many times does the digit 1 appear in the page numbers?
1) Method 1 –
must be an odd number. Then the only possibilities for the class size are: 7, 17, 27, 37, . . Divide each by
6. The first number that has a remainder of 3 is the required number. That number is 27.
Method 3 - Algebra: Let A and B be numbers such that 5A + 2 = 6B + 3. Subtract 2 from each member of
the equation. Then 5A = 6B + 1. Since 6B + 1 is an odd number, 5A is also odd. 5A may be 5, 15, 25, 35,
45, . . . Divide each of these numbers by 6. The first number that has a remainder of 1 is 25: 25/6 = 4 R1. So B = 4. Since 6B + 3 is the class size, and B = 4, the class size is 6 x 4 + 3 = 2.
2) Since the number is divisible by 2, 5, and 9, it is also divisible by the product 2 x 5 x 9 = 90. The multiple of 90 between 200 and 300 is 270.
3) Consider the frequency of appearance of the digit "1" in each of the places.
1) Suppose today is Tuesday. What day of the week will it be 100 days from now?
2) The four-digit numeral 3AA1 is divisible by 9. What does A represent?
3) A purse contains 4 pennies, 2 nickels, 1 dime, and 1 quarter. Different values can be obtained by using one or more coins in the same purse. How many different values can be obtained?
1) Every 7 days from "today" will be Tuesday. Since 98 is a multiple of 7, the 98th day from today will be Tuesday. Then the 100th day from today will be Thursday.
2) If the number is divisible by 9, then the sum of its digits is divisible by 9. The digit sum is 3 + A + A + 1 = 4 + 2A. The digit sum cannot by 9, otherwise A = 2 1/2. So 4 + 2A = 18 which produces A = 7.
3) The largest amount that can be made is $0.49. Using the given set of coins, any amount from $0.01 to $0.49 can be made. Therefore there are 49 different amounts that can be made.
We got a whole lot accomplished in August. All grade levels learned the routines and procedures of Math Lab. All grade levels have done some sort of problem solving. All grades except for kindergarten have been introduced and have started using Bar Model Drawing for problem solving which is a 7 step method we have adopted from Singapore. Grades 3rd-5th have been introduced to and have started using a graphic organizer that helps them write a constructed response in math. Kindergarten and 1st graders have been busy moving to music as they practice math skills.
Thanks to the generosity of the parents and foundation, we have been able to play several games in Math Lab including What's My Number, 24 Game, and Figuro. We also have a new rug in the math lab thanks to the PMES Foundation.
Now that we have had time to get everything in place, we can really dig in deep to Mental Math strategies. Here are the strategies we are currently working on:
Kindergarten: Subitizing- the skill of being able to determine how many of something without having to count each individual item
First Grade: Modeling numbers in a variety of ways
Second Grade: Counting on when adding 1-4 to a given number (first addend will vary depending on individual needs)
Third Grade: Counting back on a chart when taking away 1-4 (Subtrahend will vary depending on level of individual students)
Fourth Grade: Using 10 facts when multiplying by 5 (Examples from 3 different levels: 4X10=40 so I know 4X5=20, 20X10=200 so I know 20X5=100, 246X10=2,460 so I know 246X5=1,230)
Fifth Grade: Using 10 facts when dividing by 5 (Examples from 3 different levels: 20/10=2 so 20/5=4, 160/10=16 so 160/5=32, 3,200/10=320 so 3,200/5=640)
Follow @amandalovett on Twitter to see pictures from Math Lab each week.