1) In the following sequence of numbers, each number has one more 1 than the preceding number: 1, 11, 111, 1111, 11111, ... What is the tens digit of the sum of the first 30 numbers of the
2) When asked how many gold coins he had, the collector said:
If I arrange them in stacks of five, none are left over.
If I arrange them in stacks of six, none are left over.
If I arrange them in stacks of seven, one is left over.
What is the least number of coins he could have?
3) In the subtraction problem below, each letter represents a digit, and different letters represent different digits. What digit does C represent?
A B A
- C A
1) The ones column of the 30 numbers contains 30 ones making a sum of 30. Thus, the ones digit of the sum is 0, carry 3. The tens column contains 29 ones. Its sum is 29 plus the 3 from the
"carry," making 32. Therefore the tens digit of the sum is 2.
2) The number of coins must be a multiple of 30. The multiples of 30 are 30, 60, 90, 120, 150, and so on. The smallest of these multiples that leaves a remainder of 1 when divided by 7 is 120.
3) It is clear that B = 0 and A = 1. Substitute those numbers for letters as shown below. Therefore C is 9.
1 0 1
- C 1
Kindergarten- We worked on breaking groups of 4 and 5 dots into 2 groups and writing the number bond to match. Students practiced counting to 120 while exercising. We also sang a song about shapes. They also solved 2 subtraction problems using pictures and acting. Our number talk was based on the number 8.
1st Grade- We worked on breaking groups of 4 and 5 into 2 groups, writing the number bond to match, along with writing an addition and subtraction problem for each. Students reviewed lesson 16 during a move it where they added or subtracted 10 or 1 from a number. Our number talk was based on the number 9 on a ten frame. We solved a word problem using the Bar Model Drawing Method.
2nd Grade- We practiced reading expanded notation using an activity where they revealed a mystery picture by coloring in the correct numbers.
3rd Grade- We practiced adding and subtracting multiples of 10 using a 120 chart in an activity where they revealed a mystery picture. We discussed that the ones place stays the same and the tens place changes.
4th & 5th Grades- We continued practicing the strategy of halving one factor while doubling the other factor. One class discovered that the same strategy works if you divide one number by 5 and multiply the other factor by 5 which lead us to see that it really works with any number.
Kindergarten- We sorted objects based on whether the represented 5, 6, 7, 8, 9, or 10 or not. We sang songs about positional words and the days of the week. We did a number talk based on the number 8.
First Grade- We did the same activity as last time, just with different numbers. In the activity they looked for patters when adding or taking away 10 and adding or taking away 1. We did a move it where we practiced adding two numbers together. We also solved a story problem together.
Second & Third Grade- We played I Have, Who Has using double facts. We also practiced writing constructed responses for the story problems we solved in the last lesson.
Fourth& Fifth Grade- We continued to practice mental math by doubling one factor and halving another factor to create problems we can solve in our head. We also worked on multi-step story problems.
Kindergarten: We worked on sorting pictures based on whether they represented a given number or not.
1st Grade: We used patterns on a 100 chart to solve problems where we added or took away 1 or 10 to a given number.
2nd/3rd Grades: We practiced telling time to the nearest 5 minutes using a Move It activity, "What does the Clock Say". We also worked on problem solving.
4th/5th Grades: We practiced telling time to the minute using a Move It activity, "What does the Clock Say". We also worked on the strategy of splitting one factor in half while doubling the other factor to help us create problems we can solve in our heads. See examples below.