Problem No. 26. Kate and her candies

A good packing plan is difficult to make.

Kate has some number of candies. If she puts the same number of candies in each of her 7 bags, two candies will be left. If she adds one more bag and still try to put the same number of candies in each bag, seven candies will be left. We know that Kate has less then 30 candies. How many candies does Kate have?

Parent tip

Since the total number of candies is less then 30, you can try to solve a problem with real candies. Try to divide the candies in equal sized groups according to the problem's conditions.

Problem No. 25. Reading skills

Reading is the way to improve your reading skills!

To improve his reading skills, Scott reads a half and a sentence more from what he read the day before. How many sentences he has read in 7 days, if he read 30 sentences on the first day?

Student tip

Solve partially i.e. find how many sentences he read each day.

Problem No. 23. 7 families and a river

A river crossing problem!

7 families with a mother, a father and a daughter each, come to a river they need to cross. There is only one boat for two persons. Only fathers know how to sail the boat. A daughter can be alone only with one of her parents. How can these 7 families cross the river under these conditions? How many times will the river be crossed, less or more than 30?

Parent tip

Explore different combinations and have a good time drawing, sketching, writing the solution. You can even make a paper models for each member of the story and solve the problem through play.

Problem No. 20 A cup of water

"Please give me a cup of water!"

You have a 7 cup bottle and a 30 cup bottle. How can you measure one cup of water?

Parent tip

You can make your own 7 cup and 30 cup bottles. Take two bottles, measure the wanted amount of water and mark the bottles, very carefully, at their maximal levels, the first one as the 7 cup bottle, and the other one as the 30 cup bottle. Then you can all have fun, you and your children, with pouring the water in and out of the bottles.

Problem No. 18. Min-max sum

What is the minimum and what is the maximum sum of 7 numbers which product is equal to 30?

Teacher tip

Suitable for exercising the factorization of numbers.

Problem No. 16. Points on a plane

7 different colors are used for coloring 30 points on a plane. Prove that, regardless the way you color them, there will always be at least five points colored in the same color.

Parent tip

You can enjoy a fun family time with your children coloring the points in different colors and different ways.

Problem No. 14. Two sisters

There have been two sisters. When the older sister was asked about their age, she said: "We had 730 months in total, 7 years and 30 months ago. Also, you have to know that I am 7 years and 30 months older than my sister." How old is each of the sisters?

Student tip

First find their age, 7 years and 30 months ago.

Problem No. 13. Sequence of numbers

Continue the following number sequence:

7, 3, 0, 3, 3, 6, 9, 5, …

Parent tip

Children love finding solutions together with their parents. Pretend that it is a difficult problem.

Problem No. 10. Socks in a drawer

You have 7 pairs of black socks in your drawer, among 30 pairs in total. The rest of them are white socks. What is the smallest number of socks you should take out from the drawer (with your eyes closed) to be sure that you have a matching pair of white socks?

Parent tip

You can give this problem during the house chores. It is the fun way to implement the mathematical thinking outside the classroom. Children should know that math is real, fun and useful.

Problem No. 4. Airplane fly

The travel by plane from Paris,France to New York City, USA, takes about 8 hours. If a passenger starts his journey from Paris at 7.30 pm local time, when is he supposed to arrive at New York City, local time?

Teacher tip

Problems with an extra-mathematical knowledge are suitable to demonstrate the application of math and its interdisciplinary character. Here, the students should be familiar with or should first learn about time zones.

Problem No. 2. Book

Ann usually has the following problem at 7.30 in the mornings: She wakes up and wants to continue reading the book that she had read the night before, but the lamp she uses for reading has depleted batteries and she does have neither spare batteries nor another lamp nearby. But, she always manages to solve the problem very quickly, without leaving either the room or the bed, and continues to read the book. How does she do it?

Parent tip

Suitable for family time, especially with younger children to exercise their listening skills.

Problem No. 1. Digital Clock

It is 7.30 now. How long should we wait until the digital clock uses the same digits to display the time?

Teacher tip

Good recreational problem for a "warm up" activity at the beginning of the class.