Counting Stick: What is it? A 1-metre long stick divided into ten sections, each 10 cms long. What can it be used for and with what classes? The stick can be used for a variety of number activities and in all classes from infants to sixth class. Infants: Name the first mark at one end 0 and the last mark at the other end 10. Start from 0, moving along the stick a division at a time and ask which number would go at different marks. Count forwards and backwards. Point to random divisions and ask the children to identify the missing number. Start counting forwards. While counting skip a number (counting stick hiccups!). Elicit from the children what number you landed on. Hold the stick in the centre to show the position five. Ask children to count on or back to find the positions of other specified numbers. First and Second Class: The value of the step between each division could be changed, instead of incrementing by one, the teacher could once again establish the position of 0, but call the first division 2, then 4, and so on. Similarly, the increments could be 5, 10, 3, and so on. It is important that the children go forward and backwards, in other words, skip-count up and down. As above but counting in tens, naming one end of the stick 0 and the 100. Point to random divisions and ask which ten number goes there. Again, keeping the start point/ value of 0, the increment could now be, for example, ½ - 0 ½ 1 1 ½ Name one end of the stick 0 and the other end 1. Count in ten cents - ask where 5 cent would be. Estimate where other amounts will be 25c, 50c, 75c and so on. Third and Fourth Class: Count forwards and backwards using patterns of 3, 4, 7, and so on. Point at random divisions and ask which number would go there on 0 1000 Name one end of the stick 0 and the other end 30. Point to the first division, ask what it is. Ask 'how do you know?' If wrong answer count through to check. Point to eighth division, ask what it is. Ask how do you know? Ask how many threes there are in 24? Ask what is 24 divided by 8? Repeat for other divisions. Using a 0 to 50 stick estimate where 10, 25, 40 will be. Name one end of the stick 0 and the other end 1 kilometre. Count on in intervals of 100m. Ask for random divisions. Ask where 250m, 750m will be. Estimate others. Fifth and Sixth Class As above but call the end of the stick 0 and the other one tenth and count in hundredths. When children are confident with 0 to 1 counting in 0.1 intervals, name one end of the stick zero and the other end 2. Ask what the first division will be. Check answers by counting through. Ask what the middle will be. Count forwards and backwards in steps of 0.2. Identify the positions of 0.3, 0.7, 1.9, etc. Repeat for a zero to 4 stick. Count forwards and backwards in steps of 0.4. Ask Where will 1 be on this stick?, Where will 3 be?.
Target boards: are a collection of numbers. Children are asked to consider different mathematical relationships between the numbers on the board. They can be used with whole class, groups or pupils or individuals. Pupils should be asked to demonstrate and explain their methods, be given time to think before answering and explore reasons for wrong answers. Target Board 1: Juniors Language: add, addition, plus, subtract, subtraction, sum, total, altogether, how many more to make, less, how many less is... than.., take, take away, difference between, minus, equals Ask questions to reinforce language Find the two smallest numbers and add them together. What is the biggest number on the board? What is the biggest number take away the smallest number? What is the sum of the first column? Tell me two numbers that add together to make six Add up the 3 rd column. How many more to make 20? Tell me two numbers that you can take away to leave two. Activity: Mystery Number Teacher selects a number on the target board. Give 2/3 clues to enable pupils to identify the number using some of the target vocabulary e.g. Mystery no. is 5. Clues: My number is smaller than 7 and one more than four. What is my mystery number? Activity: Target Number I want you to get from 4 (on the target board) to 12 (written on whiteboard) in 1/2 steps. 4 2 6 3 10 5 0 7 1 8 9 11 Target Board 3: Seniors Language: odd/even, prime/composite, factor/multiple, 1-digit/2-digit, sum, difference, product, half/quarter, more/less than, between, double/half, the same number as, as many as, equal to, square no./ rectangular no. /triangular no, quotient, divisible by, value Activity: Mystery Number Teacher selects a number on the target board. Give 4 clues to enable pupils to identify the number using some of the target vocabulary e.g. Mystery no. is 24 Clues: It is a 2-digit no. It is between 16 and 46
The sum of its digits is 6 Now in pairs give one another clues to a mystery number. Ask a variety of questions to reinforce Maths language: 1. What is the difference between the largest and smallest numbers on the board? 50-2 Answer = 48 2. What is the total if you add the first column? 16+6+12+4 Answer = 38 3. Find the 4 th number on the second row. (28) What number on the board is a quarter of this number? Answer = 7 4. Look at the second row. Read the numbers to me in order of size staring with the largest. Answer = 50, 30, 28, 18, 6 5. Name all the multiples of 4 on the board. Answer = 4, 12, 16, 24, 28, 36, 40 6. Tell me 2 numbers that have a difference of 4. Multiple answers 7. Tell me two numbers that have a product of 30. Answer = 6, 5 8. What 2 numbers when added together make 42. Multiple answers 9. Find the number in the 3 rd row and 4 th column. (2) What is 10 more than this number? Answer = 12 10. Find me 2 numbers where 1 is half of the other. Multiple answers I want you to get from 27 to 36 in 2 steps, using only 2 operations and numbers on the board. Ask in pairs to make up their own. 16 9 24 7 11 6 18 50 28 30 12 36 5 2 14 4 45 10 40 27 MathStories.com TM Website, using stories as basis for problems. While there is a charge for this website, there is a sample of the three little pigs to view on the website or you could use this to make up your own stories. Older pupils could also make up appropriate stories to be used in the junior classes Jack and the Beanstalk: Juniors Name: Date 1. Jack sold the cow for 5.00. He spent 4.00 on beans. How much did he have left?
2. The beanstalk began to grow. It grew 2 metres an hour. How many metres did it grow in 5 hours? 3. Jack climbed the beanstalk. He counted the leaves as he climbed. He counted by fives. Fill in the missing numbers. 5, 10, 15, 20,, 30, 35,, 45,,, 60 4. It took Jack 2 hours to climb the beanstalk. He started climbing at 11:00 a.m. What time did he get to the top? 5. The giant was 4 metres tall! How many centimetres is that? 6. The giant ate an odd number of eggs for breakfast. He ate more than eight, but less than a dozen. The number has two digits. How many eggs did he eat? 7. Jack found some gold pieces. Each piece had 4 sides. The sides were all the same length. What shape were the pieces of gold? 8. Jack climbed down the beanstalk. He counted backwards as he climbed. What are the missing numbers? 22,, 20, 19,,, 16,, 14,, 12, 9. Jack used some of the gold to buy a new bike. His mother bought him a helmet for 5.50 and a horn for 3.00. How much did his mother spend? Jack's mother was so happy! She let Jack have a pizza party. Three friends will come. Today is Tuesday, October 5th. The party will be on Friday. What will be the date of the party? Answers for Jack and the Beanstalk 1) 1 2) 10 metres 3) 25, 40, 50, 55 4) 1 p.m. 5) 400 centimetres 6) 11 eggs 7) square 8) 21, 18, 17, 15, 13, 11 9) 8.50 10) October 8th Jack and the Beanstalk: Seniors Name: Date 1. Jack sold the cow for 437.00. He spent 57.00 on beans. How much did he have left? 2. The beanstalk began to grow. It grew 2.5 metres an hour. How many metres did it grow in 5.5 hours? 3. Jack climbed the beanstalk. He counted the leaves as he climbed. He counted by
sevens. Fill in the missing numbers. 7, 14, _, 28, 35, _, 49, _ 4. It took Jack 2 and a quarter hours to climb the beanstalk. He started climbing at 11:35 a.m. What time did he get to the top? 5. The giant was 4 and 3 quarters metres tall! How many centimetres is that? 6. The giant ate an odd number of eggs for breakfast. He ate more than eight, but less than a dozen. The number has two digits. How many eggs did he eat? 7. Jack found some gold pieces. Each piece had 5 sides. The sides were all the same length. What shape were the pieces of gold? 8. Jack climbed down the beanstalk. He counted backwards as he climbed. What are the missing numbers? 1003, 1002, _, 1000, _, 998 9. Jack used some of the gold to buy a new bike. His mother bought him a helmet for 5.95 and a horn for 2.60. How much did his mother spend? Jack's mother was so happy! She let Jack have a pizza party. Three friends will come. Today is Tuesday, October 5th. The party will be on Friday. What will be the date of the party? Listening Activities Examples: (1) A series of calculations. Juniors: Starting with the number 3 (on blackboard), add 3, take away 1 and double the number Starting today s date (e.g. 6 th ), add the number of sides a square has, less the number of sides a triangle has Seniors Starting with the number 5, multiply it by 5, round it to the nearest 10, and add the digits of the answer. What do you get? (3) Starting with the smallest prime number between 15 and 20, double it and add 13. What do you get? (47)
(2)Oral word problems Display four signs of operations around the classroom or give each child the four signs each. Call out a word problem and the child is asked to indicate what operation he/she would use to solve the problem. He/she must explain to class how he/she would use the operation. We will then brainstorm for more words that apply to the four signs. Juniors: (+ -) 3 people were at my party. Five more came late. How many altogether were at my party? The teacher collected 18 copies. She corrected 8 copies. How many had she left to correct? Seniors: (4 operations) e.g. Mrs Jones has a small bookshelf in her room. There are 369 books in the library. Mrs Jones put 24 large books on the bottom shelf and she puts the other books on the top above. How many books are on the top shelf? It costs 3 per day to keep a dog in the ISPCA shelter. If there are 14 dogs in the shelter, what is the weekly maintenance bill? 367 girls and 320 boys attended Summer Camp in July. 247 girls and 413 boys attended in August. How many girls attended that summer? 367 girls and 320 boys attended Summer Camp in July. 1/3 (one third) of the children went sailing. How many went sailing? (2) Oral riddles I am a day of the week. I come right after and right before days that have the same number of letters in their names as each other. What day am I? (Friday Thursday and Saturday both have 8 letters) I am a number. I am the product of the number of digits in half a million and the number of years in a decade. What number am I? (6x10=60) (3) In a circle: Group of 6-7 children. Count in 2 s starting with child x, what will child Y be? Starting with child x being 15, counting clockwise in 5 s, who is 55? Start at child A and count from 37 on, in clockwise direction. If I ask child 44 to sit down, who do you think will sit down? Counting Choir This is a listening and concentration game. Divide class into 3 groups. Give each group a certain counting task. This can be differentiated. Teacher acts as a conductor of the counting choir. He/she points to a group to indicate they are to count. The other group stops. The group starts to count, based on the last number of the prior group.
e.g. Group 1 counts in 1 s, group 2 in 2 s, group 3 in 10 s or Group 1 counts backwards in 1 s, group 2 counts in 4 s and group 3 count in halves.