Square and triangular numbers | nzmaths
This explains why the difference between integer squares is always an odd number, and the interval to the next square is the next odd number!. Children can experiment with pennies (or square tiles) to see what numbers of them This connection between square numbers and triangular numbers can be . The name square number comes from the name of the shape; see below. This is also equal to the sum of the first n odd numbers as can be.
A more formal definition: A square number is a number of the form or n2where n is any whole number. Mathematical background Objects arranged in a square array The name "square number" comes from the fact that these particular numbers of objects can be arranged to fill a perfect square.
Children can experiment with pennies or square tiles to see what numbers of them can be arranged in a perfectly square array.
- Fun Activities to Teach Even and Odd Numbers in Grades K through 2
- Surprising Patterns in the Square Numbers (1, 4, 9, 16…)
- Square and triangular numbers
And sixteen pennies can, too: But seven pennies or twelve pennies cannot be arranged that way. Numbers of objects that can be arranged into a square array are called "square numbers. Square arrays must be "full" if we are to count the number as a "square number.
The number 12 is not a square number. Children may enjoy exploring what numbers of pennies can be arranged into an open square like this. They are not called "square numbers" but do follow an interesting pattern. Squares made of square tiles are also fun to make. Again, the number of square tiles that fit into a square array is a "square number.
Connections with triangular numbers If you count the green triangles in each of these designs, the sequence of numbers you see is: If you count the white triangles that are in the "spaces" between the green ones, the sequence of numbers starts with 0 because the first design has no gaps and then continues: Remarkably, if you count all the tiny triangles in each design -- both the green and the white -- the numbers are square numbers!
This connection between square numbers and triangular numbers can be seen another way, too.
On each section of the pizza print a number. Give each child a small container of gummy worms.
Surprising Patterns in the Square Numbers (1, 4, 9, 16…) – BetterExplained
Ask them to make up their own "Worm Pizza" by placing worms to match the number in each section, and then print the word "odd" or "even" in that section. For every correct response — eat the worms! Teams Against the Clock Divide the class into two teams. Give each member of the team two pieces of paper — one for odd numbers and one for even numbers.
Set a kitchen timer for one minute and ask students to write down as many numbers as possible on the correct papers. The team with the most numbers that are correct wins.Even and Odd Numbers - 1st Grade and 2nd Grade Math Lessons
Repeat with just thirty seconds on the clock. Everyday Odds and Evens Use the attendance numbers each day to discover whether there are an odd or even number of students in class. Print the date on the board and under each number print "o" if it is an odd number or "e" if it is an even number. Compare a whole week of dates. Is there a pattern?
Number Differences : index-art.info
Patterns in the Odds and Evens Provide individual hundreds charts and ask students to color all the even numbers red. What pattern do you see? What do you notice about every number in the ones place 0,2,4,6,8 Look at the pattern made by the numbers not colored odd numbers. What do you notice about the numbers in the ones place? Are they the same length? Repeat with another handful. Present the students with simple addition equations.