The variable
The variable
Sometimes we don’t know a certain number, or it changes from case to case. Then we write a letter in its place – , , or any other letter. A letter that stands for a number is called a variable.
A box holds 12 pencils. 2 boxes hold pencils, and 5 boxes hold pencils. And any number of boxes? If the number of boxes is , they hold pencils, written for short as .
We build a row of squares out of matches, each square next to the one before. These are the first three stages:
The first square takes 4 matches, and every further square adds 3 matches: 4, 7, 10, … You can think of it like this: one match stands at the end, and every square adds 3 more. So squares take matches.
How many matches do 20 squares take? Substitute in the expression : . Writing a number in place of the variable is called substitution.
How many matches do 10 squares take?
And 100 squares? Calculate.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
We build a row of triangles out of matches, each triangle sharing a side with the one before: one triangle takes 3 matches, two triangles take 5, and three triangles take 7.
Draw the fourth stage: how many matches does it have?
Write an expression for the number of matches in triangles.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Substitute in the expression you found, and calculate how many matches 15 triangles take.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Calculate the value of the expression : a. for ; b. for ; c. for .
Start with the substitution.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power