by Monica Yuskaitis, M.A.Ed 6th Grade Algebra 3 Solving Equations with Addition & Subtraction n + 2 = 7 by Monica Yuskaitis, M.A.Ed Copyright 2013 © by Monica Yuskaitis

Essential Question How can I simplify and solve addition and subtraction equations? Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Vocabulary 3 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Vocabulary Equation – A mathematical sentence stating that 2 expressions are equal. 12 – 3 = 9 13 = 9 + 4 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Vocabulary Equation – A mathematical sentence with an equals sign. 16 – 5 = 11 17 = 14 + 3 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Vocabulary Equals Sign (=) means that the amount is the same on both sides. 4 + 2 = 6 3 = 5 – 2 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Understanding Equations 7 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis An Equation is like a balance scale. Everything must be equal on both sides. = 5 + 5 10 Copyright 2013 © by Monica Yuskaitis

When the amounts are equal on both sides it is a true equation. = 12 6 + 6 Copyright 2013 © by Monica Yuskaitis

When the amounts are unequal on both sides it is a false equation. = 2 + 2 8 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis When an amount is unknown on one side of the equation it is an open equation. = n + 2 7 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis When you find a number for n you change the open equation to a true equation. You solve the equation. = 7 n + 2 5 Copyright 2013 © by Monica Yuskaitis

Are these equations true, false or open? 11 - 3 = 5 13 + 4 = 17 n + 4 = 7 12 – 3 = 8 3 + v = 13 15 – 6 = 9 true open false open true Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Solving Addition Equations 14 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Vocabulary Inverse operation – the opposite operation used to undo the first. 4 + 3 = 7 7 – 4 = 3 6 x 6 = 36 36 / 6 = 6 Copyright 2013 © by Monica Yuskaitis

How to solve an addition equation Use the inverse operation for addition which is subtraction m + 8 = 12 12 - 8 = 4 m = 4 4 + 8 = 12 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Think of the balance scale. If you can isolate n on 1 side you can solve the equation. = n + 2 7 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Isolate n by using the inverse operation of addition, subtraction, and subtract 2 from both sides. = n + 2 7 -2 -2 Copyright 2013 © by Monica Yuskaitis

If you have +2 and –2 what is your answer? Right 0. = n + 2 7 -2 -2 5 Copyright 2013 © by Monica Yuskaitis

Now look at your balance scale. n = 5 Copyright 2013 © by Monica Yuskaitis

Substitute 5 in to see if it works. = 7 5 n+2 Copyright 2013 © by Monica Yuskaitis

Solve these equations using the inverse operation 3 n + 4 = 7 5 + n = 1 4 n + 7 = 17 8 + n = 13 n + 7 = 15 9 + n = 17 9 10 5 8 8 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Solving Subtraction Equations 23 Copyright 2013 © by Monica Yuskaitis

How to solve a subtraction equation Use the inverse operation for subtraction which is addition m - 3 = 5 5 + 3 = m m = 8 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Think of the balance scale. If you can isolate n on 1 side you can solve the equation. = 9 n - 4 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Isolate n by using the inverse operation of subtraction, addition, and add 4 to both sides. = 9 n - 4 +4 +4 Copyright 2013 © by Monica Yuskaitis

If you have +4 and –4 what is your answer? Right 0. = 9 n - 4 +4 +4 13 Copyright 2013 © by Monica Yuskaitis

Now look at your balance scale. n = 13 Copyright 2013 © by Monica Yuskaitis

Substitute 13 in to see if it works. = 9 13 n-4 Copyright 2013 © by Monica Yuskaitis

Solve these equations using the inverse operations 16 n - 7 = 9 n – 8 = 4 n - 6 = 19 n – 8 = 13 n - 10 = 16 n – 21 = 43 12 25 21 26 64 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Find the value of n 43 + n = 59 n – 20 = 0 19 + n = 37 n - 32 = 17 87 + n = 105 n – 0 = 5 n = 16 n = 20 n = 18 n = 49 n = 18 n = 5 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Problem Solving 32 Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Raking Leaves Copyright 2013 © by Monica Yuskaitis

Analysis Representation Resolution Problem Solving Steps What information do you need? What is the problem asking you to find out? Is the answer going to be larger or smaller? Representation What strategies will you use? What operations will you use? How many steps are there and in what order must you do them? How will you solve the problem? Did you check your answer? Does your answer make sense? Resolution Copyright 2013 © by Monica Yuskaitis

Copyright 2013 © by Monica Yuskaitis Marcus had $43. He worked all day Saturday raking leaves and then had a total of $89. How much did he earn raking leaves? 43 + n = 89 -43 -43 n = $46 35 Copyright 2013 © by Monica Yuskaitis

Your parents would be so proud! Copyright 2013 © by Monica Yuskaitis