Algebra Solving Problems without The Help of An Algorithm Questions

I. Mental Math

Please work on the following problems mentally and think about strategies on how you can solve these problems WITHOUT the help of an algorithm. Think about the distributive property of multiplication over addition and grouping.

a. 22 x 35 =

b. 112 x 47 =

c. 114 ÷ 6 =

d. 180 ÷ 12 =

II. Place value and number sense

Students have quite often a very limited understanding of numbers, their relationships, or place value. The result is that they are only able to solve problems with the help of algorithms, but not by thinking about the numbers/problems. That’s a skill students need to practice form the beginning, by talking about numbers, their relationships, or different strategies of problem-solving.

Look at the following problems for not more than 20 seconds and then give the correct answer. Please explain how you solved the problem

Please give the correct answer: 4003 + 5996 =

a. 9001

b. 9999

c. 11009

Please give the correct answer: 6997 + 7981 =

a) 13978

b) 14978

c) 15978

Please give the correct answer: 10001 – 9995 =

a. 1000

b. 100

c. 6

Please give the correct answer: 13999 – 7003 =

a. 5996

b. 6996

c. 7996