Intermediate Math Methods - In Class Final Review

Teaching through problem solving provides opportunities for all students to become mathematically proficient. 

Teaching through problem solving benefits all students in what way?

• Focusing on technology that will guide students to solutions.

• Focusing on procedures to find correct answers.

• Focusing on ideas and sense making.

• Focusing on the single strategy that will most effectively produce the answer.

A math teacher allows students to submit their answers to the weekly math challenge problem in any of the following ways:

a video recording of responses

written explanation of responses

picture of solution with labels

What aspect of instruction is this teacher differentiating?

• Content

• Environment

• Process

• Product

A student explains how they solved the problem 35+28 by saying:

• First, I thought about the number 28 as the number 30

• Then, I added 35+30 to get 65

• Since I added 2 at the beginning, I had to subtract this extra 2, so 65-2=63

What invented strategy is this student using?

• Add tens, add ones, then combine

• Add on tens, then add on ones

• Move some to make a ten

• Use a nice number and compensate

A 5th grade teacher is planning a lesson to meet the standard CC.2.4.5.A.1: Solve problems using conversions within a given measurement system.

Which of the following instructional activities is best aligned with this PA Core Math Standard?

• Students will measure their height in inches and then convert this measurement to feet.

• Students will measure their height in centimeters at the beginning and the end of the school year, and then identify how many centimeters they grew.

• Students will measure their height in inches and compare it to their classmates.

• Students will measure their height in centimeters and compare it to their height in inches.

The fraction 1/10 is considered to be which of the following types of fractions? (Select all that apply.)

• Unit fraction

• Decimal fraction

• Benchmark fraction

• Improper fraction

While students are working with fraction tiles, one third grader is counting out loud: "one-fourth, two-fourths, three-fourths, four-fourths."

What fractional concept is this student demonstrating?

• Partitioning

• Factoring

• Iterating

• Benchmarks

Which of the following fraction manipulatives is classified as a LENGTH model for fractions?

• Pattern Blocks

• Two Color Counters

• Fraction Strips

• Fraction Circles

A student solves the problem 2/3 + 1/4 = 3/7. 

What is the most appropriate instructional response from the teacher, to help the student understand the concept of adding fractions?

• "Great job...you are correct!"

• "You need to find a common denominator first...try 12."

• "Adding fractions is different than adding whole numbers - try again."

• "Show me how you solved this problem with your fraction strips."

A teacher demonstrates how folding paper can be used to understand multiplication with fractions.

What fraction multiplication problem is being shown with this model, which represents a piece of paper that has been folded?

• 1/3 x 1/5

• 1/3 x 3/5

• 2/3 x 1/5

• 2/3 x 3/5

A fourth grader solves the following decimal comparison problem:

0.375 > 0.97

What would be the most appropriate response to this student's answer?

• Great job...you are correct!

• Remember that decimals are different than whole numbers.

• Show me these two decimals with base ten blocks.

• Use the calculator to check if this is correct.