PSSA-MATH-GRADE-5 // EducatorSharmin // The Pennsylvania System of School Assessment

 

PSSA-MATH-GRADE-5 

The Pennsylvania System of School Assessment

Mathematics Item and Scoring Sampler

2022–2023 

Q.1. Multiply: 372 X    108

Ans: C. 40,176

2. The 10-by-10 grid shown below represents one whole.

The decimal number q is represented by the shaded part of the grid. Which statement correctly compares the value of q with two other numbers?

Ans: B.    The value of q is greater than 0.305 and less than 0.35.
Correction: identifies 0.34 as the value of q since 34 of 100 squares are shaded, compares 0.34 to 0.305 either by comparing the digits in the tenths place and then the digits in the hundredths place.

3. Four number sentences are shown below, some of which are not true

                      436.04 = 444.03

                      236.76 = 235.84

                      505.64 ＞505.55

                     325.64  ＞ 325.54

Each number is rounded to the nearest tenth. The comparison symbol in each number sentence remains the same. Which number sentence is rounded correctly and is true?

Ans: D. The number sentence 325.64 > 325.54

               becomes   325.64 > 325.54

Correction: Rounds 325.64 down to 325.6 based on the 4 in the hundredths place, rounds 325.54 down to 325.5 based on the 4 in the hundredths place, and then compares 325.6 to 325.5 by comparing the digits in the hundreds place, then the digits in the tens place, then the digits in the ones place, and then the digits in the tenths place.

 

4. Serena has one large and one small beehive. Information about the hives and the bees living in each hive is listed below.

* There are 1,050 bees living in the large hive.

* The number of bees living in the small hive is 0.7 times the number of bees living in the large hive.

* The bees living in the small hive viist 2,500 flowers each day

* The bees living in the large hive visit 0.8 times the number of flowers visited each day by the bees living in small hive.

Which statement about the bees is true?

Ans: D. The bees living in the large hive visit 2,000 flowers each day

5. Which step should be performed first when subtracting 1/5 from 5/7?

Ans: Find a common denominator by multiplying 5 and 7.

6. Aaron's fish bowl contains 2 3/5 gallons of water. Bryan's fish bowl contains 1 7/8 gallons of water. How many more gallons of water does Aaron's fish bowl contain than Bryan's fish bowl?

Ans: C. 29/40

7. Which story matches the expression (18 - 3 X 4) ➗ 2 ?

Ans: D. Ed had $18. He bought 3 pens for $ each and then shared the rest of the money equally with his sister.

8. When finding the value of the expression 81 - (24 ➗ 3 X 2) ➗ 18, which operation should be completed first?

Ans: B. 24 ➗ 3

Correction: Recognizes that the operations inside the grouping symbols should be completed first, identifies that division and multiplication are equal in the order of operations, and performs the operations from left to right within the grouping symbols, starting with division.

9. Andrew has 3 1/2 litres of juice. For a party, he needs 1 1/2 times the amount of juice he has already. The expression shown below represents the total amount of juice, in litres, Andrew needs, but one number is missing.

                                                   (3 +1/2) (⬜➕½)

What number should go into the box so the expression represents the total amount of juice, in liters, Andrew needs?

Ans: 1

10. The first five values in a number pattern are represented by the expressions below.

      4 X 1       4 X 2        4 X 3           4 X4                      4 X 5

The pattern continues. How many values in the pattern are less than 100?

Ans: B. 24

11. Julian has 4 videos. Each video is the same length. The total time for all of the videos is 300 seconds. How many minutes long is each video?

Ans: B. 1.25 minutes

5th Grade     Math    Worksheets

Table of Contents:

Chapter-1:

Place Value

• a) Patterns with Exponents & Powers of 10
• b) Whole-Number Place Value
• c) Decimals to Thousandths
• d) Decimal Place Value
• e) Compare Decimals
• f) Round Decimals

Chapter - 2:

Add & Subtract Decimals

• a) Mental Math
• b) Estimate Sums & Differences of Decimals
• c) Use Models to Add & Subtract Decimals
• d) use strategies to add Decimals
• e) Use Strategies to Subtract Decimals
• f) Problem-solving

Chapter- 3:

Fluently multiply Multi-Digit Whole Numbers

• a) Multiply Greater Numbers by Powers of 10
• b) Estimate Products
• c) Multiply by 1 -digit Numbers
• d) Multiply 2-digit by 2-Digit Numbers
• e) Multiply 3 -Digit by 2-digit numbers
• f) Multiply Whole Numbers With Zeros
• g) Practice Multiplying Multi-Digit Numbers
• h) Solve Word Problems
• i) Critique Reasoning

Chapter- 4:

Multiply Decimals

a) Multiply Decimals by Powers of 10

b) Estimate the Product of a Decimal & a Whole

c) Use Models to Multiply a decimal & a Whole

d) Multiply a Decimal & a Whole Number

e) Multiply Decimals Using Partial Products

f) Use Properties to Multiply Decimals

g) Use Number Sense to Multiply Decimals

Chapter - 5:

Divide Whole Numbers

a) Use Patterns & Mental Math to Divide

b) Estimate Quotients with 2-Digit Divisors

c) Use Models & Properties to Divide With 2-Digit Divisors

d) Use Partial Quotients to Divide

e) Use Sharing to Divide: Two-Digit Divisors

f) Use Sharing to Divide: Greater Dividends

g) Choose a Strategy to Divide

h) Make sense & Persevere

Chapter - 6: 

Use Models & Strategies to Divide Decimals

a) Patterns for Dividing With Decimals

b) Estimate Decimal Quotients

c) Use Models to Divide by a 1-Digit Whole Number

d) Divide by a 2-Digit Whole Number

e) Divide By a Decimal

f) Reasoning

Chapter-7:

Use Equivalent fractions to Add & Subtract Fractions

a) Estimate Sums & Differences of Fractions

b) Find Common Denominators

c) Add Fractions with Unlike Denominators

d) Add & Subtract Fractions

e) Estimate Sums & Differences of Mixed Numbers

f) Use Models to Add Mixed Numbers

g) Add Mixed Numbers

h) Use Models to Subtract Mixed Numbers

i) Subtract Mixed Numbers

Place Value

Chapter-1

What is Place Value?

Place value is the value of a digit depending on its position in a number. Use a place value chart to represent numbers.

Understanding the Place Value Chart:

Each digit has a place value.

The value of a digit changes depending on its place value position in a number.

A digit in one place represents ten times what it represents in the place to its right.

a) Patterns with Exponents & Powers of 10

The exponent is the number that tells how many times a base number is used as a factor.

The number of Zeros in the product is the same as the exponent.

b) Whole-Number Place Value:

Q.1. According to the 2010 US Census, the population of Phoenix. Arizona is about 1,440,000. What is the relationship between the value of the two 4s in this number?

Solution:

Standard form:

1,440,000

Expanded form:

1 X 1,000,000 + 4 X 100,000 + 4 X 10,000

Using exponents, this can be written as:

                   * Rounding replaces one number with another number that tells about how many or                                  about how much. round 2.36 to the nearest tenth. Is 2.36 closer to 2.3 or 2.4?

      * Find the rounding place. Look at the digit to the right of the rounding place.

                      * If the digit is 5 or greater, add 1 to the rounding digit. If the digit is less than 5,                                     leave the rounding digit alone.

                                    Since  6 ＞5,

                                  Add 1 to the 3.

                                   *Drop the digits to the right of the rounding digit.

                                    2.36 rounds to 2.4

You can download the Worksheet:

file:///C:/Users/Sharmin%20Jahan/Desktop/Word-problems-key-words-educatorsharmin.pdf