Eureka Math Grade 5 Module 1 Mid Module Assessment Answer Key

Engage NY Eureka Math 5th Grade Module 1 Mid Module Assessment Answer Key

Eureka Math Grade 5 Module 1 Mid Module Assessment Task Answer Key

Question 1.
Compare using >, <, or =.
a. 0.4 0.127
Answer:- 0.4 0.127

b. 2 thousandths + 4 hundredths 0.036
Answer:- 2 thousandths + 4 hundredths 0.036

c. 2 tens 3 tenths 1 thousandth 20.31
Answer:- 2 tens 3 tenths 1 thousandth 20.31

d. 24 tenths 2.5
Answer:- 24 tenths 2.5

e. 4 × 10³ + 2 × 100 + 3 × \(\frac{1}{10}\) 4 × 1000 + 2 × 10² + 3 × \(\frac{1}{10}\)
Answer:- 4 × 10³ + 2 × 100 + 3 × \(\frac{1}{10}\) 4 × 1000 + 2 × 10² + 3 × \(\frac{1}{10}\)

f. 3 × \(\frac{1}{10}\) + 4 × \(\frac{1}{1000}\) 0.340
Answer:- 3 × \(\frac{1}{10}\) + 4 × \(\frac{1}{1000}\) 0.340

Question 2.
Model the number 8.88 on the place value chart.
Answer:-

a. Use words, numbers, and your model to explain why each of the digits has a different value. Be sure to use “ten times as large” and “one tenth as large” in your explanation.
Answer:- Even though there are 8 dicks in each column, they are different digits so they have
different values. 8 in ones place is 10 times as large as 8 in tenths place.
8 in hundredths place is 1/10 as large as 8 tenths.

b. Multiply 8.88 × 10⁴. Explain the shift of the digits and the change in the value of each digit.
Answer:-  8.88 x 10⁴ = 88800

When multiplying by 10⁴ , each digit shifts 4 places to the left. 10⁴ equals 10 x  10 x 10 x 10 or
1000, So each digit becomes 10,000 times as large.

c. Divide the product from (b) by 10². Explain the shift of the digits and the change in the value of each digit.
Answer:- 88800 ÷ 10² = 888

When dividing by 10², each digit shifts 2 places to the right, 10² equals 10 x 10 or 100, So each digit becomes 1/100 as large.

Question 3.
Rainfall collected in a rain gauge was found to be 2.3 cm when rounded to the nearest tenth of a centimeter.
a. Circle all the measurements below that could be the actual measurement of the rainfall.

Answer:-

b. Convert the rounded measurement to meters. Write an equation to show your work.
Answer:- 2.3 ÷ 10² = 0.023
2.3 cm = 0.023m

Question 4.
Average annual rainfall totals for cities in New York are listed below.

Rochester	0.97 meters
Ithaca	0.947 meters
Saratoga Springs	1.5 meters
New York City	1.268 meters

a. Put the rainfall measurements in order from least to greatest. Write the smallest total rainfall in word form and expanded form.
Answer:-  The rainfall measurements in order from least to greatest are
0.947m, 0.97m, 1.268m, 1.5m.
Nine hundred forty-seven thousandths. 9 x 1/10 + 4 x 1/100 + 7 x 1/1000

b. Round each of the rainfall totals to the nearest tenth.
Answer:-  0.97 m = 1.0m
0.947m = 0.9m
1.5m = 1.5m
1.268m = 1.3m

c. Imagine New York City’s rainfall is the same every year. How much rain would fall in 100 years?
Answer:- 1.268 m x 100 = 126.8m
126.8 m would fall in 100 years

d. Write an equation using an exponent that would express the 100-year total rainfall. Explain how the digits have shifted position and why.
Answer:- 1.268m x 10² = 126.8m.  Each digit shifts 2 places to the left when multiplying by 10². The value of each digit becomes 100 times as large.
1 x 100 = 100
0.2 x 100 = 20
0.06 x 100 = 6
0.008 x 100 = 0.8