What grade does Eureka math go to?

Eureka Math offers a full complement of Prekindergarten through Grade 12 print materials including Teacher Editions, student workbooks, and more. Spanish language editions are available for Grades K–8.

What are the four core components of a Eureka Math TEKS lesson?

Lesson Components Within every lesson, students experience the same four core components: - Fluency Practice, - Application Problem, - Concept Development (which includes a Problem Set), and - Student Debrief (which includes an Exit Ticket) .

Eureka Math is a program that was written by teachers and math experts who wrote the curriculum to be aligned with the new college- and career-ready standards, which emphasize deeper learning, critical thinking, and conceptual understanding of math.

What is the hardest math in 5th grade?

Some of the hardest math problems for fifth graders involve multiplying: multiplying using square models, multiplying fractions and whole numbers using expanded form, and multiplying fractions using number lines .

What is the hardest math grade?

Generally speaking, the most rigorous math courses in high school include Advanced Placement (AP) Calculus AB and BC, AP Statistics, and for some, Multivariable Calculus (which might be offered at your school or at a local college).

Is Eureka Math no longer free?

Anyone can download the entire PK–12 Eureka Math curriculum, along with a variety of instructional materials and support resources, for free . Some materials, such as our printed workbooks, Eureka Digital Suite, Affirm, Eureka Math Equip, and Eureka Math in Sync must be purchased.

How long does a Eureka Math lesson take?

Eureka Math is 1 hour for all grade levels (except in Kindergarten lessons are 50 minutes) . We have always designed our elementary day with 1 hour dedicated to mathematics instruction.

What kind of math is taught in 5th grade?

In fifth grade, students focus on adding, subtracting, multiplying, and dividing whole numbers, fractions, and decimals . Your kid will become fluent with computing these types of numbers and understanding the relationship between them. Students should also be able to use these numbers in real-world scenarios.

What math is 8th grade level?

Eighth-grade math is typically a course in pre-algebra to help prepare students for high school algebra.

What math level is 5th grade?

In fifth grade, students focus on adding, subtracting, multiplying, and dividing whole numbers, fractions, and decimals . Your kid will become fluent with computing these types of numbers and understanding the relationship between them. Students should also be able to use these numbers in real-world scenarios.

What grade does prodigy math go up to?

With 1,500+ curriculum-aligned math skills for 1st to 8th grade , Prodigy Math is so much more than a game. Prodigy Math is an engaging game-based learning platform that's dedicated to improving students' confidence and achievements in math.

What is the highest math class there is?

Wrap up with Calculus , the highest level of math offered by many high schools and often considered the gold standard of pre-college math preparation.

Eureka Math Grade 5 Module 3 Lesson 2 Answer Key (2024)

Engage NY Eureka Math 5th Grade Module 3 Lesson 2 Answer Key

Eureka Math Grade 5 Module 3 Lesson 2 Sprint Answer Key

A
Find the Missing Numerator or Denominator

Question 1.
\(\frac{1}{2}\) = \(\frac{}{4}\)
Answer:
\(\frac{1}{2}\) = \(\frac{2}{4}\)
Explanation :
\(\frac{1}{2}\) = \(\frac{x}{4}\)
x = \(\frac{1}{2}\) × 4
x = \(\frac{4}{2}\)
x = 2 .

Question 2.
\(\frac{1}{5}\) = \(\frac{2}{}\)
Answer:
\(\frac{1}{5}\) = \(\frac{2}{10}\)
Explanation :
\(\frac{1}{5}\) = \(\frac{2}{x}\)
x = \(\frac{5}{1}\) × 2
x = 10 .

Question 3.
\(\frac{2}{5}\) = \(\frac{}{10}\)
Answer:
\(\frac{2}{5}\) = \(\frac{4}{10}\)
Explanation :
\(\frac{2}{5}\) = \(\frac{x}{10}\)
x = \(\frac{2}{5}\) × 10
x = \(\frac{20}{5}\)
x = 4 .

Question 4.
\(\frac{3}{5}\) = \(\frac{}{10}\)
Answer:
\(\frac{3}{5}\) = \(\frac{6}{10}\)
Explanation :
\(\frac{3}{5}\) = \(\frac{x}{10}\)
x = \(\frac{3}{5}\) × 10
x = \(\frac{30}{5}\)
x = 6 .

Question 5.
\(\frac{4}{5}\) = \(\frac{}{10}\)
Answer:
\(\frac{4}{5}\) = \(\frac{8}{10}\)
Explanation :
\(\frac{4}{5}\) = \(\frac{x}{10}\)
x = \(\frac{4}{5}\) × 10
x = \(\frac{40}{5}\)
x = 8 .

Question 6.
\(\frac{1}{3}\) = \(\frac{2}{}\)
Answer:
\(\frac{1}{3}\) = \(\frac{2}{}\)
Explanation :
\(\frac{1}{3}\) = \(\frac{2}{x}\)
x = \(\frac{3}{1}\) × 2
x = 3 × 2
x = 6 .

Question 7.
\(\frac{2}{3}\) = \(\frac{}{9}\)
Answer:
\(\frac{2}{3}\) = \(\frac{6}{9}\)
Explanation :
\(\frac{2}{3}\) = \(\frac{x}{9}\)
x = \(\frac{2}{3}\) × 9
x = \(\frac{18}{3}\)
x = 6 .

Question 8.
\(\frac{1}{3}\) = \(\frac{3}{}\)
Answer:
\(\frac{1}{3}\) = \(\frac{3}{9}\)
Explanation :
\(\frac{1}{3}\) = \(\frac{3}{x}\)
x = \(\frac{3}{1}\) × 3
x = 3 × 3
x = 9 .

Question 9.
\(\frac{2}{3}\) = \(\frac{}{9}\)
Answer:
\(\frac{2}{3}\) = \(\frac{6}{9}\)
Explanation :
\(\frac{2}{3}\) = \(\frac{x}{9}\)
x = \(\frac{2}{3}\) × 9
x = \(\frac{18}{3}\)
x = 6 .

Question 10.
\(\frac{1}{4}\) = \(\frac{}{8}\)
Answer:
\(\frac{1}{4}\) = \(\frac{2}{8}\)
Explanation :
\(\frac{1}{4}\) = \(\frac{x}{8}\)
x = \(\frac{1}{4}\) × 8
x = \(\frac{8}{4}\)
x = 2 .

Question 11.
\(\frac{3}{4}\) = \(\frac{}{8}\)
Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\)
Explanation :
\(\frac{3}{4}\) = \(\frac{x}{8}\)
x = \(\frac{3}{4}\) × 8
x = \(\frac{24}{4}\)
x = 6 .

Question 12.
\(\frac{1}{4}\) = \(\frac{3}{}\)
Answer:
\(\frac{1}{4}\) = \(\frac{3}{12}\)
Explanation :
\(\frac{1}{4}\) = \(\frac{3}{x}\)
x = \(\frac{4}{1}\) × 3
x = 4 × 3
x = 12 .

Question 13.
\(\frac{3}{4}\) = \(\frac{9}{}\)
Answer:
\(\frac{3}{4}\) = \(\frac{9}{12}\)
Explanation :
\(\frac{3}{4}\) = \(\frac{9}{x}\)
x = \(\frac{4}{3}\) × 9
x = \(\frac{36}{3}\)
x = 12 .

Question 14.
\(\frac{2}{4}\) = \(\frac{}{2}\)
Answer:
\(\frac{2}{4}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{2}{4}\) = \(\frac{x}{2}\)
x = \(\frac{2}{4}\) × 2
x = \(\frac{4}{4}\)
x = 1 .

Question 15.
\(\frac{2}{6}\) = \(\frac{1}{}\)
Answer:
\(\frac{2}{6}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{2}{6}\) = \(\frac{1}{x}\)
x = \(\frac{6}{2}\) × 1
x = \(\frac{6}{2}\)
x = 3 .

Question 16.
\(\frac{2}{10}\) = \(\frac{1}{}\)
Answer:
\(\frac{2}{10}\) = \(\frac{1}{5}\)
Explanation :
\(\frac{2}{10}\) = \(\frac{1}{x}\)
x = \(\frac{10}{2}\) × 1
x = 5 .

Question 17.
\(\frac{4}{10}\) = \(\frac{}{5}\)
Answer:
\(\frac{4}{10}\) = \(\frac{2}{5}\)
Explanation :
\(\frac{4}{10}\) = \(\frac{x}{5}\)
x = \(\frac{4}{10}\) × 5
x = \(\frac{20}{10}\)
x = 2 .

Question 18.
\(\frac{8}{10}\) = \(\frac{}{5}\)
Answer:
\(\frac{8}{10}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{8}{10}\) = \(\frac{x}{5}\)
x = \(\frac{8}{10}\) × 5
x = \(\frac{40}{10}\)
x = 4 .

Question 19.
\(\frac{3}{9}\) = \(\frac{}{3}\)
Answer:
\(\frac{3}{9}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{3}{9}\) = \(\frac{x}{3}\)
x = \(\frac{3}{9}\) × 3
x = \(\frac{9}{9}\)
x = 1 .

Question 20.
\(\frac{6}{9}\) = \(\frac{}{3}\)
Answer:
\(\frac{6}{9}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{6}{9}\) = \(\frac{x}{3}\)
x = \(\frac{6}{9}\) × 3
x = \(\frac{18}{9}\)
x = 2 .

Question 21.
\(\frac{3}{12}\) = \(\frac{1}{}\)
Answer:
\(\frac{3}{12}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{3}{12}\) = \(\frac{1}{x}\)
x = \(\frac{3}{12}\) × 1
x = 4 .

Question 22.
\(\frac{9}{12}\) = \(\frac{}{4}\)
Answer:
\(\frac{9}{12}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{9}{12}\) = \(\frac{x}{4}\)
x = \(\frac{9}{12}\) × 4
x = \(\frac{36}{12}\)
x = 3 .

Question 23.
\(\frac{1}{3}\) = \(\frac{}{12}\)
Answer:
\(\frac{1}{3}\) = \(\frac{4}{12}\)
Explanation :
\(\frac{1}{3}\) = \(\frac{x}{12}\)
x = \(\frac{1}{3}\) × 12
x = \(\frac{12}{3}\)
x = 4 .

Eureka Math Grade 5 Module 3 Lesson 2 Problem Set Answer Key

Question 1.
Show each expression on a number line. Solve.
a. \(\frac{2}{5}\)+ \(\frac{1}{5}\)
b. \(\frac{1}{3}\) + \(\frac{1}{3}\)+ \(\frac{1}{3}\)
c. \(\frac{3}{10}\) + \(\frac{3}{10}\) + \(\frac{3}{10}\)
d. 2 × \(\frac{3}{4}\) + \(\frac{1}{4}\)
Answer:
a. \(\frac{2}{5}\)+ \(\frac{1}{5}\) = \(\frac{3}{5}\)

Explanation :
Number line is represented from 0 to 1 and is divided into 5 parts .\(\frac{2}{5}\) is marked from 0 and then \(\frac{1}{5}\) is marked from it to get sum of \(\frac{3}{5}\).
b. \(\frac{1}{3}\) + \(\frac{1}{3}\)+ \(\frac{1}{3}\) = \(\frac{3}{3}\) = 1

Explanation :
Number line is represented from 0 to 1 and is divided into 3 parts .\(\frac{1}{3}\) is marked from 0 and then \(\frac{1}{3}\) is marked from it and again \(\frac{1}{3}\) is marked to get sum of \(\frac{3}{3}\) = 1
c. \(\frac{3}{10}\) + \(\frac{3}{10}\) + \(\frac{3}{10}\)= \(\frac{9}{10}\)

Explanation :
Number line is represented from 0 to 1 and is divided into 10 parts .\(\frac{3}{10}\) is marked from 0 and then \(\frac{3}{10}\) is marked from it and again \(\frac{3}{10}\) is marked to get sum of \(\frac{9}{10}\).
d. 2 × \(\frac{3}{4}\) + \(\frac{1}{4}\)
\(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{1}{4}\) = \(\frac{7}{4}\)

Explanation :
Number line is represented from 0 to 2 and is divided into 8 parts .\(\frac{3}{4}\) is marked from 0 and then \(\frac{3}{4}\) is marked from it and again \(\frac{1}{4}\) is marked to get sum of \(\frac{7}{4}\).

Question 2.
Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation. Show Part (a) on a number line.
a. \(\frac{6}{7}\)
b. \(\frac{9}{2}\)
c. \(\frac{12}{10}\)
d. \(\frac{27}{5}\)
Answer:
a. \(\frac{6}{7}\) = \(\frac{2}{7}\) + \(\frac{2}{7}\) + \(\frac{2}{7}\) = 3×\(\frac{2}{7}\)

Explanation :
Number line is represented from 0 to 1 and is divided into 7 parts .\(\frac{2}{7}\) is marked from 0 and then \(\frac{2}{7}\) is marked from it and again \(\frac{2}{7}\) is marked to get sum of \(\frac{6}{7}\).
b. \(\frac{9}{2}\) = \(\frac{3}{2}\) + \(\frac{3}{2}\) + \(\frac{3}{2}\) .= 3 × \(\frac{3}{2}\)
c. \(\frac{12}{10}\) = \(\frac{6}{10}\) +\(\frac{6}{10}\)= 2×\(\frac{6}{10}\)
d. \(\frac{27}{5}\) = \(\frac{9}{5}\) + \(\frac{9}{5}\) + \(\frac{9}{5}\) = 3×\(\frac{9}{5}\)

Question 3.
Express each of the following as the sum of a whole number and a fraction. Show Parts (c) and (d) on number lines.
a. \(\frac{9}{7}\)
c. \(\frac{32}{7}\)
d. \(\frac{24}{9}\)
Answer:
a. \(\frac{9}{7}\) =\(\frac{7}{7}\) + \(\frac{2}{7}\) .
c. \(\frac{32}{7}\) = \(\frac{28}{7}\) + \(\frac{4}{7}\) = 4 + \(\frac{4}{7}\).

Explanation :
Number line is represented from 0 to 5 and each whole is divided into 7 parts .4 is marked from 0 and then \(\frac{4}{7}\) is marked from it to get sum of \(\frac{32}{7}\).
d. \(\frac{24}{9}\) = \(\frac{18}{9}\) + \(\frac{6}{9}\) = 2 + \(\frac{6}{9}\) .

Explanation :
Number line is represented from 0 to 3 and each 1 whole divided into 9 parts .2 is marked from 0 and then \(\frac{6}{9}\) is marked from it to get sum of \(\frac{24}{9}\).

Question 4.
Marisela cut four equivalent lengths of ribbon. Each was 5 eighths of a yard long. How many yards of ribbon did she cut? Express your answer as the sum of a whole number and the remaining fractional units. Draw a number line to represent the problem.
Answer:

Explanation :
Length of each ribbon = \(\frac{5}{8}\).
Number of ribbons = 4
Total Length of ribbon = \(\frac{5}{8}\) + \(\frac{5}{8}\) + \(\frac{5}{8}\) + \(\frac{5}{8}\) = \(\frac{20}{8}\) .
\(\frac{20}{8}\) = 2 + \(\frac{4}{8}\) .

Eureka Math Grade 5 Module 3 Lesson 2 Exit Ticket Answer Key

Question 1.
Show each expression on a number line. Solve.
a. \(\frac{5}{5}\) + \(\frac{2}{5}\)
b. \(\frac{6}{3}\)+ \(\frac{2}{3}\)
Answer:
a. \(\frac{5}{5}\) + \(\frac{2}{5}\) = \(\frac{7}{5}\)

Explanation :
Number line is represented from 0 to 2 and each 1 whole divided into 5 parts .1 is marked from 0 and then \(\frac{2}{5}\) is marked from it to get sum of \(\frac{7}{5}\).
b. \(\frac{6}{3}\)+ \(\frac{2}{3}\) = 2 + \(\frac{2}{3}\) = \(\frac{8}{3}\)

Explanation :
Number line is represented from 0 to 3 and each 1 whole divided into 3 parts .2 is marked from 0 and then \(\frac{2}{3}\) is marked from it to get sum of \(\frac{8}{3}\).

Question 2.
Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation. Show Part (b) on a number line.
a. \(\frac{6}{9}\)
b. \(\frac{15}{4}\)
Answer:
a. \(\frac{6}{9}\) = \(\frac{3}{9}\) + \(\frac{3}{9}\) = 2 × \(\frac{3}{9}\)
b. \(\frac{15}{4}\) = \(\frac{4}{4}\) + \(\frac{4}{4}\) + \(\frac{4}{4}\) + \(\frac{3}{4}\) = 3 + \(\frac{3}{4}\) .

Explanation :
Number line is represented from 0 to 4 and each 1 whole divided into 4 parts .3 is marked from 0 and then \(\frac{3}{4}\) is marked from it to get sum of \(\frac{15}{4}\).

Eureka Math Grade 5 Module 3 Lesson 2 Homework Answer Key

Question 1.
Show each expression on a number line. Solve.
a. \(\frac{4}{9}\) + \(\frac{1}{9}\)
b. \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\)
c. \(\frac{2}{7}\) + \(\frac{2}{7}\) + \(\frac{2}{7}\)
d. 2 × \(\frac{3}{5}\) + \(\frac{1}{5}\)
Answer:
a. \(\frac{4}{9}\) + \(\frac{1}{9}\) = \(\frac{5}{9}\) .

Explanation :
Number line is represented from 0 to 1 and each 1 whole divided into 9 parts .\(\frac{4}{9}\) is marked from 0 and then \(\frac{1}{9}\) is marked from it to get sum of \(\frac{5}{9}\).
b. \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) = \(\frac{4}{4}\) = 1

Explanation :
Number line is represented from 0 to 1 and each 1 whole divided into 4 parts .\(\frac{1}{4}\) is marked from 0 and then \(\frac{1}{4}\) is marked again \(\frac{1}{4}\) and \(\frac{1}{4}\) from it to get sum of \(\frac{4}{4}\).
c. \(\frac{2}{7}\) + \(\frac{2}{7}\) + \(\frac{2}{7}\) = \(\frac{6}{7}\)

Explanation :
Number line is represented from 0 to 1 and each 1 whole divided into 7 parts .\(\frac{2}{7}\) is marked from 0 and then \(\frac{2}{7}\) is marked and again \(\frac{2}{7}\) is marked from it to get sum of \(\frac{6}{7}\).
d. 2 × \(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{3}{5}\) + \(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{7}{5}\) .

Explanation :
Number line is represented from 0 to 2 and each 1 whole divided into 5 parts .\(\frac{3}{5}\) is marked from 0 and then \(\frac{3}{5}\) is marked and \(\frac{1}{5}\) from it to get sum of \(\frac{7}{5}\).

Question 2.
Express each fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation. Show Part (a) on a number line.
a. \(\frac{6}{11}\)
b. \(\frac{9}{4}\)
c. \(\frac{12}{8}\)
d. \(\frac{27}{10}\)
Answer:
a. \(\frac{6}{11}\) = \(\frac{3}{11}\) + \(\frac{3}{11}\) = 2 × \(\frac{3}{11}\) .

b. \(\frac{9}{4}\) = \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) = 3 × \(\frac{3}{4}\)
c. \(\frac{12}{8}\) =\(\frac{4}{8}\) + \(\frac{4}{8}\) + \(\frac{4}{8}\)= 3 × \(\frac{4}{8}\)
d. \(\frac{27}{10}\) = \(\frac{9}{10}\) + \(\frac{9}{10}\) + \(\frac{9}{10}\) = 3 × \(\frac{9}{10}\) .

Question 3.
Express each of the following as the sum of a whole number and a fraction. Show Parts (c) and (d) on number lines.
a. \(\frac{9}{5}\)
b. \(\frac{7}{2}\)
c. \(\frac{25}{7}\)
d. \(\frac{21}{9}\)
Answer:
a. \(\frac{9}{5}\) = \(\frac{5}{5}\) + \(\frac{4}{5}\) = 1 + \(\frac{4}{5}\) .
b. \(\frac{7}{2}\) = \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{1}{2}\) =
1+ 1 + 1 + \(\frac{1}{2}\) = 3 + \(\frac{1}{2}\) .
c. \(\frac{25}{7}\) = \(\frac{7}{7}\) + \(\frac{7}{7}\) + \(\frac{7}{7}\) + \(\frac{4}{7}\) = 1+ 1+ 1+ \(\frac{4}{7}\) =3 + \(\frac{4}{7}\) .

Explanation :
Number line is represented from 0 to 4 and each 1 whole divided into 7 parts .3 1′ are marked from 0 and then \(\frac{4}{7}\) is marked from it to get sum of \(\frac{25}{7}\).
d. \(\frac{21}{9}\) = \(\frac{9}{9}\) + \(\frac{9}{9}\) + \(\frac{3}{9}\) = 1+ 1+ \(\frac{3}{9} \) = 2 + \(\frac{3}{9}\) .

Explanation :
Number line is represented from 0 to 3 and each 1 whole divided into 9 parts .2 1’s are marked from 0 and then \(\frac{3}{9}\) is marked from it to get sum of \(\frac{21}{9}\).

Question 4.
Natalie sawed five boards of equal length to make a stool. Each was 9 tenths of a meter long. What is the total length of the boards she sawed? Express your answer as the sum of a whole number and the remaining fractional units. Draw a number line to represent the problem.
Answer:

Explanation :
Number of boards = 5
Length of each board = 9 tenths = \(\frac{9}{10}\) .
Total Length of board = 5 × \(\frac{9}{10}\) = \(\frac{45}{10}\).
\(\frac{45}{10}\) = \(\frac{10}{10}\) + \(\frac{10}{10}\) + \(\frac{10}{10}\) + \(\frac{10}{10}\) + \(\frac{5}{10}\) = 1+ 1+ 1+ 1+ \(\frac{5}{10}\) = 4 + \(\frac{5}{10}\) .

Eureka Math Grade 5 Module 3 Lesson 2 Answer Key (2024)

Engage NY Eureka Math 5th Grade Module 3 Lesson 2 Answer Key

Eureka Math Grade 5 Module 3 Lesson 2 Sprint Answer Key

Eureka Math Grade 5 Module 3 Lesson 2 Problem Set Answer Key

Eureka Math Grade 5 Module 3 Lesson 2 Exit Ticket Answer Key

Eureka Math Grade 5 Module 3 Lesson 2 Homework Answer Key

FAQs

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References