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

A Story of Units (Grades PK-5) Each lesson in A Story of Units is comprised of four critical components: fluency practice, concept development (including the problem set), application problem, and student debrief (including the Exit Ticket) .

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).

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What is the highest level of math in 9th grade?

9th grade math usually focuses on Algebra I , but can include other advanced mathematics such as Geometry, Algebra II, Pre-Calculus or Trigonometry.

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 grade level does prodigy math go up to?

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What is the highest math class in high school?

Begin with Algebra 1 and Geometry, often considered the building blocks of higher level math and science classes. 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 4 Module 5 Lesson 14 Answer Key (2024)

Engage NY Eureka Math 4th Grade Module 5 Lesson 14 Answer Key

Eureka Math Grade 4 Module 5 Lesson 14 Problem Set Answer Key

Question 1.
Compare the pairs of fractions by reasoning about the size of the units. Use >, <, or =.
a. 1 fourth _____ 1 fifth

Answer:
1 fourth = 1 fifth.

Explanation:
In the above-given question,
given that,
compare the pairs of fractions by reasoning about the size of the units.
1 fourth = 1/4.
1/4 = 0.25.
1 fifth = 1/5.
1/5 = 0.2.
0.25 = 0.2.
1/4 = 1/5.

b. 3 fourths _____ 3 fifths

Answer:
3 fourths > 3 fifths.

Explanation:
In the above-given question,
given that,
compare the pairs of fractions by reasoning about the size of the units.
3 fourths = 3/4.
3/4 = 0.75.
3 fifths = 3/5.
3/5 = 0.6.
0.75 > 0.6.
3/4 > 3/5.

c. 1 tenth __>___ 1 twelfth

Answer:
1 tenth > 1 twelfth.

Explanation:
In the above-given question,
given that,
compare the pairs of fractions by reasoning about the size of the units.
1 tenth = 1/10.
1/10 = 0.1.
1 twelfth = 1/12.
1/12 = 0.083.
0.1 > 0.08.
1/10 > 1/12.

d. 7 tenths _____ 7 twelfths

Answer:
7 tenths > 7 twelfths

Explanation:
In the above-given question,
given that,
compare the pairs of fractions by reasoning about the size of the units.
7 tenths = 7/10.
7/10 = 0.7.
7 twelfths = 7/12.
7/12 = 0.58.
0.7 > 0.58.
7/10 > 7/12.

Question 2.
Compare by reasoning about the following pairs of fractions with the same or related numerators.
Use >, <, or =. Explain your thinking using words, pictures, or numbers. Problem 2(b) has been done for you.
a. \(\frac{3}{5}\) _____ \(\frac{3}{4}\)

Answer:
\(\frac{3}{5}\) __<___ \(\frac{3}{4}\).

Explanation:
In the above-given question,
given that,
\(\frac{3}{5}\).
3/5 = 3 fifths.
3/5 = 0.6.
\(\frac{3}{4}\).
3/4 = 3 fourths.
3/4 = 0.75.
0.6 < 0.75.
3 fifths are less than 3 fourths.
3/5 < 3/4.

b. \(\frac{2}{5}\) < \(\frac{4}{9}\) because \(\frac{2}{5}\) = \(\frac{4}{10}\)
4 tenths is less than 4 ninths because tenths are smaller than ninths.

Answer:
\(\frac{2}{5}\) __>___ \(\frac{4}{9}\).

Explanation:
In the above-given question,
given that,
\(\frac{2}{5}\).
2/5 = 2 fifths.
2/5 = 0.4.
\(\frac{4}{9}\).
4/9 = 4 ninths.
4/9 = 0.11.
0.4 > 0.11.
2 fifths are greater than 4 ninths.
2/5 > 4/9.

c. \(\frac{7}{11}\) _____ \(\frac{7}{13}\)

Answer:
\(\frac{7}{11}\) __>___ \(\frac{7}{13}\).

Explanation:
In the above-given question,
given that,
\(\frac{7}{11}\).
7/11 = 7 elevenths.
7/11 = 0.63.
\(\frac{7}{13}\).
7/13 = 7 thirteens.
7/13 = 0.53.
0.6 > 0.5.
7 thirteens are less than 7 elevenths.
7/11 > 7/13.

d. \(\frac{6}{7}\) _____ \(\frac{12}{15}\)

Answer:
\(\frac{6}{7}\) __<___ \(\frac{12}{15}\).

Explanation:
In the above-given question,
given that,
\(\frac{6}{7}\).
6/7 = 6 sevenths.
6/7 = 0.85.
\(\frac{2}{15}\).
2/15 = 2 fifteenths.
2/15 = 0.13.
0.8 < 0.13.
6 sevenths are less than 12 fifteenths.
6/7 < 12/15.

Question 3.
Draw two tape diagrams to model each pair of the following fractions with related denominators.
Use >, <, or = to compare.
a. \(\frac{2}{3}\) _____ \(\frac{5}{6}\)

Answer:
\(\frac{2}{3}\) __<___ \(\frac{5}{6}\).

Explanation:
In the above-given question,
given that,
\(\frac{2}{3}\).
2/3 = 2 thirds.
2/3 = 0.6.
\(\frac{5}{6}\).
5/6 = 5 sixths.
5/6 = 0.83.
0.6 < 0.83.
2 thirds are less than 5 sixths.
2/3 < 5/6.

b. \(\frac{3}{4}\) _____ \(\frac{7}{8}\)

Answer:
\(\frac{3}{4}\) __<___ \(\frac{7}{8}\).

Explanation:
In the above-given question,
given that,
\(\frac{3}{4}\).
3/4 = 3 fourths.
3/4 = 0.6.
\(\frac{7}{8}\).
7/8 = 7 eighths.
7/8 = 0.87.
0.6 < 0.8.
3 fourths are less than 7 eighths.
3/4 < 7/8.

c. 1\(\frac{3}{4}\) _____ 1\(\frac{7}{12}\)

Answer:
1\(\frac{3}{4}\) __>___ 1\(\frac{7}{12}\).

Explanation:
In the above-given question,
given that,
1\(\frac{3}{4}\).
1 (3/4) = 7 fourths.
7/4 = 1.75.
1\(\frac{7}{12}\).
1(7/12) = 19 twelfths.
19/12 = 1.58.
1.75 > 1.58.
3 fourths are greater than 7 twelfths.
3/4 > 7/12.

Question 4.
Draw one number line to model each pair of fractions with related denominators. Use >, <, or = to compare.
a. \(\frac{2}{3}\) _____ \(\frac{5}{6}\)

Answer:
\(\frac{2}{3}\) __<___ \(\frac{5}{6}\).

Explanation:
In the above-given question,
given that,
\(\frac{2}{3}\).
2/3 = 2 thirds.
2/3 = 0.6.
\(\frac{5}{6}\).
5/6 = 5 sixths.
5/6 = 0.83.
0.6 < 0.83.
2 thirds are less than 5 sixths.
2/3 < 5/6.

Eureka Math Grade 4 Module 5 Lesson 14 Exit Ticket Answer Key

Question 1.
Draw tape diagrams to compare the following fractions:
\(\frac{2}{5}\) ________ \(\frac{3}{10}\)

Answer:
\(\frac{2}{5}\) __>___ \(\frac{3}{10}\).

Explanation:
In the above-given question,
given that,
\(\frac{2}{5}\).
2/5 = 2 fifths.
2/5 = 0.4.
\(\frac{3}{10}\).
3/10 = 3 tenths.
3/10 = 0.3.
0.4 > 0.3.
2 fifths are greater than 3 tenths.
2/5 > 3/10.

Question 2.
Use a number line to compare the following fractions:
\(\frac{4}{3}\) ________ \(\frac{7}{6}\)

Answer:
\(\frac{4}{3}\) __>___ \(\frac{7}{6}\).

Explanation:
In the above-given question,
given that,
\(\frac{4}{3}\).
4/3 = 4 thirds.
4/3 = 1.33.
\(\frac{7}{6}\).
7/6 = 7 sixths.
7/6 = 1.16.
1.33 > 1.16.
4 thirds are greater than 7 sixths.
4/3 > 7/6.

Eureka Math Grade 4 Module 5 Lesson 14 Homework Answer Key

Question 1.
Compare the pairs of fractions by reasoning about the size of the units. Use >, <, or =.
a. 1 third _____ 1 sixth

Answer:
1 third > 1 sixth.

Explanation:
In the above-given question,
given that,
compare the pairs of fractions by reasoning about the size of the units.
1 third = 1/3.
1/3 = 0.33.
1 sixth = 1/6.
1/6 = 0.1.
0.33 > 0.1.
1/3 > 1/6.

b. 2 halves _____ 2 thirds

Answer:
2 halves = 2 thirds.

Explanation:
In the above-given question,
given that,
compare the pairs of fractions by reasoning about the size of the units.
2 halves = 2/2.
2/2 = 1.
2 thirds = 2/3.
2/3 = 0.66
1 > 0.66.
2/2 > 2/3.

c. 2 fourths _____ 2 sixths

Answer:
2 fourths > 2 sixths.

Explanation:
In the above-given question,
given that,
compare the pairs of fractions by reasoning about the size of the units.
2 fourths = 2/4.
2/4 = 0.5.
2 sixths = 2/6.
2/6 = 0.33.
0.5 > 0.33.
2/4 > 2/6.

d. 5 eighths _____ 5 tenths

Answer:
5 eights > 5 tenth.

Explanation:
In the above-given question,
given that,
compare the pairs of fractions by reasoning about the size of the units.
5 eights = 5/8.
5/8 = 0.625.
5 tenths = 5/10.
5/10 = 0.5.
0.625 > 0.5.
5/8 > 5/10.

Answer:
\(\frac{3}{6}\) __>___ \(\frac{3}{7}\).

Explanation:
In the above-given question,
given that,
\(\frac{3}{6}\).
3/6 = 3 sixths.
3/6 = 0.5.
\(\frac{3}{7}\).
3/7 = 3 sevenths.
3/7 = 0.42.
0.5 > 0.42.
3 sixths are greater than 3 sevenths.
3/6 > 3/7.

b. \(\frac{2}{5}\) < \(\frac{4}{9}\) because \(\frac{2}{5}\) = \(\frac{4}{10}\)
4 tenths is less than 4 ninths because tenths are smaller than ninths.

c. \(\frac{3}{11}\) _________ \(\frac{3}{13}\)

Answer:
\(\frac{3}{11}\) __>___ \(\frac{3}{13}\).

Explanation:
In the above-given question,
given that,
\(\frac{3}{11}\).
3/11 = 3 elevenths.
3/11 = 0.27.
\(\frac{3}{13}\).
3/13 = 3 elevenths.
3/13 = 0.23.
0.27 > 0.23.
3 elevenths are greater than 3 thirteens.
3/11 > 3/13.

d. \(\frac{5}{7}\) _________ \(\frac{10}{13}\)

Answer:
\(\frac{5}{7}\) __>___ \(\frac{10}{13}\).

Explanation:
In the above-given question,
given that,
\(\frac{5}{7}\).
5/7 = 5 sevenths.
5/7 = 1.33.
\(\frac{10}{13}\).
10/13 = 10 thirteens.
10/13 = 0.769
1.33 > 0.769.
5 sevenths are greater than 10 thirteens.
5/7 > 10/13.

c. \(\frac{3}{11}\) ______ \(\frac{3}{13}\)

Answer:
\(\frac{3}{11}\) __>___ \(\frac{3}{13}\).

Explanation:
In the above-given question,
given that,
\(\frac{3}{11}\).
3/11 = 3 elevenths.
3/11 = 0.27.
\(\frac{3}{13}\).
3/13 = 3 elevens.
3/13 = 0.23.
0.27 > 0.23.
3 elevens are greater than 3 thirteens.
3/11 > 3/13.

d. \(\frac{5}{7}\) _______ \(\frac{10}{13}\)

Answer:
\(\frac{5}{7}\) __<___ \(\frac{10}{13}\).

Explanation:
In the above-given question,
given that,
\(\frac{5}{7}\).
5/7 = 5 sevens.
4/3 = 1.33.
\(\frac{10}{13}\).
10/13 = 10 thirteens.
10/13 = 3.33
1.33 < 3.33.
5 sevens are greater than 10 thirteens.
5/7 < 10/13.

Question 3.
Draw two tape diagrams to model each pair of the following fractions with related denominators. Use >, <, or = to compare.
a. \(\frac{3}{4}\) _________ \(\frac{7}{12}\)

Answer:
\(\frac{3}{4}\) __>___ \(\frac{7}{12}\).

Explanation:
In the above-given question,
given that,
\(\frac{3}{4}\).
3/4 = 3 fours.
3/4 = 0.75.
\(\frac{7}{12}\).
7/12 = 7 twelves.
7/12 = 0.58.
0.75 > 0.58.
3 fourths are greater than 7 twelves.
3/4 > 7/12.

b. \(\frac{2}{4}\) ___________ \(\frac{1}{8}\)

Answer:
\(\frac{2}{4}\) __>___ \(\frac{1}{8}\).

Explanation:
In the above-given question,
given that,
\(\frac{2}{4}\).
2/4 = 2 fourths.
2/4 = 0.5.
\(\frac{1}{8}\).
1/8 = 1 eights.
1/8 = 0.125.
0.5 > 0.125
2 fourths are greater than 1 eights.
2/34 > 1/8.

c. 1\(\frac{4}{10}\) ________ 1\(\frac{3}{5}\)

Answer:
\(\frac{4}{10}\) __<___ \(\frac{3}{5}\).

Explanation:
In the above-given question,
given that,
\(\frac{4}{10}\).
4/10 = 4 tenths.
4/10 = 0.4.
\(\frac{3}{5}\).
3/5 = 3 fifths.
3/5 = 0.6.
0.4 < 0.6.
4 tens are greater than 3 fives.
4/10 < 3/5.

Question 4.
Draw one number line to model each pair of fractions with related denominators. Use >, <, or = to compare.
a. \(\frac{3}{4}\) _________ \(\frac{5}{8}\)

Answer:
\(\frac{3}{4}\) __>___ \(\frac{5}{8}\).

Explanation:
In the above-given question,
given that,
\(\frac{3}{4}\).
3/4 = 3 fourths.
3/4 = 0.75
\(\frac{5}{8}\).
5/8 = 5 eights.
5/8 = 0.625.
0.75 > 0.625.
3 fourths are greater than 5 eights.
3/4 > 7/6.

b. \(\frac{11}{12}\) _________ \(\frac{3}{4}\)

Answer:
\(\frac{11}{12}\) __>___ \(\frac{3}{4}\).

Explanation:
In the above-given question,
given that,
\(\frac{11}{12}\).
11/12 = 11 twelves.
11/12 = 0.91.
\(\frac{3}{4}\).
3/4 = 3 fourths.
3/4 = 0.75
0.91 > 0.75.
11 twelves are greater than 3 fourths.
11/12 > 3/4.

c. \(\frac{4}{5}\) _________ \(\frac{7}{10}\)

Answer:
\(\frac{4}{5}\) __>___ \(\frac{7}{10}\).

Explanation:
In the above-given question,
given that,
\(\frac{4}{5}\).
4/5 = 4 fifths.
4/5 = 0.8
\(\frac{7}{10}\).
7/10 = 7 tenths.
7/10 = 0.7.
0.8 > 0.7.
4 fifths are greater than 7 tenths.
4/5 > 7/10.

d. \(\frac{8}{9}\) _________ \(\frac{2}{3}\)

Answer:
\(\frac{8}{9}\) __>___ \(\frac{2}{3}\).

Question 5.
Compare each pair of fractions using >, <, or =. Draw a model if you choose to.

a. \(\frac{1}{7}\) ________ \(\frac{2}{7}\)

Answer:
\(\frac{1}{7}\) __<___ \(\frac{2}{7}\).

Explanation:
In the above-given question,
given that,
\(\frac{1}{7}\).
1/7 = 1 sevenths.
1/37 = 0.027.
\(\frac{2}{7}\).
2/7 = 2 sevenths.
2/8 = 0.25.
1.33 < 1.16.
1 seventh is less than 2 sevenths.
1/7 < 2/7.

b. \(\frac{5}{7}\) _______ \(\frac{11}{14}\)

Answer:
\(\frac{5}{7}\) __>___ \(\frac{11}{14}\).

Explanation:
In the above-given question,
given that,
\(\frac{5}{7}\).
5/3 = 5 thirds.
5/3 = 1.6.
\(\frac{11}{14}\).
11/14 = 11 fourteens.
11/14 = 2.75.
1.6 < 2.75
5 sevens are less than 11 fourteens.
5/7 < 11/14.

c. \(\frac{7}{10}\) _________ \(\frac{3}{5}\)

Answer:
\(\frac{7}{10}\) __>___ \(\frac{3}{5}\).

Explanation:
In the above-given question,
given that,
\(\frac{7}{10}\).
7/10 = 7 tenths.
7/10 = 0.7.
\(\frac{3}{5}\).
3/5 = 3 fifths.
3/5 = 0.6.
0.7 > 0.6.
7 tenths are greater than 3 fifths.
7/10 > 3/5.

d. \(\frac{2}{3}\) ________ \(\frac{9}{15}\)

Answer:
\(\frac{2}{3}\) __=___ \(\frac{9}{15}\).

Explanation:
In the above-given question,
given that,
\(\frac{2}{3}\).
2/3 = 2 thirds.
2/3 = 0.66.
\(\frac{9}{15}\).
9/15 = 9 fifteens.
9/15 = 0.6.
0.66 = 0.6.
2 thirds is equal to 9 fifteens.
2/3 = 9/15.

e. \(\frac{3}{4}\) _________ \(\frac{9}{12}\)

Answer:
\(\frac{3}{4}\) __>___ \(\frac{9}{12}\).

Explanation:
In the above-given question,
given that,
\(\frac{3}{4}\).
3/4 = 3 fourths.
3/4 = 0.75
\(\frac{9}{12}\).
9/12 = 9 twelfths.
9/12 = 0.75.
0.75 = 0.75.
3 fourths are equal to 9 twelfths.
3/4 = 9/12.

f. \(\frac{5}{3}\) ________ \(\frac{5}{2}\)

Answer:
\(\frac{5}{3}\) __<___ \(\frac{5}{2}\).

Explanation:
In the above-given question,
given that,
\(\frac{5}{3}\).
5/3 = 5 thirds.
5/3 = 1.66.
\(\frac{5}{2}\).
5/2 = 5 twos.
5/2 = 2.5.
1.66 < 2.5.
5 thirds less than 5 twos.
5/3 < 5/2.

Question 6.
Simon claims \(\frac{4}{9}\) is greater than \(\frac{1}{3}\). Ted thinks \(\frac{4}{9}\) is less than \(\frac{1}{3}\). Who is correct? Support your answer with a picture.

Answer:
\(\frac{4}{9}\) __>___ \(\frac{1}{3}\).

Explanation:
In the above-given question,
given that,
\(\frac{4}{9}\).
4/9 = 4 nines.
4/9 = 0.44.
\(\frac{1}{3}\).
1/3 = 1 thirds.
1/3 = 0.33.
0.44 > 0.33.
4 nines are greater than 1 third.
4/9 > 1/3.

Eureka Math Grade 4 Module 5 Lesson 14 Answer Key (2024)

Engage NY Eureka Math 4th Grade Module 5 Lesson 14 Answer Key

Eureka Math Grade 4 Module 5 Lesson 14 Problem Set Answer Key

Eureka Math Grade 4 Module 5 Lesson 14 Exit Ticket Answer Key

Eureka Math Grade 4 Module 5 Lesson 14 Homework Answer Key

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What grade does Eureka math go up to? ›

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