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## Texas Go Math Grade 4 Lesson 5.1 Answer Key Add and subtract parts of a whole

**Essential Question**

When con you odd or subtract ports of o whole?

Answer:

Explanation:

When the denominators are same

we can add or subtract

Materials

- fraction circles
- color pencils

Ms. Clark has the following pie pieces left over from a bake sale.

She will combine the pieces so they are on the same dish. How much pie will be on the dish?

Answer: \(\frac{2}{3}\)

Explanation:

\(\frac{4}{6}\) that is \(\frac{2}{3}\) pie will be on the dish

A. Model the problem using fraction circles. Draw a picture of your model. Then write the sum.

So, ___________ of a pie is on the dish.

Answer:

So, \(\frac{4}{6}\) of a pie is on the dish.

B. Suppose Ms. Clark eats 2 pieces of the pie. How much pie will be left on the dish? Model the problem using fraction circles. Draw a picture of your model. Then write the difference.

______________ – ____________ = ____________

So, _____________ of the pie is left on the dish.

Answer:

Explanation:

So, \(\frac{4}{6}\) of the pie is left on the dish.

**Make connections**

You can only join or separate parts that refer to the same whole.

Suppose Randy has \(\frac{1}{4}\) of a round cake and \(\frac{1}{4}\) of a square cake.

a. Are the wholes the same? Explain.

Answer: No,

Explanation:

Both the shapes are different.

The wholes are not same.

b. Does the sum \(\frac{1}{4}+\frac{1}{4}=\frac{2}{4}\) make sense in this situation? Explain.

Answer: No.

Explanation:

Both the shapes are different

The sum \(\frac{1}{4}+\frac{1}{4}=\frac{2}{4}\) make sense in this situation

**Math Talk**

Mathematical Processes

Give an example of a situation where the equation \(\frac{1}{4}+\frac{1}{4}=\frac{2}{4}\) makes sense. Explain your

Answer:

Explanation:

The equation \(\frac{1}{4}+\frac{1}{4}=\frac{2}{4}\) makes sense in this situation.

The whole is same when the shapes are same

**Share and Grow**

Use the model to write an equation.

Question 1.

Answer:

Explanation:

\(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{4}{5}\)

Question 2.

Answer:

Explanation:

A trapezoid is divided into 3 triangles

In that 2 are shaded

1 part is not shaded

Question 3.

Multi-Step Sean has \(\frac{1}{5}\) of a cupcake and \(\frac{1}{5}\) of a large cake.

a. Are the wholes the same? Explain.

Answer: No,

Explanation:

The size cup cake and large cake are different.

b. Does the sum \(\frac{1}{5}+\frac{1}{5}\) = \(\frac{2}{5}\) make sense in this situation? Explain.

Answer: No,

Explanation:

Equation is correct but not in this situation.

**Use the model to solve the equation.**

Question 4.

\(\frac{3}{4}-\frac{1}{4}\) = _____________

Answer: \(\frac{2}{4}\)

Explanation:

According to this equation \(\frac{3}{4}-\frac{1}{4}\) simplest form is \(\frac{2}{4}\)

Question 5.

\(\frac{5}{6}+\frac{1}{6}\) = _____________

Answer:

\(\frac{5}{6}+\frac{1}{6}\) = 1

Explanation:

When you divide a number with the same number the answer is 1.

**Problem Solving**

**H.O.T.** Sense or Nonsense?

Question 6.

Samantha and Kim used different models to help find \(\frac{1}{3}+\frac{1}{3}\) Whose model makes sense? Whose Model is nonsense? Explain your reasoning below each model.

Answer:

Explanation:

Kim’s model make sense.

Question 7.

H.O.T. Justify If there is \(\frac{4}{6}\) of a pie on a plate. what part of the pie is missing from the plate? Write an equation to justify your answer.

Answer:

\(\frac{4}{6}\) + \(\frac{2}{6}\) = 1

Explanation:

\(\frac{2}{6}\) of the pie is missing from the plate

**Daily Assessment Task**

Fill in the bubble completely to show your answer.

Use models to solve.

Question 8.

At lunch yesterday, Ryan ate \(\frac{2}{6}\) of an apple and I ate \(\frac{2}{6}\) of the apple. Together, how much of the apple did we eat?

(A) \(\frac{2}{6}\)

(B) \(\frac{4}{6}\)

(C) \(\frac{2}{12}\)

(D) \(\frac{4}{12}\)

Answer: B

Explanation:

\(\frac{2}{6}\) + \(\frac{2}{6}\) = \(\frac{4}{6}\)

\(\frac{4}{6}\) they ate the apple.

Question 9.

At the start of art class, Logan had \(\frac{7}{12}\) of a block of clay. After class, \(\frac{5}{12}\) of the block was left. What fraction of the block did Logan use during class?

(A) \(\frac{7}{12}\)

(B) \(\frac{12}{12}\)

(C) \(\frac{5}{12}\)

(D) \(\frac{2}{12}\)

Answer: D

Explanation:

\(\frac{7}{12}\) – \(\frac{5}{12}\) = \(\frac{2}{12}\)

Used the simplest form

Question 10.

Multi-Step Samantha is mixing batter for muffins. She mixes \(\frac{2}{4}\) cup of flour and \(\frac{1}{4}\) cup of sugar, Then she adds \(\frac{1}{4}\) cup of milk. How much muffin batter has she mixed so far?

(A) \(\frac{3}{8}\) cup

(B) \(\frac{2}{4}\) cup

(C) 1 cup

(D) \(\frac{3}{4}\) cup

Answer: C

Explanation:

\(\frac{2}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) = 1

Used the simplest form

**TEXAS Test Prep**

Question 11.

Which equation matches the model?

(A) \(\frac{1}{4}+\frac{3}{4}=\frac{4}{4}\)

(B) \(\frac{1}{4}+\frac{2}{4}=\frac{3}{4}\)

(C) \(\frac{3}{4}+\frac{2}{4}=\frac{5}{4}\)

(D) \(\frac{1}{8}+\frac{2}{8}=\frac{3}{8}\)

Answer: B

Explanation:

\(\frac{1}{4}+\frac{2}{4}=\frac{3}{4}\) This equation matches the model

### Texas Go Math Grade 4 Lesson 5.1 Homework and Practice Answer Key

**Use the model to write an equation.**

Question 1.

Answer:

\(\frac{2}{6}\) + \(\frac{3}{6}\) = \(\frac{5}{6}\)

Explanation:

Written equation for above model.

Question 2.

Answer:

\(\frac{3}{4}\) – \(\frac{1}{4}\) = \(\frac{2}{4}\)

Explanation:

The above parallelogram is divided into 4 equal parts in that 3 are shaded

in that 1 is filled with image

**Use the model to solve an equation.**

Question 3.

Answer: \(\frac{2}{5}\)

Explanation:

\(\frac{4}{5}\) – \(\frac{2}{5}\) = \(\frac{2}{5}\)

By using the model solved the equation.

Question 4.

Answer:

\(\frac{1}{4}\) + \(\frac{1}{4}\) = \(\frac{2}{4}\)

Explanation:

By using the model solved the equation.

Question 5.

If there is \(\frac{6}{8}\) of a pizza on a plate, what part of the pizza is missing from the plate? Write an equation to justify your answer.

Answer: \(\frac{2}{8}\)

Explanation:

1 – \(\frac{6}{8}\) = \(\frac{2}{8}\)

\(\frac{2}{8}\) part of the pizza is missing from the plate.

**Problem Solving**

Question 6.

If there is \(\frac{3}{8}\) of a pizza on a plate? what part of the pizza is missing from the plate? Write an equation to justify your answer.

Answer: \(\frac{5}{8}\)

Explanation:

1 – \(\frac{3}{8}\) = \(\frac{5}{8}\)

\(\frac{5}{8}\) part of the pizza is missing from the plate.

Question 7.

Maria is making cupcakes. She fills \(\frac{4}{12}\) of the cups with chocolate batter and \(\frac{7}{12}\) of the cups with vanilla batter. How many of the cups has Maria filled? Write an equation to justify your answer.

Answer: \(\frac{11}{12}\)

Explanation:

\(\frac{4}{12}\) + \(\frac{7}{12}\) = \(\frac{11}{12}\)

Maria filled \(\frac{11}{12}\) cups.

**Lesson Check**

Fill in the bubble completely to show your answer.

Question 8.

which equation matches the model?

(A) \(\frac{2}{8}+\frac{1}{8}=\frac{3}{8}\)

(B) \(\frac{2}{4}+\frac{3}{4}=\frac{5}{4}\)

(C) \(\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)

(D) \(\frac{1}{4}+\frac{3}{4}=\frac{4}{4}\)

Answer: C

Explanation:

\(\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\) equation matches the model

Question 9.

Which equation matches the model?

(A) \(\frac{5}{7}-\frac{2}{7}=\frac{3}{7}\)

(B) \(\frac{7}{7}-\frac{5}{7}=\frac{2}{7}\)

(C) \(\frac{7}{7}-\frac{2}{7}=\frac{5}{7}\)

(D) \(\frac{5}{7}-\frac{3}{7}=\frac{2}{7}\)

Answer: A

Explanation:

\(\frac{5}{7}-\frac{2}{7}=\frac{3}{7}\) equation matches the model

Question 10.

In Dylan’s family \(\frac{5}{6}\) of the children have brown hair. The rest of the children have blond hair.

What fraction of the children has blond hair?

(A) \(\frac{4}{6}\)

(B) \(\frac{2}{6}\)

(C) \(\frac{3}{6}\)

(D) \(\frac{1}{6}\)

Answer: D

Explanation:

1 – \(\frac{5}{6}\) = \(\frac{1}{6}\)

\(\frac{1}{6}\) fraction of the children has blond hair

Question 11.

Miranda made a poster for her science project. She filled \(\frac{3}{8}\) of the poster with photos and \(\frac{4}{8}\) of the poster with written information. how much space has she filled on lier poster so far?

(A) \(\frac{7}{8}\)

(B) \(\frac{1}{8}\)

(C) \(\frac{6}{8}\)

(D) \(\frac{2}{8}\)

Answer: B

Explanation:

\(\frac{3}{8}\) + \(\frac{4}{8}\) = \(\frac{7}{8}\)

\(\frac{1}{8}\) space has she filled on lier poster so far

Question 12.

Multi-Step Carrie’s dance class learned \(\frac{1}{5}\) of a new dance on Monday, and \(\frac{2}{5}\) of the dance on Tuesday. What fraction of the dance is left for the class to learn on Wednesday?

(A) \(\frac{4}{5}\)

(B) \(\frac{3}{5}\)

(C) \(\frac{2}{5}\)

(D) \(\frac{1}{5}\)

Answer: D

Explanation:

\(\frac{1}{5}\) + \(\frac{2}{5}\) = \(\frac{3}{5}\)

1 – \(\frac{3}{5}\) = \(\frac{1}{5}\)

\(\frac{1}{5}\) fraction of the dance is left for the class to learn on Wednesday

Question 13.

Multi-Step Mrs. Simon planted \(\frac{4}{12}\) of her flowers in her front yard, \(\frac{3}{12}\) of her flowers in her back yard, and \(\frac{2}{12}\) of her flowers on the side of her house. What fraction of her flowers has she planted so far?

(A) \(\frac{2}{12}\)

(B) \(\frac{9}{12}\)

(C) \(\frac{3}{12}\)

(D) \(\frac{10}{12}\)

Answer: B

Explanation:

As the denominators are same

we can directly add the numerators

\(\frac{4}{12}\) + \(\frac{3}{12}\) + \(\frac{2}{12}\) = \(\frac{9}{12}\)