eureka math lesson 19 homework answers

eureka math lesson 19 homework answers

Eureka Math Lesson 19 Homework Answers

1. Introduction

You should understand this as our past learning on straight line graphs. Any extra practice on this can be found in the GCSE text integral unit 7.

We will end our one last review question.

Moreover, we will apply this understanding towards finding the equation of situations that may not begin from (0,0) i.e. non-directly proportional, using understanding of y = mx + b. This is simple algebra, thus we will move fast. This is focusing towards our first capable of the first three syllabus statements.

In this topic, we will apply our understanding of linear equations by exploring how to find the beginning value, or y-intercept, of an equation. Remember, linear equations are equations of straight lines. The standard form of a linear equation is y = mx + b. If we can find the value of m and b (m is the constant of x and b is the y-intercept), we can know exactly what the line looks like. We have done much work on finding the b value when we have the y and x values of an equation. We are now applying this into equations form y = (finding the beginning value, b).

2. Problem Solving Strategies

This is an important problem to the understanding of rate * time = distance wave problems. This problem is more of a variable translation. Where you need to determine two similar items and add them to find the total. Then take that total information and plug it into a variable equation in the form of Ax + Ay = B, where A and B are certain values. Both equations here are going to be D = RT. Then you will throw in the general formula into the total equation. Set of problems and are quite common in algebra 1. Step-by-step processes help a lot in solving these problems.

Did you understand the question? What is it asking you to solve for? (speed of boat) What information is important, and what is the problem about? (trying to find out the speed of the boat, knowing it took a 7-hour total trip) Draw a picture or diagram. (Draw a picture of a river moving left to right with the boat going up and down)

Example: A certain river has a flow of 4 miles per hour. A boat travels 48 miles up the river and then turns around and returns to the starting point. The total trip took 7 hours. What is the speed of the boat?

The key is to teach students to slow down, reread the question, and visualize what is happening. This will also decrease the chance for random number picking and help students understand the problem.

Teach your students strategies for solving the word problems with these simple steps: – Underline the question. – Circle the key numbers. – Draw a picture. – Write a number sentence. – Explain the answer.

3. Step-by-Step Solutions

Angle measure and plane figures 3. Midpoints and segment bisectors If ΔABC ≅ ΔDEF and AB is in ΔABC and DE is in ΔDEF, then AB corresponds to DE. A midpoint is equidistant from an endpoint. A segment bisector is the line or line segment that passes through the midpoint and is perpendicular to a segment at its midpoint. On p. 30 of the prototype. Construct a midpoint of a segment using a compass (p. 41) and straightedge. Discover/develop figures and illustrate concepts using technology component. (Copy into Word.) Exploration: (Use compass and straight edge or dynamic geometry software) Given a segment, locate the midpoint. How do you know that it is the midpoint? How many segment bisectors could a segment have? Justify your answer by constructing a segment and then constructing the line that is perpendicular to the segment at its midpoint. Repeat this process constructing several lines to different points on the original segment. Now construct a line that is not perpendicular to the segment and passing through the segment’s midpoint. How does this line compare to your others? Now construct a segment and then construct another segment that is the same length with one endpoint coinciding with the midpoint of the original segment. Do the two segments lie on top of one another? How do you know? What can you conclude about the congruence of segments? (Use notes for answers)

4. Practice Exercises

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6. There are several rectangular pools with the same perimeter as the patio below. Draw as many possible shapes for the pools on the grid. Then choose one of the pools and find its area. How do you know the area of the pool you chose is maximized? Patio: 10×14 Answer:

5. Maria makes an 8 quart fruit punch by mixing together 2 quarts of grape juice, 3 quarts of orange juice, and some pineapple juice. She uses the same amount of pineapple juice as grape juice. How much pineapple juice does she use? Answer:

4. Sou Vang draws a rectangle on a coordinate grid as shown. Explain how you can find the area of the rectangle by examining the coordinates of the vertices. Then find the coordinates of the fourth vertex and the area of the rectangle. Coordinates: (3,3) (7,3) (7,1) Answer:

3. Amir built a small rectangular fish pond with a length of 5 feet and a width of 4 feet. He plans to surround the pond with a cement walking strip of uniform width as shown. If Amir wants the area of the walkway to be equal to the area of the pond, how wide should Amir build the walkway? Answer:

2. Christian built a rectangular picture frame with an area of 15 square feet. What could the length and width of his frame be? Draw a picture or diagram of each possible rectangle. Answer:

1. Mrs. Gibbons bought a new rug. The rug is 4 feet wide and 8 feet long. If she buys 2 more rugs of the same size, what is the total area the three rugs take up? Answer:

Solve each problem. Check your work with a partner. All work should be shown.

4. Practice Exercises

Lesson 1 Grade 3

5. Conclusion and Review

In conclusion, we have reviewed what multiplication is, and how can we show multiplication using equal groups, arrays, and the distributive property. We also explored strategies to help us multiply factors up to 10. In this investigation, we built on many of the concepts from throughout Grade 3. For example, drawing arrays to represent numbers, distributed numbers using the place value chart, and using properties of operations (the Commutative and Associative Properties) all have their roots in work that was first explored during the earlier part of this school year. All of these experiences are enriching our depth of understanding of these concepts and of students’ flexibility with numbers. As always, we want students to be able to select the best strategy to fit the numbers they are working with, and their new knowledge about multiplication will help to clarify when it might be best to multiply, as opposed to add. Now we are ready to go back and look at The Distributive Property and multiplication of two-digit numbers, using the same place value strategies that were so effective in this investigation. Primarily though, through completing this investigation we are starting to have a clearer understanding of the relationship between addition and multiplication, and how the two operations are related.