Description

The number of square units needed to fill up a region on a flat surface.
The distance around a figure on a flat surface.
A combination of individual terms separated by plus or minus signs.
The result of a multiplication problem.
Multiplying these two numbers will give you a product.
A graph representing categorical data with rectangular bars.
A graphical display of data where the data is grouped into ranges and then plotted as bars.
A special table where each data value is split into a “stem” (the first digit/digits) and “leaf” (the last digit).
A graphical display of data that has an order and can be placed on a small number line.
A diagram used to compare and contrast two or more things.
The distance of the number from zero.
The comparison of two numbers by division.
A ration that compares a number out of 100.
To reduce an expression.
Consists of a numerator and a denominator.
To make larger.
To make smaller.
Chapter 3 Chapter 4 4 Opening 4.1.1 4.1.2 4.1.3 4.2.1 4.2.2 4.2.3 4.2.4 4 Closure Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Reference Teacher Lesson (ENG) Lección (ESP) Answers Teacher Notes My Notes Sharing [Hide Toolbars] Core Connections, Course 1, Chapter 4 Closure. Reflection and Synthesis. What have I learned? The activities below offer you a chance to reflect about what you have learned during this chapter. As you work, look for concepts that you feel very comfortable with, ideas that you would like to learn more about, and topics you need more help with. 1. SUMMARIZING MY UNDERSTANDING This section gives you an opportunity to show your understanding of how to enlarge and reduce figures and how to use ratios, two of the main ideas of this chapter. Team Poster picYou have learned many things in this chapter: how to enlarge and reduce figures while maintaining their shapes, how to use ratios to describe relationships between shapes of different sizes, how to use ratios in other contexts, and how to find the value of an unknown variable in a specific situation involving a ratio. This section gives you an opportunity to demonstrate what you know so far about these concepts. Today you and your team will create a poster that illustrates the skills and knowledge that you have developed in these areas. Brainstorm Situations: Follow your teacher’s instructions to brainstorm a list of different situations where a ratio could be used to answer a question. Situation Descriptions: Work with your team to think of four different situations for which a ratio could be used. Then each person should write a description of one of the situations and suggest a ratio to use for the situation. Be sure to provide enough information so that someone unfamiliar with the situation would understand what you mean. Write a Problem: Follow your teacher’s instructions to select one situation randomly. Then work with your team to use that situation to write a problem. Remember that you will need to provide all of the necessary information and details for someone else to be able to solve the problem. Show your problem to your teacher before the next step. Solve Your Problem: Now your team should find the answer to your problem. This should include writing a ratio and then showing how to get the answer. Be sure to include your reasoning for your process and enough of your steps that anyone looking at them will know what you did. Team Poster: Follow the model above to label and construct the sections of your poster from the pieces that your team has created. Decide together on a creative title for your poster. 2. WHAT HAVE I LEARNED? Doing the problems in this section will help you to evaluate which types of problems you feel comfortable with and which ones you need more help with. Solve each problem as completely as you can. The table at the end of this closure section provides answers to these problems. It also tells you where you can find additional help and where to find practice problems like them. CL 4-85. Draw a number line and place a point for each of the following portions on it. 0.003 30% 0.75 CL 4-86. Evaluate the following algebraic expressions. Find the value of 7m + 9 for m = 2. Find the value of a · b for a = 10 and b = 4. CL 4-87. Write an expression to represent the length of each of the ropes shown below. Then find the length of each rope if x = 20, j = 10, and k = 7. pic pic CL 4-88. Simplify each expression. CL 4-89. Copy the dot pattern below and draw Figures 0, 4, and 7. Write an expression to describe how the pattern is growing. CL 4-90. Draw a right triangle on graph paper that has a base of 4 units and a height of 2 units. Enlarge it so that each side is 2.5 times as long as the original. CL 4-91. Describe how each of the following enlargement or reduction ratios would change the size of a photograph. The given ratios are from the new figure to the original figure. CL 4-92. Use a coordinate grid to plot the points (−2, 3) and (4, 5). Then plot two more points so that all four points form vertices of a rectangle with a horizontal length. Next, find the length of each side. Write an absolute value expression to show how you calculated each length. CL 4-93. For each of the problems above, do the following: Draw a bar or number line that represents 0 to 10. Color or shade in a portion of the bar that represents your level of understanding and comfort with completing that problem on your own. If any of your bars are less than a 5, choose one of those problems and do one of the following tasks: Write two questions that you would like to ask about that problem. Brainstorm two things that you DO know about that type of problem. If all of your bars are at 5 or above, choose one problem and do one of these tasks: Write two questions you might ask or hints you might give to a student who was stuck on the problem. Make a new problem that is similar and more challenging than that problem and solve it. 3. WHAT TOOLS CAN I USE? You have several tools and references available to help support your learning: your teacher, your study team, your math book, and your Toolkit, to name only a few. At the end of each chapter, you will have an opportunity to review your Toolkit for completeness. You will also revise or update it to reflect your current understanding of big ideas. The main elements of your Toolkit should be your Learning Log, Math Notes, and the vocabulary used in this chapter. Math words that are new appear in bold in the text. Refer to the lists provided below and follow your teacher’s instructions to revise your Toolkit, which will help make it useful for you as you complete this chapter and as you work in future chapters. Learning Log Entries Lesson 4.1.3 - Variable Lesson 4.2.2 - Enlarging Figures Lesson 4.2.3 - Ratios Math Notes Lesson 4.1.1 - Dividing Lesson 4.1.2 - Mixed Numbers and Fractions Greater than One Lesson 4.1.3 - Adding and Subtracting Mixed Numbers Lesson 4.2.1 - Using Variables to Generalize Lesson 4.2.2 - Evaluating Algebraic Expressions Lesson 4.2.4 - Ratios Mathematical Vocabulary The following is a list of vocabulary found in this chapter. Some of the words have been seen in a previous chapter. The italicized words are new to this chapter. Make sure that you are familiar with the terms below and know what they mean. Click on the word for a "pop-up" definition. For more information, refer to the glossary or index. You might also add these words to your Toolkit so that you can reference them in the future. algebraic expression enlarge equivalent expressions equivalent fractions equivalent ratios expression evaluate ratio reduce similar figures substitution variable vertex (vertices) Answers and Support for Closure Problems What Have I Learned? Note: MN = Math Note, LL = Learning Log Problem Solution Need Help? More Practice CL 4-85. pic Section 3.1 MN: 3.1.5 LL: 3.1.4 and 3.1.5 Problem CL 3-138 and 4‑74 CL 4-86. 7(2) + 9 = 14 + 9 = 23 10 · 4 = 40 Section 4.1 MN: 4.2.1 Problems 4-29, 4-39, and 4-83 CL 4-87. x + x + x + x + 9 or 4x + 9; 89 j + j + k + 11 or 2j + k + 11; 38 Section 4.1 MN: 4.2.2 LL: 4.1.3 Problems 4-7, 4-29, 4-39, and 4-82 CL 4-88. 16 6 6 Lessons 3.2.3 and 3.2.4 MN: 3.2.4 LL: 3.2.3 Problems 3-128, 4-37, 4-42, and 4-60 CL 4-89. pic Two dots are added to each figure: one on the far right and one on the top. (n + 2) + n Lesson 1.1.3 Problems CL 1-95, CL 2-92, 3-20, and 4-59 CL 4-90. pic Section 4.2 LL: 4.2.2 Problems 4-47, 4-58, and 4-70 CL 4-91. Each of the sides would get a lot (more than 7 times) longer. Each of the sides would get a little bit longer. Each of the sides would get a little bit shorter. Each of the sides would stay exactly the same length. Section 4.2 LL: 4.2.2 and 4.2.3 Problems 4-54 and 4-70 CL 4-92. Points: (−2, 5) and (4, 3) Length: pic units Width: pic units Lessons 3.2.3 and 3.2.4 MN: 3.2.4 LL: 3.2.3 Problems 3-128, 3-129, 4-42, and 4-60 [Hide Toolbars] Tools ▲ Calculators ▲ Translate CPM Tutorials CPM Help CPM Assessment © 2015 CPM Educational Program. All rights reserved. Privacy Policy variable close A symbol used to represent an unknown number.
Replacing one symbol with a number.
When two or more ratios, fractions, or expressions have the same value.
Two or more straight lines on a flat surface that do not intersect.
A polygon with four sides.
A polygon with three sides.
A quadrilateral with at least one pair of parallel sides.
A number that consists of an integer and a fraction.
A ratio comparing two quantities with different units.
A rate with a denominator of 1.
To find the numerical value of.

Customize
Add, edit, delete clues, and customize this puzzle.

Laundry

Crossword

Wearable

Crossword

Frequently Asked Questions

What is a crossword?

Crossword puzzles have been published in newspapers and other publications since 1873. They consist of a grid of squares where the player aims to write words both horizontally and vertically.

Next to the crossword will be a series of questions or clues, which relate to the various rows or lines of boxes in the crossword. The player reads the question or clue, and tries to find a word that answers the question in the same amount of letters as there are boxes in the related crossword row or line.

Some of the words will share letters, so will need to match up with each other. The words can vary in length and complexity, as can the clues.

Who is a crossword suitable for?

The fantastic thing about crosswords is, they are completely flexible for whatever age or reading level you need. You can use many words to create a complex crossword for adults, or just a couple of words for younger children.

Crosswords can use any word you like, big or small, so there are literally countless combinations that you can create for templates. It is easy to customise the template to the age or learning level of your students.

How do I create a crossword template?

For the easiest crossword templates, WordMint is the way to go!

Pre-made templates

For a quick and easy pre-made template, simply search through WordMint’s existing 500,000+ templates. With so many to choose from, you’re bound to find the right one for you!

Create your own from scratch

  • Log in to your account (it’s free to join!)
  • Head to ‘My Puzzles’
  • Click ‘Create New Puzzle’ and select ‘Crossword’
  • Select your layout, enter your title and your chosen clues and answers
  • That’s it! The template builder will create your crossword template for you and you can save it to your account, export as a word document or pdf and print!

How do I choose the clues for my crossword?

Once you’ve picked a theme, choose clues that match your students current difficulty level. For younger children, this may be as simple as a question of “What color is the sky?” with an answer of “blue”.

Are crosswords good for students?

Crosswords are a great exercise for students' problem solving and cognitive abilities. Not only do they need to solve a clue and think of the correct answer, but they also have to consider all of the other words in the crossword to make sure the words fit together.

Crosswords are great for building and using vocabulary.

If this is your first time using a crossword with your students, you could create a crossword FAQ template for them to give them the basic instructions.

Can I print my crossword template?

All of our templates can be exported into Microsoft Word to easily print, or you can save your work as a PDF to print for the entire class. Your puzzles get saved into your account for easy access and printing in the future, so you don’t need to worry about saving them at work or at home!

Can I create crosswords in other languages?

Crosswords are a fantastic resource for students learning a foreign language as they test their reading, comprehension and writing all at the same time. When learning a new language, this type of test using multiple different skills is great to solidify students' learning.

We have full support for crossword templates in languages such as Spanish, French and Japanese with diacritics including over 100,000 images, so you can create an entire crossword in your target language including all of the titles, and clues.