1st Grade - Gateway 2

The instructional materials reviewed for Ready Classroom Mathematics Grade 1 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. 

In i-Ready, Assess & Teach, Ready Classroom Mathematics, Classroom Resources students develop conceptual understanding. For example:

• In Lesson 11, Session 1, Explore, Try It states, “Ask How can you and your partner show 13? Listen for One partner holds up 10 fingers and the other holds up 3 fingers.” The teacher also leads a discussion about 10 fingers showing 1 group of 10 fingers building conceptual understanding of ten ones being a one bundle of ten. (1.NBT.2.a)
• In Lesson 21, Session 1 Explore, Try It states, “Use 1 Ten to Model a Number.” Each student gets 32 connecting cubes to make a model of 32 using just “one ten-train.” Students then find other ways to make 32 using two other ways (2 tens and 12 ones, 3 tens and 2 ones) building conceptual understanding of 1.NBT.2. In Session 3, Develop, students continue to use base-ten blocks to find different ways to make a given number. For example: 38 is 3 tens and 8 ones, 2 tens and 18 ones, or 1 ten and 28 ones.
• In Lesson 35, Student Worktext, Session 2, Develop, Model It states, “Draw some ways to fold the square into parts.” Three squares are shown, two are labeled equal parts and one is labeled unequal parts, helping students develop conceptual understanding of fair share. (1.G.3)

 Examples of students independently demonstrating conceptual understanding include:

• In Lesson 12, Session 2, Develop, Practice Making a Ten to Add, Problem 4, students are given 9+6 and expected to be able to make a ten to solve. (1.NBT.4)
• In Lesson 19, Session 1, Explore, Additional Practice states,  “Have children visit each station and notice how tens and ones are shown in the models. If children need additional support for the problem, have them make models using connecting cubes or counters.” On the next page students color in three ten frames to tell how many ones and how many tens. (1.NBT.2)
• In Lesson 27, Session 1 Explore, Additional Practice, Prepare For Adding Tens to Any Number, the directions state, “Think about what you know about finding 10 more. Fill in each box. Use words, numbers, and pictures. Show as many ideas as you can.” (1.NBT.2)
• In Interactive Practice, Make a Ten to Add, students add to sums greater than ten by making a ten. The interactive practice has students using ten frames, number bonds, and matching equations with sums. (1.OA.6)
• In Interactive Practice, Add Two-Digit and One-Digit Numbers, students use virtual connecting cubes to add a two-digit and one-digit number. (1.NBT.4)

The instructional materials reviewed for Ready Classroom Mathematics Grade 1 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency. The materials include problems and questions, interactive games, and math center activities that develop procedural skill and fluency and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade. 

In i-Ready, Assess & Teach, Ready Classroom Mathematics, Classroom Resources students develop procedural skill and fluency throughout the grade level. For example:

• In Lesson 4, Session 2, Develop, Connect It, Problem 3, students subtract while using addition to support the problems: “6+___=9 to help solve 9-6=___” along with completing a number bond to represent the related addition and subtraction.
• In Lesson 12, Fluency and Skills Practice states, “Fill in the number bonds to make a ten. Find 9+3.” The materials show the 9 boxed and the 3 with a number bond framed around it with the 1 and 2 decomposed so that 9 and 1 can make 10. “10+2=? and 9+3=?”.
• In Lesson 30, Session 2, Develop, Model It states, “Find the shortest and longest pencils. Lay the pencils on the table. Line up the ends. Put them in order from shortest to longest.” (1.MD.1) Students are developing the procedural skill of measuring by lining up objects evenly at one end. 

1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10) requires students to develop grade level fluency. This standard is addressed in several lessons, including:

• In Lesson 2, Session 1, Explore, Developing Fluency states, “Materials: For each child: 8 two-color counters. Why: Build fluency with adding doubles that total less than 10. How: Have children use two-color counters to copy the pairs of dot cards and find the total number of dots for each pair. Use red counters for one card and yellow counters for the corresponding card to reinforce visually the concept of duplication and doubling. Ask them what they notice about the cards in every pair.”  
• In Lesson 10, Student Worktext, Session 2, Develop, Try It states, “Hugo tries to figure out the total 4+5. He knows some other facts that can help him. What facts could help him? What is the total?”

The instructional materials provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade level. Within each lesson, there are Fluency and Skills Practice pages that children complete on their own.  Some examples of when students get opportunities to demonstrate procedural skill and fluency in the Classroom Resources include:

• In Lesson 10, Fluency and Skills Practice, the sheet provides a number of math facts with some missing sums. Students must complete the missing sums and color facts with an addend of 1 red, an addend of 2 blue, and sums of 10 green. 
• In Lesson 15, Fluency and Skills Practice worksheets are available on which students can use a number line, number bond, or other strategy to find differences such as 15-7=___.
• Learning Games which provide independent practice include:
• In Match, students match the card that has two numbers or a number and dots that are being added/subtracted to the other card that shows the correct answer. Levels Intro to Add; Addition to 3-5, 6-10, 11-15, 16-20; and Subtraction 3-5, 6-10, 11-15, 16-20 are appropriate for Grade 1.
• In Hungry Fish, students combine the numbers in the bubble together until they equal the amount shown on the fish. Levels Addition to 3-5, 6-10, 11-15, 16-20 and Subtraction 3-5, 6-10, 11-15, 16-20 are appropriate for Grade 1.
• In the Math Center Activities, there are games provided to work on facts to 10, including:
• In the Lesson 2 game Doubles and Near Doubles, students use dice to roll and double numbers covering a game board based as students play. 
• The Lesson 5 game is Match to Make a Ten, which students play like Concentration, where they put number cards face down, turn over two, and if those to add to ten it is a match. 
• In the Lesson 6 game Count on to Subtract, students use equations and counters to check their partner.

The instructional materials reviewed for Ready Classroom Mathematics Grade 1 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied. 

Opportunities for students to independently demonstrate the use of mathematics flexibly are present in a variety of contexts. The instructional materials demonstrate multiple opportunities for students to engage in routine application of mathematics of the grade level in the i-Ready, Assess & Teach, Classroom Resources, including:

• In Lesson 7, Student Worktext, Session 1, Explore, Connect It states, “1 animal drinks from a pool. More animals come. Now there are 4 animals. How many more animals came?”
• In Lesson 8, Session 1, students subtract to compare the number of objects. The materials state, “There are 4 umbrellas. There are 6 animals. Are there more animals or umbrellas? There are 5 children. There are only 3 rain hats. How many children will not have rain hats?”   
• In Lesson 17, Student Worktext, Session 2, Develop, Problem 5 states, “Aram has 11 crayons. Aram has 6 more crayons than Ray. How many crayons does Ray have?” 
• In Lesson 22, Student Worktext, Session 1, Explore states, “Rosa carries 24 books. Ryan carries 37 books. Who carries more books? Who carries fewer?” 

The instructional materials include multiple opportunities for students to engage in non- routine application of mathematical skills and knowledge of the grade level. 

For example, in Classroom Resources:

• In Lesson 7, Student Worktext, Session 2, Develop, Connect It, Problem 2 states, “There are 8 pencils. 4 are yellow. The rest are blue. How many are blue?” 
• In Lesson 14, Session 1, Explore, Try It states, “Joe picks up 7 pencils. Carla picks up 3 pencils. Pete picks up 4 pencils. How many pencils do the children pick up?” 
• In Lesson 18, Session 3, Develop, Connect It states, “Children tell what pets they have. They make a picture graph with the data. How many have dogs or cats? How many children have a bird, dog, or cat?” Non-routine problems include: “What other questions can you ask about the data? What answers can you find?”

The instructional materials reviewed for Ready Classroom Mathematics Grade 1 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.  

All three aspects of rigor are present independently throughout the program materials. The instructional materials attend to conceptual understanding, procedural skill and fluency, and application independently throughout the grade level.

Students engage in instruction to develop conceptual understanding of grade appropriate mathematics:

• In Lesson 9, Session 1, Explore, Act Out the Problem, the teacher has 6 girls and 2 boys go to one side of the room, and 4 boys and 4 girls go to the other side of the room. The teacher sets the visual model for students to see that two expressions can be compared.

Students engage in instruction to develop procedural skills and fluency appropriate for Grade 1:

• In Lesson 5, Session 1, Explore, Connect to Prior Knowledge, students practice skill and fluency using a printed copy page containing number bonds for 9. The directions state, “Why: Use mathematical reasoning about number patterns for 9 in preparation for work with number patterns that equal 10. How: Write 4 different pairs of number partners for 9 using number bonds.”

Students use mathematical understanding and skill to solve application problems:

• In Lesson 8, Student Worktext, Session 1, Explore, Problem 3 states, “Boom says there are fewer cats than dogs. Is he right? Explain.” Students must complete the problem by applying subtraction skills. 

Multiple aspects of rigor are engaged simultaneously at times to develop students’ mathematical understanding of a single topic/unit of study throughout the materials.

Examples where two or more of the aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials include:

• In Lesson 10, Student Worktext, Session 1, Explore states, “I have 8 marbles. 5 marbles are red, the rest are yellow. How many are yellow?” Students combine their conceptual understanding and application of subtraction and addition to complete this real-life problem. They must show the problem using counters and then provide an equation to accompany their work. 
• In Lesson 15, Session 2, Develop, students develop conceptual understanding of subtraction facts within 20 using a hundreds chart and a number bond. As their understanding of part/part/whole and place value develops, they also gain fluency with subtraction problems appropriate to Grade 1.
• In Lesson 2, Session 5, Refine, students develop procedural skill with addition equations, conceptual understanding with determining missing numbers, and application with solving word problems.

The instructional materials reviewed for Ready Classroom Mathematics Grade 1 meet expectations for carefully attending to the full meaning of each practice standard.  

The instructional materials attend to the full meaning of each mathematical practice in i-Ready, Assess & Teach, Ready Classroom Mathematics, Classroom Resources.

Ready Classroom Mathematics materials fully meet the intent of the following math practices:

Math Practice 1: Make sense of problems and persevere in solving them.

• In Lesson 7, Session 2, Develop, Deepen Understanding, the directions state, “MP1 Make sense of problems. Generalize: What other equation could you have used to solve this problem? Listen for children’s awareness of inverse operations and how a subtraction equation could relate to a missing addend equation.”  
• In Lesson 17, Session 2, Develop, Deepen Understanding, the directions state, “MP1 Make sense of problems. When discussing the equations and number path in Model It, prompt children to communicate how they can connect the problem to strategies and models. Generalize: Could you use addition to solve this problem? Listen for children’s understanding that the missing addend equation 6 + ? = 15 would also solve this problem.”

Math Practice 2: Reason mathematically and quantitatively. 

• In Lesson 16 Find the Unknown Number, Session 3 Develop, Deepen Understanding, the directions state, “MP2 Reason abstractly and quantitatively. Writing an equation with numerals and symbols for the unknown number requires children to think abstractly about the situation. Ask: In the equation 14-?=9 what does the 14 represent? What does the 9 represent? What does the question mark represent? Listen for, 14 is the total number of cherries in the bag at the beginning; 9 is the number of cherries left after some were eaten; the question mark shows the unknown number of cherries that were eaten.” 
• In Lesson 14, Session 2, Develop, Deepen Understanding, the directions state, “MP2 Reason abstractly and quantitatively. Generalize: In any problem with 3 addends, will the total be the same no matter how you group the addends? Listen for children’s understanding that the same three addends can be combined in any order and will still yield the same total.” 
• In Lesson 27, Session 3, Develop states, “In this session, children add two-digit numbers and multiples of ten. The purpose of this problem is to show how decomposing one addend using a number bond model can be helpful for combining the tens.” Try it, Make Sense of the Problem states, “Read the problem aloud. To support children in making sense of the problem, prompt them to identify how many balloons there are of each color. Ask What does the problem as you to find? How many red balloons are there? How many blue balloons?” Discuss it, Support Partner Discussion states, “Encourage children to name the model or strategy they used as they discuss their solutions. Support as needed with questions such as: What did you do? Can you explain why you did it that way?”

Math Practice 4: Model with mathematics.

• In Lesson 17, Session 3, Develop, Deepen Understanding states, “Jody puts some lemons in a basket. Matt puts 6 more lemons in the basket. Now there are 14 lemons in the basket. How many lemons does Jody put in?” In the Teacher book it states “MP4 Model with mathematics. When discussing the 10-frames in Model It, prompt children how to identify how they can think about the quantities in different ways. Ask: Does it matter that the 6 red counters come first in the 10-frame? Listen for: Even though the 6 more lemons come second in the word problem, it doesn’t make a difference in the total. It helps to start with 6 and add more until there are 14.” 
• In Lesson 18, Session 2, Develop, Deepen Understanding states, “What color are the pencils? How many of each color?” Teacher guidance states “MP4 Model with mathematics. As children organize and display data by sorting, counting, and making picture graphs, they make connections between different models.”
• In Lesson 27, Session 3, Develop states, “50 blue balloons and 13 red balloons. How many balloons altogether?” Teacher guidance states, “In this session, children add two-digit numbers and multiples of ten. The purpose of this problem is to show how decomposing one addend using a number bond model can be helpful for combining the tens.” Deepen Understanding Using a Number Bond to Add Two-Digit Numbers states, “Point out that number bonds can be used to decompose numbers into many pairs of number partners. Using number bonds to break apart two-digit numbers into tens and ones makes it easier to add them to a multiple of ten. Ask How can a number bond help you add a two-digit number and a tens number? Listen for I can use the number bond to break apart the two-digit number into tens and ones. 13 is a ten and 3 ones. I add the ten to 50 and get 60. Ask How does the number bond help you know how many ones to add on? Listen for After I circle 50+10, I see the 3 ones in the other square of the number bond, so I know to add 3 more. 60+3=63. Generalize How is a number bond helpful for solving this kind of problem?”

Math Practice 5: Use appropriate tools strategically.

• In Lesson 14, Student Worktext, Session 2, Develop, in the math toolkit students are given the option of using counters, ten frames, or connecting cubes to solve, “Pat collects 8 cans of food. Max collects 2 cans. May collects 4 cans. How many cans do they collect in all?”
• In Lesson 28, Student Worktext, Session 3, Develop, in the math toolkit students are given the option of using base-ten blocks, counters, ten frames, or hundred charts to solve, “Malia picks 47 apples from the tree. She gets 5 apples from the ground. How many apples does Malia have?

Math Practice 6: Attend to Precision

• In Lesson 8, Session 1, Explore, Try It, students attend to precision when deciding if there are enough umbrellas for six animals. The teacher is prompted to ask, “Are there enough umbrellas for all of the animals to have one? (No) Are there more umbrellas or more animals? How do you know? Listen for There are more animals. 2 animals didn’t get an umbrella.”
• In Lesson 23, Session 2, Develop, Apply It, students attend to precision as they draw an hour hand to show 8 o’clock and 9 o’clock. 

Math Practice 7: Look for and make use of structure.

• In Lesson 34, Session 2, the Deepen Understanding section provides guidance to ensure students can look for structure. This section states, “As children compose shapes, they are building understanding of patterns and iterating units. Encourage attention equivalency as children notice both the composite shape and the shapes that form the composite shape.”
• In Lesson 2, Session 3, Develop, Deepen Understanding, the directions state, “MP7 Use structure. Children may observe patterns and structure as they discover that any number can be doubled to make a doubles fact and that one more can always be added to make a near doubles fact.” 
• In Lesson 15, Session 2, Develop, Deepen Understanding, the directions state, “MP7 Use structure. Discuss how to decompose the lesser number when making a ten to subtract.” 

 Math Practice 8: Look for and express regularity in repeated reasoning.

• In Lesson 5, Session 2, the Deepen Understanding section provides guidance to ensure students use repeated reasoning. This section states, “When discussing the colored cube models and missing addend equations in Model It, prompt children to use a related subtraction equation.”

The instructional materials reviewed for Ready Classroom Mathematics Grade 1 meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade level mathematics. 

Student materials consistently prompt students to construct viable arguments and to analyze the arguments of others. In the Program Implementation tab, Implementation Support, Try-Discuss-Connect Routine Resources, teachers find different ways to encourage Math Practice 3 in their math classrooms. Try It provides Three Reads routine, Co-Craft Questions and Problems, and Turn and Talk routine. Discuss It provides the Turn and Talk, Collect and Display, Say It Another Way, and Compare and Connect routines. Connect It provides Collect and Display, Turn and Talk, and Say It Another Way routines. 

These routines provide students with opportunities to construct viable arguments. Examples include:

• In Lesson 7, Session 2, Develop, Connect It, Problem 2 states, “There are 8 pencils. 4 are yellow. The rest are blue. How many are blue? Buzz: 4 + 8 = ? Boom: 4 + ? = 8. Who is right and how do you know?”
• In Lesson 8, Student Worktext, Session 2, Develop, Problem 1 states, “There are 6 children. There are 4 hats. Are there more hats or children? How many children do not get a hat?” Problem 2 states, “How can subtracting help you compare the number of hats and children?” Students explain their reasoning for why they subtract in order to answer the previous question. 

• In Lesson 28, Session 3, Develop, students have opportunities to construct viable arguments when they discuss, “How would you explain 47 + 5 to a partner? Show and tell a partner how you would solve the problem. Then listen to them tell it back to you the way they understood it.”

Ready Classroom Mathematics materials give students opportunities to analyze the mathematical arguments of others. Examples include:

• In Lesson 10, Session 2, Develop, Try It states, “Lila notices patterns on the fact table. What could be some patterns she notices? Color to show patterns.” Students color their individual charts. They move to partnerships. As they look at their partners work, the student agrees or disagrees with the work of their partner.
• In Lesson 28, Student Worktext, Session 1, Explore, Problem 2 states, “Jack says 24 has 2 tens and 4 ones. Maya says 24 has 24 ones. Who is right? Why?” Students partner to use connecting cubes to model both Jack’s and Maya’s responses and discuss who was correct.
• In Lesson 13, Student Worktext, Session 2, Develop, Problem 5 states, “Boom says the equation 9 + 18 = 17 is true. Do you agree? Explain.” Students independently explain in their worktext.

The instructional materials reviewed for Ready Classroom Mathematics Grade 1 meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

In the i-Ready, Teach and Assess, Ready Classroom Mathematics, Program Implementation, Teaching and Learning Resources, there are Discourse Cards. The cards support teachers to engage students in answering questions such as “Do you agree with the strategy, answer, or explanation? Do you disagree with the strategy, answer, or explanation? What do you think about what another student said?” In Implementation Support, the Student Handbook lists the eight Mathematical Practices in student-friendly language. For example, MP3 states, “Show and explain. Share your math ideas to help others understand you.” Discuss It states, “Ask your partner: Do you agree with me? Why or why not? Tell your partner: The strategy I used to find the answer was ...” 

Ready Classroom Mathematics instructional materials support teachers to engage students in constructing viable arguments. Examples include:

• In Lesson 12, Session 1, Explore, Act Out Making a Ten states, “Read the problem aloud together. Arrange 13 or more chairs (or 13 Xs taped to the floor) in a 10-frame configuration plus others to the side to represent seats on the bus. Invite 9 children to sit down “on the bus.” Have 4 other children stand to the side. Ask If you have more children get on the bus until there are 10 on the bus altogether, how many more can get on the bus? Listen for Encourage a variety of answers then say : Let’s find out! Have 1 child sit as the class counts from 9 up to 10. Ask You don’t have all the children on the bus yet, but can you tell how many there will be? How can you tell? Listen for There are 10 seats filled, and 3 more children, for a total of 13.  Have children work in pairs to represent the problem they acted out using counters on the “bus” workmat on the Student Work Text page.”
• In Lesson 28, Session 3, Develop, Deepen Understanding states for MP3 Construct Arguments, the teacher is supported to help students articulate the steps of a problem, “Explaining the steps in an addition problem will help children articulate their understanding of a multi-step strategy. Partners will be challenged to listen to another’s strategy and tell it back in their own words.” 
• InLesson 30, Session 3, Develop, the teacher is provided with the following questions to support engaging students in constructing viable arguments, “How can you explain what you did to show Ron’s books in order?”

Ready Classroom Mathematics instructional materials support teachers to engage students in analyzing the arguments of others. Examples include:

• In Lesson 10, Session 2, Develop, Try It states, “Hugo tries to figure out the total 4 + 5. He knows some other facts that can help him. What facts could help him? What is the total?” In Discuss It, Support Partner Discussion states, “Encourage children to share their solutions and the number facts that helped them find the total.” Guiding questions for the discussion are listed: “What did you notice about your partner’s approach? Did your partner find the same total as you did? How were you sure your answer was right?”
• In Lesson 16, Session 2, Develop, the teacher is provided with the following questions to support engaging students in constructing viable arguments, “How did you get started? Can you explain your model to your partner? Did you solve this in a different way than your partner solved it?”
• In Lesson 30, Session 3, Develop, the teacher is provided with the following questions to support engaging students in analyzing the reasoning of others, “Do you agree with Buzz that the red flower is the shortest? Why or why not?”

The instructional materials reviewed for Ready Classroom Mathematics Grade 1 meet expectations that materials explicitly attend to the specialized language of mathematics. 

The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols. In the Program Implementation tab, an Academic Vocabulary Glossary is provided. This is set up with the vocabulary explicit to each unit. There is a “Build Your Vocabulary” Sheet that goes along with each unit to help develop the vocabulary within the unit. This page can be found in the Beginning of the Unit link for each unit. There is also a “Connect Language Development to Mathematics” that helps to develop language routines with students. 

The Ready Classroom Mathematics materials provide explicit instruction on the use of mathematical language in the Classroom Resources tab. Examples include:

• First Grade has 6 Units. For each unit, there is a Beginning of Unit tab. Within this tab there is a Build Your Vocabulary page and a Connect Language Development to Mathematics page. The Build Your Vocabulary page is a student work page. The Connect Language Development to Mathematics page provides information on how to use the student vocabulary page and provides a language development routine: Assess prior knowledge, Pronounce the word, Define the word, Use the word. This routine is defined in detail only in Unit 1 but is referenced in all later units.
• On the Build Your Vocabulary page, students are given two different sets of words, “My Math Words” and “My Academic Words.” The guidance provided to the teacher under the Connect Language Development to Mathematics page states, “My Math Words provides access to prior knowledge and understanding of critical math words and phrases through teacher-guided activities. My Academic Words provides an early entry point to those all-purpose academic words students will engage with throughout their study of mathematics. The Academic Vocabulary Routine provides explicit instruction and active engagement.” The Academic Vocabulary Routine directions are provided and broken up into four parts in Unit 1. The four parts listed are, “Assess Prior Knowledge, Pronounce the Words, Define the Words, Use the Words.” 
• In Lesson 9, Session 2, Develop, Develop Language states, “Why: Clarify the meaning of the phase How can you tell (if) as used to indicate knowledge about a topic. How: Read the Discuss It question a loud. Explain that the phrase how can you tell (if) means to know, notice, recognize or observe that something is a certain way. Ask questions that contain the phrase, such as: How can you tell if someone is sleepy? How can you tell if it’s cold? How can you tell if it’s lunch time?” 
• In Lesson 16, Session 2, Develop, the materials provide explicit instruction on the use of mathematical language. Teachers define the word some and examine how it is used in word problems with unknown numbers. “Ask children to circle the word some. Read the first sentence of the Try It problem and then ask: How many pies are on the table? [some] Explain that some means and unknown number or amount. Point to the groups of objects around the room and use the modifier some. Examples: Here are some books. There are some pencils in the cup. Some children are wearing sneakers.”

Ready Classroom Mathematics materials support students to learn and use precise and accurate terminology. Examples in the Classroom Resources tab include:

• There is a “Build Your Vocabulary” Sheet that goes along with each unit to help develop the vocabulary within the unit. This page can be found in the Beginning of the Unit link for each unit. 
• Lesson Vocabulary is listed on every Lesson Overview page for each section. For example, Lesson 9 Understand True and False Equations, Lesson Overview page, the following Lesson Vocabulary is listed: 
• equal sign = a symbol that means is the same as.
• equation: a mathematical sentence that uses an equal sign (=) to show that two things are equal. 

In Program Implementation tab there is:

• An Academic Vocabulary Glossary which contains the vocabulary explicit to each unit. 
• A Teacher’s Guide Table of Contents provides the overall view of each unit. In each unit there is a Build Your Vocabulary section with the vocabulary addressed in the unit.