1st Grade - Gateway 1

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations that they assess grade-level content. Above grade-level assessment items are present and all but one assessment could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

The series is divided into topics with an assessment for each topic that can be delivered online and/or paper and pencil, and a topic performance assessment. Additional assessments include a Kindergarten Readiness Test and four Cumulative/Benchmark Assessments addressing Topics 1-4, 1-8, 1-11, and 1-15. Assessments can be found in the Assessment Resource Book online or in print. The materials also include an ExamView Test Generator. Examples of grade-level assessment items include:

• Topic 2, Topic 2 Assessment, Item 11, students solve an addition word problem, using a ten frame. “Julie has 2 cards. Michael gives her 5 more. How many cards does Julie have in all?” (1.OA.1)
• Topic 1-8 Cumulative Assessment, Item 8, “Lisa draws 7 pictures. Then she draws 9 more pictures. How many pictures does Lisa draw in all? Solve the problem. Explain the strategy you used.” (1.OA.1)
• Assessment Sourcebook, Topics 1-8 Cumulative/Benchmark Assessment, Problem 9, “Tell if the equation is True or False. 16 - 6 = 9 + 2. Explain how you know your answer is correct.”  (1.OA.7)
• Topic 9 Assessment, Item 6, “What number is 10 less than 55? What number is 10 more than 55?” (1.NBT.5)
• Assessment Sourcebook Topic 11, Topic 11 Assessment, Problem 4, “Solve the problem. Use any strategy. Explain why you picked the strategy. Write an addition equation to check your answer.  90 - 50 = ___” (1.NBT.6)

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations for spending a majority of instructional time on major work of the grade. The evidence was collected from Topics, Performance Tasks, Topic Assessments, Benchmarks, Centers, and 3-Act activities.

• The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 12 out of 15, which is 80%. 
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 87 out of 107, which is approximately 81%.
• The number of days spent on major work of the grade (including supporting work connected to major work of the grade) is 117 days of 145 days, approximately 81%.

A lesson level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each topic. As a result, approximately 81% of the instructional materials focus on major work of the grade. 

​The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The publishers identify connections between supporting content and major work in the Topic Planner pages in the Teacher Edition. For example:

Topic 6 addresses supporting standard 1.MD.4 (represent and interpret data) which connects to major work in 1.OA.1 (use addition and subtraction within 20 to solve word problems) and 1.OA.5 (relate counting to addition and subtraction). 

• Lesson 6-2, Teacher Edition, Problem Solving, Item 7, students use data from a tally chart to create a picture graph and answer the question related to the graph, “How many students voted in all?” (1.OA.5)
• Lesson 6-2, Problem Solving Reading Activity,  Teacher Edition, page 260, students answer the questions using data from the given tally chart.  Item 2, “How many more students like toast than eggs?” Item 3 “How many students like bagels or toast?”  Item 6. “How many students were surveyed in all?” (1.OA.5)
• Lesson 6-3, Independent Practice, page 263, Item 7, students use the information in the picture graph to answer, “2 students changed their vote from blue to red. Use this equation to determine how many fewer students like red than purple. ___ + 6 = 8.” (1.OA.1)
• Lesson 6-4,  Teacher Edition, Guided Practice, page 266, Item 1, students complete a picture graph as they solve the word problem: “Jim asks 9 members of his family for their favorite fruit. 6 people say they like oranges. The rest say they like apples. How many people say they like apples?” (1.OA.1)
• Lesson 6-5, Teacher Edition, Solve and Share, page 269, students complete a tally chart as they solve a word problem: “Kelly asks 12 students if they like octopuses, whales, or sharks best. The tally chart shows their responses. How many students would need to change their vote from whales to sharks to make sharks the favorite? Complete the new chart to explain.” (1.OA.1)

Topic 13 addresses supporting standard 1.MD.3 (tell and write time) which connects to major work in standards 1.NBT.1 (Count to 120) and 1.OA.5 (Relate counting to addition and subtraction). 

• Lesson 13-4, Teacher Edition, Independent Practice, Item 11, students “think about how hands move on the clock to help solve the problem. Mary writes a pattern. Then she erases some of the times. Write the missing times. 6:00, 8:00, _____, 12:00, _____.” (1.OA.5)
• Lesson 13-5, Solve and Share, page 537, students practice the counting sequence when counting the number of minutes that make up 1 hour. “The minute hand travels all the way around the clock every hour. Each little mark is 1 minute of time. Count how many minutes make up 1 hour. How many marks are there if the minute hand goes only halfway around the clock? Explain your answer.” (1.NBT.1, 1.OA.5)

Topic 14 addresses supporting standard 1.G.1 (reason with shapes and their attributes) which is connected to major work of 1.NBT.1 (Count to 120) and 1.NBT.2 (Understand that the two digits of a two-digit number represent amounts of tens and ones).  

• Lesson 14-3, Solve and Share, students solve, “Find square corners and rectangle shapes in the classroom. Tell your partner why a shape you find is a rectangle. Count how many square corners you find. Use the chart to help you keep track.” Students mark the corners on a hundred chart to count and keep track of the total number of square corners they find. (1.NBT.1)
• Lesson 14-5, Solve and Share, page 573, students solve, “Use exactly 10 pattern blocks to make a picture of a boat. Trace the shapes in the space below to show your boat. Then use what you know about tens. How many pattern blocks would you need to make 6 boats?” (1.NBT.2)

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet the expectations for the amount of content designated for one grade-level being viable for one school year in order to foster coherence between grades. 

The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. As designed, the instructional materials can be completed in 145 days. Teacher’s Edition Program Overview p.22, “Each core lesson, including differentiation, takes 45-75 minutes.”

Included are 15 topics for the grade. Each Topic is broken down into lessons which include additional resources for differentiation, additional time, and additional practice activities. Each Topic also includes an assessment (Teacher’s Edition Program Overview, page 22). For example:

• There are 107 content focused lessons.
• There are 8 days for 3-Act Math Activities.
• 30 days of Topic Reviews and Assessments.

Additional Resources that are optional and not counted in the program days include:

• Math Diagnosis and Intervention System
• 10 Step-Up to Grade 2 Lessons to use after the last topic
• Readiness Test; Review What You Know; Cumulative/Benchmark Assessment (4 in all); Progress Monitoring Assessment Forms A, B and C (3 in all)

Lessons 13-1 and 13-2 (money) are not included in the above count as they are identified as optional by the publisher in the Table of Contents, in the Teacher’s Edition Page F18.

​​The instructional materials reviewed for enVision Mathematics 2020 Common Core Grade 1 meet the expectations for being consistent with the progressions in the standards. Content from prior grades is identified and connected to grade-level work, and students are given extensive work with grade-level problems. 

The Teacher Edition contains a Topic Overview Coherence: Look Back and Look Ahead, and a Lesson Overview Coherence: Look Back and Look Ahead, which identify connections to content taught in previous grades, indicating the relevant topics and/or lessons. In addition, the sections include connections to content taught in future grades, topics, or lessons. For example, in Topic 5, the Math Background, Coherence: Look Back includes:

• “Gr K: “In Topic 4, “students began to develop an understanding of equality when they determined whether two groups of objects are equal in number and when they compared two numbers between 1 and 10.”  “In Topics 6, 7, and 8, students built a foundational understanding of addition as “put together” and “add to” and subtraction as “take apart” and “take from”.”  
• Earlier in Grade 1: “In Topics 1 and 2, students developed fluency with addition and subtraction within 10.  In Topics 3 and 4, students used strategies, properties, and the relationship between addition and subtraction to add and subtract within 20.” “In Topics 2, 3, and 4, students applied the Commutative Property, as well as doubles, near doubles, and make-10 strategies to help them learn basic addition facts. These strategies go hand-in-hand with the Associative Property to help make addition problems easier.” “In Topic 4, students continued to explore algebraic reasoning by thinking of subtraction as a missing addend problem. Students represented an unknown quantity with a question mark.”

In Topic 5, The Look Ahead, includes: 

• Later in Grade 1: “In Topic 9, students will use >,<,= to compare numbers. They will apply their understanding of equality and use the equal sign when the values on both sides of an equation are the same.” “In Topics 10 and 11, students will add and subtract within 100. Much of this content will involve working with addition and subtraction equations.”
• In Grade 2, “students will continue to work with addition and subtraction equations. They will interpret, write and complete equations as they develop fluency with addition and subtraction within 100 and practice strategies for adding and subtracting.”

The instructional materials support the progressions of grade-level standards, as evidenced by the sequencing of the topics in the curriculum. For example, in developing number concepts:

• Operations and Algebraic Thinking is addressed in Topic 1: Understand Addition and Subtraction, Topic 2: Fluently Add and Subtract Within 10, Topic 3: Addition Facts to 20: Use Strategies, Topic 4 Subtraction Facts to 20: Use Strategies, and Topic 5: Work with Addition and Subtraction Equations
• Number and Operations in Base Ten is addressed in Topic 7: Extend the Counting Sequence,  Topic 8: Understand Place Value, Topic 9: Compare 2-Digit Numbers, Topic 10: Use Models and Strategies to Add Tens and Ones, and Topic 11: Use Models and Strategies to Subtract Tens
• Measurement is addressed in Topic 12: Measure Lengths
• Time and Money is addressed in Topic 13: Time and Money, however the Money concepts do not support the progressions in the standards
• Geometry is addressed in Topic 14: Reason with Shapes and their Attributes and in Topic 15: Equal Shares of Circles and Rectangles.

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. All Topics include a topic project, and every other topic incorporates a 3-Act Mathematical Modeling Task. During the Solve and Share, Visual Learning Bridge, and Convince Me!, students explore ways to solve problems using multiple representations and prompts to reason and explain their thinking. Guided Practice provides students the opportunity to solve problems and check for understanding before moving on to the Independent Practice. During Independent Practice, students work with problems in a variety of formats to integrate and extend concepts and skills. The Problem Solving section includes additional practice problems for each of the lessons. For example:

• Lesson 1-8, Solve and Share, students solve, “5 pebbles are brown. The other pebbles are black. There are 7 pebbles in all. How many pebbles are black.” (1.OA.1)
• Lesson 9-4, Problem Solving, Problem 12, students solve, “Mary has 21 red ribbons. She has 12 yellow ribbons. Does Mary have more red ribbons or yellow ribbons? Write >, <, or = to compare the numbers.” (1.NBT.3)
• Lesson 7-2, Problem Solving, Problem 15, students solve, “Pick a number greater than 99 and less than 112. Write the number in the box. Then write the 3 numbers that come before it and the number that comes after it.” (1.NBT.1)
• Lesson 10-7, Problem Solving, Problem 10, students solve, “Jon reads 24 pages. Then he reads 27 more pages. How many pages does he read in all? Write an addition equation to show the problem.” (1.NBT.4)

The instructional materials explicitly state connections between prior grades and current grade level work. Each topic contains a Math Background: Coherence document with Look Back narratives that identify connections to what students learned in Kindergarten and previously in Grade 1: 

• Topic 3, Coherence: Look Back states, Grade K: “In Topics 6 and 7, students were introduced to various meanings of addition and subtraction. Students used objects, drawings, and equations to represent addition and subtraction word problems within 10 and to decompose numbers less than or equal to 10. By the end of Kindergarten, students fluently added and subtracted within 5. In Topic 8, students showed different ways to decompose numbers to 10. Earlier in Grade 1: “In Topic 1, students were introduced to ways to think about addition and subtraction. They solved “add to,” “put together,” “take from,” “take apart,” and “compare” problems.” “In Topic 2, students solved addition and subtraction problems to 10. They were introduced to strategies including counting on and counting back, using doubles and near doubles, adding within 5, adding to 10, adding in any order, and thinking addition to subtract.”
• Lesson 7-3, Coherence: Look Back “In Lesson 7-2, students counted by 1s to 120, beginning at any number.”
• Topic 8, Coherence: Look Back, Grade K: “In Topic 9, students were introduced to numbers greater than 10 by counting and writing numbers to 20. In Topic 10, students composed and decomposed numbers between 11 and 19 using ten frames.” Earlier in Grade 1: “In Topic 7, students read and wrote numbers to 120. They counted groups of objects by 10s.”
• Lesson 10-4, Coherence: Look Back: “In Lesson 7-5, students used an open number line to count on by 10s and 1s.”

The instructional materials reviewed for enVision Mathematics Common Core Grade 1 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

Examples of learning objectives visibly shaped by CCSSM cluster headings include:

• Topic 2, Lesson 2-6 and 2-7, Lesson Objectives, ”Count back to solve subtraction problems,” and  “Use addition facts to 10 to solve subtraction problems,” respectively. These objectives are shaped by 1.OA.C, Add and subtract within 20.
• Topic 5, Lessons 5-1 and 5-2, Lesson Objectives, “Find the unknown number in an equation,” and “Determine if addition and subtraction equations are true or false,” respectively.  These objectives are shaped by 1.OA.D, Work with addition and subtraction equations.
• Topic 8, Lessons 8-4 and 8-5, Lesson Objectives,  “Count tens and ones to find a two-digit number,” and  “Use drawings to solve problems with tens and ones,” respectively. These objectives are shaped by 1.NBT.B, Understand place value.
• Topic 12, Lesson 12-3, Lesson Objectives, “Use small same-size objects to measure length” which is shaped by 1.MD.A, Measure lengths indirectly and by iterating length units.

Materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where the connections are natural and important. For example:

• Topic 1, Lesson 1-2, Guided Practice, Problem 2, connects major clusters, 1.OA.A, Solve addition word problems to 1.OA.D, Write equations to represent the mathematics in the problem.  Students solve “1 white egg and 6 blue eggs. How many eggs in all?”
• Topic 4, Lesson 4-3, Problem Solving,  Problem 7, connects 1.OA.A, Represent and solve problems involving addition and subtraction to 1.OA.C, Add and subtract within 20, and to 1.OA.B, Understand and apply properties of operations and the relationship between addition and subtraction. Students solve, “Sage has 13 stickers. She gives 7 to her brother. How many stickers does Sage have left? How can you make 10 to solve?”
• Topic 5, Lesson  5-5, Construct Arguments, connects 1.OA.A Represent and solve problems involving addition and subtraction and 1.OA.B. Understand and apply properties of operations and the relationship between addition and subtraction. The sample classroom conversation states, “Why do you think the numbers are grouped this way? [To use the make- 10 strategy.]”