1st Grade - Gateway 1

The materials reviewed for enVision Mathematics Grade 1 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. 

The series is divided into topics that include a Topic Assessment, available for online and/or paper and pencil delivery, and a Topic Performance Task. Additional assessments include a Grade 1 Readiness Test; Basic-Facts Timed Tests; four Cumulative/Benchmark Assessments addressing Topics 1–4, 1–8, 1–12, and 1–15; and Progress Monitoring Assessments A–C. Assessments can be found in the digital teacher interface and the Assessment Sourcebook online or in print. The materials also include an ExamView Test Generator that allows teachers to build customized tests. 

Examples of items that assess grade-level content include:

• Topic 9, Assessment, Problem 2, “Choose two ways to compare the place-value blocks. Explain.” Students choose amongst the following five answers: 76 > 73; 73 has fewer ones than 76. 73 < 76; 73 has fewer ones than 76. 73 > 76; 73 has fewer ones than 76. 73 = 76; 73 and 76 have the same number of tens. 76 < 73; 76 has more ones than 73. (1.NBT.3)

• Topic 10, Performance Task, Problem 4, “The farm has 34 sheep in a barn. There are 18 sheep outside the barn. How many sheep are there in all? Part A Draw blocks to help you solve the problem. Part B Write an equation that matches the story.” (1.NBT.4)

• Topic 13, Online Assessment, Problem 2, “Which clock shows the same time as the clock face?” Students match the time shown on an analog clock to the time shown on a digital clock. (1.MD.3)

• Topics 1–8, Cumulative/Benchmark Assessment, Problem 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)

The materials reviewed for enVision Mathematics Grade 1 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The 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. During Independent Practice, students work with problems in various formats to integrate and extend concepts and skills. The Problem Solving section includes additional practice problems for each of the lessons. Examples of extensive work with grade-level problems to meet the full intent of grade-level standards include:

• In Topic 6, Lessons 6-1 through 6-3, students engage in extensive work with grade-level problems to meet the full intent of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another). In Lesson 6-1, Visual Learning Bridge, students use tally marks to organize data into three categories: black, red, and blue. In Lesson 6-2, Independent Practice, Problems 2-5, students use data given in a tally chart, entitled “Favorite Rainy Day Activity,” to answer questions about the data. In problem two students use the tally chart to create a picture graph.“3. Which activity is the favorite? 4. How many students chose Read? 5. Higher Order Thinking Look at the picture graph you made for Item 2. Write two sentences that are true about the data.” For problem two students use the tally chart which shows three images in columns labeled: Games, Paint, and Read, to create a picture graph. In Lesson 6-3, Reteach to Build Understanding, Problems 1-3, students organize data from a tally chart into a picture graph and answer questions about the data presented. For problem one students use the tally chart which shows three images in columns labeled: Apple, Carrot, and Banana, to create a picture graph.  “2. Look at the picture graph above. How many students chose apple? students How many students chose banana? students 3. Compare data. How many more students chose carrot than apple? Subtract to find the answer.” Given is the subtraction equation: “___ - ___ = ___ more students”

• In Topic 8, Lessons 8-2, 8-6, and 8-7, students engage in extensive work with grade-level problems to meet the full intent of 1.NBT.2 (Understand that the two digits of a two-digit number represent amounts of tens and ones). In Lesson 8-2, Game: Gobbling Globs - Tens and Ones, students gobble globs to reach a target number. For example, to reach the target number of 23, students click to direct a bubble in the direction of small yellow blobs (worth 1 point) and larger pink blobs (worth 10). In Lesson 8-6, Independent Practice, Problems 3 and 4, students count/write the number of tens and ones given arrangements of counters, draw models and write two ways to break apart two-digit numbers. “3. Draw models and write two ways to break apart 59.”  Provided are two empty boxes and two fill-in-the-blank sentences, that both say “59 is ___ tens and ___ ones.” “4. Show two ways to break apart 44.” Provided are two fill-in-the-blank sentences, that both say “44 is ___ tens and ___ ones.” In Lesson 8-7, Independent Practice, Problem 4, students show all the ways a number can be shown as tens and ones. “Seth wants to show 33 as tens and ones. What are all the ways?”

• In Topic 12, Lessons 12-1, 12-2, and 12-4, students engage in extensive work with grade-level problems to meet the full intent of 1.MD.1 (Order three objects by length; compare the lengths of two objects indirectly by using a third object). In Lesson 12-1, Enrichment, students fit a paintbrush, chalk, eraser, and a tube of paint into an art supplies case. Pictured is the partitioned case, which has one section for each item. Students also determine which object is the shortest and the longest. In Lesson 12-2, Additional Practice, Problem 7, students explain how candle B can be used to find out if candle A is shorter or taller than candle C. Pictured are three candles of different heights labeled A, B, and C. In Lesson 12-4, Guided Practice, Problem 2, students decide between using one item or two items in order to measure a third item. “Circle whether you need just straws or the straws and a string to measure the length of each object. Then measure. about ___ straws.” Students are shown a picture of a big marker.

• In Topic 15, Lessons 15-1 through 15-4, students engage in extensive work with grade-level problems to meet the full intent of 1.G.3 (Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares). In Lesson 15-1, Problem Solving, Problem 17, students determine which objects are divided into equal shares.“17. Be Precise Ruth picks a flag with equal shares. Which flag did she pick? Circle the correct flag.” Pictured are two flags: one divided into two equal shares and the other divided into two unequal shares. In Lesson 15-2, Independent Practice, Problem 5, students color various shapes to represent “one half,” “one quarter,” and “one fourth.” Problem 5 shows a rectangle, circle, and a square equally divided into fourths and prompt “one quarter green.” In Lesson 15-3, Convince Me!, students reason about the relative size of decomposing a shape into more equal shares. “David has a sandwich. Is half of the sandwich more or less food than one fourth of the sandwich? Explain.” In the Guided Practice, Problem 4, students circle the shape with more equal shares and put an “x” on the shape that has larger equal shares. Provided for Problem 4 are two rectangles divided into equal parts and the labels “quarters” and “halves.”In Lesson 15-4, Problem Solving, Performance Task, Problems 5-7, students model, reason, and explain in response to questions that involve the situation, “Pizza Shares Kim cuts a pizza into 4 equal shares. She gives half of the pizza to Stephen.” They draw a picture to show the shares of pizza that Stephen has, they reason about how many shares are left when Kim gives half to Stephen “___ out of ___ shares are are left”, and they explain how one can find the number of shares left if Kim shared only 1 share of pizza.

The materials reviewed for enVision Mathematics Grade 1 meet expectations for that, when implemented as designed the majority of the materials address the major clusters of each grade. The materials devote at least 65% of instructional time to the major clusters of the grade.

• 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 the major work) is 117 out of 145, which is approximately 81%.

A lesson-level analysis is most representative of the 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 materials focus on the major work of the grade.

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

Materials are designed so that supporting standards/clusters are connected to the major standards/ clusters of the grade. These connections are listed for teachers within the Teacher’s Edition, Lesson Overview, Coherence, Cross-Cluster Connections on a document titled “Lessons and Standards” found within the Course Guide tab for each unit. Connections are also listed in a document titled “Scope and Sequence.” Examples of connections include:

• Topic 6, Lesson 6-3 connects the supporting work of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.) to the major work of 1.OA.2 (Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20). In Independent Practice, Problems 5-8, students use data in a three-category tally chart to create a picture graph and answer questions about favorite colors. “5. How many more students like purple than red? ___  more students. 6. Which color is the favorite of the most students? 7. Algebra 2 students changed their vote from blue to red. Use this equation to determine how many fewer students like red than purple. ___ + 6 = 8 ___ fewer students. 8. Higher Order Thinking Write and answer a question about the data in the picture graph.”

• Topic 13, Lessons 13-3 and 13-5 connect the supporting work of 1.MD.3 (Tell and write time in hours and half-hours using analog and digital clocks.) to the major work of 1.NBT.2 (Understand that the two digits of a two-digit number represent amounts of tens and ones). In Lesson 13-3, Problem Solving, Problem 15, students indicate “one hour after 5 o’clock” on an analog clock. “Karen starts playing soccer one hour after 5 o’clock. Draw the hour and minute hands on the clock to show what time Karen starts playing soccer. Then write a sentence about an activity you might do at that time.” In Lesson 13-5, Problem Solving, Problem 12, students match the time shown on an analog clock (2:30) with one of four digital clocks. “Which clock below shows the same time as the clock face?”

• Topic 14, Lesson 14-4 connects the supporting work of 1.G.2 (Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.) to the major work of 1.OA.2 (Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20). In Solve & Share, students use a parallelogram, trapezoid, and triangle to make a hexagon. “Fill in the hexagon by coloring it in to make the shapes below. How many of each shape do you use? Then add the three numbers to find how many shapes you color in all. See if you can make the hexagon with less than 15 pieces in all!”

The materials reviewed for enVision Mathematics Grade 1 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

There are connections from major work to major work throughout the grade-level materials, when appropriate. These connections are listed for teachers in the Topic Overview, Scope and Sequence, and Teacher Guides within each topic. Examples include:

• In Topic 1, Lessons 1-1 and 1-4, students solve problems using addition and subtraction and write equations. In Lesson 1-1, Guided Practice, Problem 1, the directions state, “Solve. Use cubes to help. How many cows now?” The materials show a picture of 3 cows, a picture of 3 cows that join, and the traceable equation "3 + 3 = 6 cows.” In Lesson 1-4, Guided Practice, Problem 2, the directions state, “Solve. Use cubes to help. Write a subtraction equation.  There are 7 bunnies. 1 bunny hops away. How many bunnies are left?” The materials show a picture of 7 bunnies as 1 of the bunnies darts off and the development of the equation “___ \bigcirc ___ \bigcirc ___ bunnies”. This connects the major work of 1.OA.A (Represent and solve problems involving addition and subtraction) to the major work of 1.OA.D (Work with addition and subtraction equations).

• In Topic 5, Lesson 5-6, Interactive Practice Buddy, Problems 1 and 4, students represent and solve problems involving addition and subtraction within 20. Problem 1 states, “Sal has 7 more magazines than Gemma. Sal has 16 magazines. How many magazines does Gemma have?” The materials provide fill-in-the-blank fields within the partial equation “7 + ▭ = ▭” and the statement “Gemma has ▭ magazines.” The materials show a table entitled “Sal’s magazines.” The first row of the table indicates 16; the second row of the table indicates “?” for Gemma’s magazines and “7” for “7 more magazines.”  Problem 4 states, “Ashlyn had some grapes. She gives 5 grapes to Anna. Now Ashlyn has 7 grapes. Enter how many grapes Ashlyn had before.” Students fill in the blank within the sentence, “Ashlyn had ▭  grapes before.” This connects the major work of 1.OA.A (Represent and solve problems involving addition and subtraction) to the major work of 1.OA.C (Add and subtract within 20). 

• In Topic 7, Lesson 7-4, Independent Practice, Problems 4–6, students count by tens and count by ones from different starting points. The directions state, “Write the numbers to continue each pattern. Use a number chart to help you.” In Problem 4, students extend the pattern,  “Count by 10s. 10, 20, 30” through 120. In Problem 5, students extend the pattern “Count by 10s. 35, 45, 55” through 115. In Problem 6, students extend the pattern “Count by 1s. 102, 103, 104” through 113. This connects the major work of 1.NBT.A (Extend the counting sequence) to the major work of 1.NBT.B (Understand place value).

• In Topics 10 and 11, students use number lines, hundred charts, place value blocks, and connecting cubes to add and subtract. In Lesson 10-5, Reteach to Build Understanding, Problem 1, the materials state, “You can use blocks to add. You can draw the blocks to show your work. Find 34 + 20. Draw blocks to help you add. Use lines for tens and dots for ones. Show how to add the tens. Then add the ones. 34 + 20 = ___ .” In Lesson 11-1, Independent Practice, Problem 3, the materials show eight groups of ten place value blocks, 3 of them crossed out, that students use to complete the equations “___ tens - ___ tens = ___ tens and ___ - ___ = ___.”  This connects the major work of 1.NBT.B (Understand place value) to the major work of 1.NBT.C (Use place value understanding and properties of operations to add and subtract). 

Given their content focus, the supporting work of grade-level standards 1.MD.B (Tell and write time), 1.MD.C (Represent and interpret data), and 1.G.A (Reason with shapes and their attributes) are not connected.

The materials reviewed for enVision Mathematics Grade 1 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. 

Prior and Future connections are identified within the Teacher Edition Math Background: Focus, Math Background: Coherence, and Lesson Overview. Examples of connections to future grades include:

• Topic 2 connects 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on, making ten, decomposing a number leading to a ten, using the relationship between addition and subtraction, and creating equivalent but easier or known sums) to the work of future grades. In Topic 2, “students practice a variety of strategies to find sums to 10.” In Grade 2, Topic 1, students will “develop fluency with addition and subtraction within 20 … In Topics 4 and 6, students will develop fluency with addition and subtraction within 100.”

• Topic 8, Lessons 8-1 and 8-2 connect 1.NBT.2 (Understand that the two digits of a two-digit number represent amounts of tens and ones) to the work of future grades. “In Lesson 8-1, students understand that 10 can be thought of as a bundle of 10 ones, which is called a ‘ten.’ Students learn that each number from 11 to 19 has 1 ten and some ones. In Lesson 8-2, students show groups of 10 with connecting cubes, and count by 10s to find how many in all. They understand that numbers made with only groups of 10 have some tens, but no leftover ones.” In Grade 2, Topics 3 and 5, students will “extend their understanding of addition and subtraction of 2-digit numbers, using a variety of strategies. In Topics 4 and 6, they will develop fluency with adding and subtracting within 100.”

• Topic 12, Lessons 12-1 and 12-2 connect 1.MD.1 (Order three objects by length; compare the lengths of two objects indirectly by using a third object) to the work of future grades. In Lesson 12-1, students “compare and order the length of three objects to determine which is longest and which is shortest.” In Lesson 12-2, “students compare the length of two objects to determine which is longer or shorter. They indirectly measure two objects by using a third object to compare them.” In Grade 2, Topic 12, students will “use standard measurement units such as inches, feet, centimeters, and meters, to determine and compare the lengths of objects.”

Examples of connections to prior knowledge include:

• Topic 3, Lessons 3-1 - 3-4 connect 1.OA.5 (Relate counting to addition and subtraction) to the work of previous grades. In Kindergarten, Topics 6 and 7,  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 the Kindergarten, students fluently added and subtracted within 5.” “In Lesson 3-1 and 3-2, students count on to add within 20. … In Lessons 3-3 and 3-4, students learn to recognize doubles and near doubles when they add within 20.”

• Topic 10, Lesson 10-2 connects 1.NBT.5 (Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used) to the work of previous grades. In Kindergarten, Topic 11, “students used cubes to model numbers to 100 and used a hundred chart to count by ones and tens.” In this lesson, students “find numbers that are 10 more than a given two-digit number by using models, mental math, and addition equations. They connect adding 10 to a number to basic addition facts.”

• Topic 14, Lessons 14-1 - 14-3 connect 1.G.1 (Distinguish between defining attributes versus non-defining attributes; build and draw shapes to possess defining attributes) to the work of previous grades. In Kindergarten, students “learned to distinguish between 2-D and 3-D shapes and describe them as flat or solid.” In Lesson 14-1, students “identify attributes of 2-D shapes: number of sides, number of vertices, and being closed.” In Lesson 14-2, students learn to distinguish “between defining and non-defining attributes of a shape.” In Lesson 14-3, students “use defining attributes to build and draw shapes.”