2nd Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Partially Meets Expectations | 64% |
|---|---|
Criterion 1.1: Focus | 4 / 6 |
Criterion 1.2: Coherence | 5 / 8 |
The materials reviewed for Math Mammoth Grade 2, Light Blue Series, partially meet expectations for focus and coherence. For focus, the materials do assess grade-level content, but they partially provide all students with extensive work with grade-level problems to meet the full intent of grade-level standards. The materials partially meet expectations for coherence and consistency with the CCSSM, as they do not have content from prior and future grades connected to grade-level work. The materials partially meet expectations for making connections between clusters and domains. The materials do address the major clusters of the grade and have supporting content connected to major work.
Criterion 1.1: Focus
Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials reviewed for Math Mammoth Grade 2, Light Blue Series, partially meet expectations for focus as they do assess grade-level content, but they partially provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.
Indicator 1a
Materials assess the grade-level content and, if applicable, content from earlier grades.
The materials reviewed for Math Mammoth Grade 2, Light Blue Series, meet expectations for assessing grade-level content and, if applicable, content from earlier grades. The curriculum has a Grade 2 Tests and Cumulative Reviews section which, includes an End-of-Chapter test for each chapter, a Cumulative Review for every chapter after Chapter 1 and one End-of-the-Year test. There are assessment items that are aligned to above grade level skills, but these materials can be removed or modified without impacting the structure of the materials.
Note: The user guide identifies the tests as optional; however, the publisher orientation session identified these assessments as a required component for school use. Therefore, the tests are included in this review.
Examples of assessment items that assess grade-level content include:
Tests and Cumulative Reviews, Chapter 1 Test, Question 4, “You read 23 pages in a story book. Your friend Sally read double that many pages. How many pages did Sally read?” (2.OA.1)
Tests and Cumulative Reviews, Chapter 5 Test, Question 5, “Divide these shapes. Then color as you are asked to. d. Divide this into fourths. Color \frac{3}{4} . ” (2.G.3)
Tests and Cumulative Reviews, End of Year Test, Question 18, “Jennifer bought two vacuum cleaners for $152 each. What was the total cost?” (2.NBT.7)
Examples of mathematically reasonable assessment items that align to above-grade-level standards that could be removed or modified without impacting the structure or intent of the materials include, but are not limited to:
Tests and Cumulative Reviews, Chapter 3 Test, Question 3, “Write <, >, or =. c. \frac{1}{2} of 20 ______ \frac{1}{2} of 18” (3.NF.1)
Tests and Cumulative Reviews, Chapter 5 Test, Question 4, “Write the fraction.” Part a has a picture of a circle divided into five equal parts, one of which is colored green. Part b has a picture of a circle divided into six equal parts, five of which are colored green. (3.NF.1)
Tests and Cumulative Reviews, Chapter 10 Test, Question 5, “Multiply. a 4 x 3 =, 3 x 10 =” (3.OA.1)
Indicator 1b
Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials reviewed for Math Mammoth Grade 2, Light Blue Series, partially meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. The materials provide limited opportunities for all students to meet the full intent with grade-level-problems for the following standards including but not limited to: 2.OA.1, 2.MD.7, and 2.G.3 . The materials provide limited opportunities for all students to engage in extensive work with the following standards: 2.NBT.1a and 2.NBT.6 . and some off-grade-level work negatively impacts students’ work with grade-level content.
The materials are divided into two Worktexts, 2-A and 2-B. Each Worktext is divided into chapters. Each chapter is divided into lessons that contain content instruction, mental math problems, puzzle corners, and practice problems, in addition to chapter reviews and a chapter test.
Examples of extensive work with grade-level problems to meet the full intent of some grade-level standards include:
Worktext 2-A, Chapter 4: Regrouping in Addition, Regrouping with Tens, Question 1, students use representations of tens and ones to add with regrouping. “Circle ten cubes to make a new ten. Count the tens, including the new one. Count the ones. Write the tens and ones in their own columns. You can use manipulatives.” a. Shows a picture of three tens and three ones and a group of 9 ones. The problem is given vertically as 33 + 9, in boxes to show the place values of tens and ones. Question 2, students use more abstract representations of tens and ones to add with regrouping. “Circle ten ones to make a new ten. Add the tens and ones in columns.” Drawings of ten sticks and ones are shown, along with columns for showing addion with place value. c. A picture of three tens and five ones, and a group of nine ones and one ten is provided. The problem 35 + 19 is given in vertical format with place value names of ten and one above the place value boxes. A 1 is above the tens box to show the regrouping. Question 5. “Show the additions on the number line by drawing lines that are that long. a. 13 +9 + 11= ___.” Students use drawings, number lines, and mental strategies to add within 1000. Students engage in extensive work with grade-level problems to meet the full intent of 2.NBT.7 (Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.)
Worktext 2-B, Chapter 6: Three-Digit Numbers, Which Number is Greater?, Question 1, “Can you tell which number is more? Try! Write < or > between the numbers.” Students are shown a picture of 5 hundreds, 1 ten, 3 ones and 3 hundreds, 1 ten, and 5 ones, “d. 513 _____ 315”. Question 2, students are asked to draw hundreds, tens, and ones for the numbers. Then compare and write < or >. “a. 120 ______ 130” Question 4, “Write either < or > in between the numbers. f. 600 ___ 860” Students engage in extensive work with grade-level problems to meet the full intent of 2.NBT.4 (Compare two three-digit numbers based on meanings of hundreds, tens, and ones digits using >,=, and < symbols to record the results of comparisons.)
Worktext 2-B, Chapter 10: Exploring Multiplication, Multiplication and Addition, Question 1, students are shown an array with 3 groups of two dots, “Write an addition and multiplication sentence for each problem. a. _____ + ____ + _____ = _____ _____ x ____ = ______ Question 2, “Draw groups to match the sum. Then write a multiplication sentence. c. 5 + 5 + 5 = _____ x ____ = ______” Question 3, students are asked to fill in the blanks using the picture to solve. The problem shows 2 groups of 4 carrots, “d. ______ groups, _____ carrots in each. _____ x ______ carrots = _______ carrots _____ + ______ “ Students engage in extensive work with grade-level problems to meet the full intent of 2.OA.4 (Use additions to find the total number of objects arranged in rectangular arrays with up to 5 rows and and up to 5 columns; write an equation to express the total as a sum of equal addends.)
The materials do not provide opportunities for students to meet the full intent of most of the standards. Examples include, but are not limited to:
Students are not provided the opportunity to engage with the full intent of 2.MD.7 (Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.). Throughout the materials students do not tell and write time from digital clocks to the nearest five minutes, using a.m. and p.m.
The materials provide limited opportunities for all students to engage in extensive work with the following standards:
Students do not have the opportunity to engage in extensive work with 2.NBT.1a (100 can be thought of as a bundle of ten tens — called a "hundred."). In Worktext 2-B, Chapter 6: Three-Digit Numbers, Three-Digit Numbers, students are told that “Ten ten-pillars make ONE HUNDRED:” A picture of ten ten-pillars is set equal to one hundred flat and the equation 10 tens = 100 is written under it. Question 5, “The dots are ones, the pillars are tens. Group together 10 ten-pillars to make a hundred. b. ______ “An image is provided with 15 pillars and four dots. These are the only problems in the lesson that allow students to bundle the ten tens to make a hundred. All other problems in the lesson, which is the only lesson that addresses this standard, have students using one hundred flats. Students are provided with limited opportunities to understand that 100 can be thought of as a bundle of ten tens.
Students do not have the opportunity to engage in extensive work with 2.NBT.6 (Add up to four two-digit numbers using strategies based on place value and the properties of operations.). In Worktext 2-A, Chapter 4: Regrouping in Addition, Adding Three or Four Numbers Mentally, Question 7, “Add mentally. Think, what would the easiest order to add the numbers!”a. 30 + 2 + 40 + 8 = ______ … d. 20 +10 + 8 + 9 = ______” Students are provided with limited opportunities to use strategies based on the properties of operations.
The materials include some off-grade-level content that negatively impacts students’ work with the grade-level standards. Examples include, but are not limited to:
Worktext 2-A, Chapter 2: Clock, How Many Hours Pass?, Question 6, “a. Dad’s workday starts at 8:00 in the morning, and ends at 5PM. How many hours is Dad at work?” Students are asked to engage in solving problems involving elapsed time, which does not align to a second grade standard.
Worktext 2-A, Chapter 5: Geometry and Fractions, Comparing Fractions, Question 5, “Color. Then compare and write <, >, or =. Which is more ‘pie’ to eat?” “b. \frac{3}{4} \frac{3}{5}” This question displays two circles. One is partitioned into 4 equal parts, one into 5 equal parts. Students are asked to engage in solving problems involving comparing fractions, which does not align to a second grade standard.
Worktext 2-B, Chapter 7: Measuring, Weigh in Kilograms, Question 7, “d. Weigh yourself with and without a heavy book. I weigh ___ kg. I weigh ___ kg with a heavy book. What is the difference? ___kg. So, the book weighs ___kg.” Students are asked to engage in solving problems involving measurement with kilograms, which does not align to a second grade standard.
Criterion 1.2: Coherence
Each grade’s materials are coherent and consistent with the Standards.
The materials reviewed for Math Mammoth Grade 2, Light Blue Series, partially meet expectations for coherence. The majority of the materials, when implemented as designed, address the major clusters of the grade and have supporting content that enhances focus and coherence simultaneously by engaging students in the major work of the grade. The materials partially include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. The materials do not have content from future grades that is identified and related to grade-level work and do not relate grade-level concepts explicitly to prior knowledge from earlier grades.
Indicator 1c
When implemented as designed, the majority of the materials address the major clusters of each grade.
The materials reviewed for Math Mammoth Grade 2, Light Blue Series, meet expectations 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 number of chapters devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6 out of 10, approximately 60$$\%$$.
The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 78 out of 118, approximately 66$$\%$$.
The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 118.5 out of 168, approximately 70$$\%$$.
A day-level analysis is most representative of the instructional materials as the lessons typically cover multiple days that focus on major work of the grade. As a result, approximately 70$$\%$$ of the instructional materials focus on major work of the grade.
Indicator 1d
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The materials reviewed for Math Mammoth Grade 2, Light Blue Series, meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Materials are designed to connect supporting standards/clusters to the grade's major standards/clusters. The materials include a Common Core Alignment Document that does not provide guidance for connections between supporting and major work of the grade.
Examples of connections between supporting and major work include:
Worktext 2-A, Chapter 2: Clock, The Minutes, connects the supporting work of 2.MD.7 (Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.) to the major work of 2.NBT.2 (Count within 1000; skip-count by 5s, 10s, and 100s.) For example, Question 3, e. students are shown an analog clock showing 9:25, “Write the time using the normal clock. Remember, the numbers for the minute hand are not shown, and they go by fives!” Students skip count and write time to the nearest five minutes.
Worktext 2-B, Chapter 8: Regrouping in Addition and Subtraction, Graphs and Problems, connects the supporting work of 2.MD.10 (Draw a picture graph and a bar graph to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.) to the major work of 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.) For example, Question 1, “The table lists the eye colors of some children. Draw the bars for the bar graph. a. How many children have either brown or hazel eyes?” Students add to find the total number of children from the bar graph data.
Worktext 2-B, Chapter 9: Money, Adding Money Amounts, connects the supporting work of 2.MD.8 (Solve word problems involving dollar bills, quarters, dimes, nickels and pennies, using \$ and ¢ symbols appropriately.) to the major work of 2.OA.1 (Use addition and subtraction within 100 to solve one and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions) For example, Question 3, “Find the total cost in each case. b. Judy bought hot chocolate and a side of pizza.” Students solve a word problem involving the addition of dollar bills based on the information provided in a menu that a hot chocolate costs $$\$1.05$$ and a slice of pizza cost $$\$2.75$$.
Indicator 1e
Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.
The materials reviewed for Math Mammoth Grade 2, Light Blue Series, partially 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. Materials contain multiple connections of major work to major work throughout, however, multiple connections from supporting work to supporting work are entirely absent from the grade-level materials. Included within the materials is a Common Core Alignment document, however, the document does not provide explicit guidance for connections between or among domains and clusters.
Materials provide connections from major work to major work throughout the grade-level when appropriate. Examples include:
Worktext 2-A, Chapter 1: Some Old, Some New, Adding with Whole Tens, connects the major work of 2.OA.A (Represent and solve problems involving addition and subtraction.) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract.) For example, Question 2, “Add. Break the second number into tens and ones first. Then add the tens. b. 10 + 28 = ______ (10 + _____ + _______)” Students use place value understanding to find the sum of an addition problem.
Worktext 2-A, Chapter 3: Addition and Subtraction Facts Within 0-18, Subtract to Ten, connects the major work of 2.OA.A (Represent and solve problems involving addition and subtraction.) to the major work of 2.OA.B (Add and subtract within 20.) For example, Question 1, “Subtract the ‘ones’ that are not in the ten group. You should only have ten left! d. 13 - _____ = 10” Students solve subtraction problems within 20.
Worktext 2-B, Chapter 6: Three-Digit Numbers, Practice with Whole Hundreds, connects the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract.) to the major work of 2.MD.B (Relate addition and subtraction to length.) For example, Question 7, “a. John’s family is driving to Grandma’s place, and from there they are going to a zoo. Dad says, ‘To Grandma’s is 150 km, and from there to the zoo is 100 km.’ How far will the family drive from their home to the zoo?” Students use mental math and place value strategies to solve word problems involving lengths that are given in the same unit.
The following connections are entirely absent from the materials:
No connections are made between the supporting work of 2.OA.C (Work with equal groups of objects to gain foundations for multiplication.), the supporting work of 2.MD.C (Work with time and money), the supporting work of 2.MD.D (Represent and interpret data.) and/or the supporting work of 2.G.A (Reason with shapes and their attributes.).
Indicator 1f
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.
The materials reviewed for Math Mammoth Grade 2, Light Blue Series, do not 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. While some references to future or earlier grade work does occur in the introduction lesson, these references are limited, and are not always related to grade-level concepts or work. The materials include a Common Core Alignment Document that lists the grade-level standards addressed in each lesson, however, the document does not include information regarding the progression of the lesson standards between grade-level bands.
There are some examples of references to future grade content, however these references are not always identified and/or related to grade-level work. Examples include, but are not limited to:
Worktext 2-B, Chapter 7: Measuring, Introduction, “The concrete activities we do in second grade are laying an important foundation for familiarizing the children with measuring units. In third grade, the study of measuring turns toward conversions between the different units. In case you wonder about volume, we will study that in third grade and onward.”
Worktext 2-B, Chapter 8: Regrouping in Addition and Subtraction, Introduction, “After this, it is time to study regrouping in subtraction with three-digit numbers. There are four cases: 1. Regrouping one ten as 10 ones, such as necessary in 546 - 229. 2. Regrouping one hundred as 10 tens, such as is necessary in 728 - 441. 3. Regrouping two times (on ten as 10 ones, and one hundred as 10 tens), such as 725 - 448. 4. Regrouping with zero tens, such as necessary in 405 - 278. In second grade, we only study cases (1) and (2) from the list above. The other two cases are left for third grade.”
The materials do not reference prior grade learning, so they do not relate grade-level concepts explicitly to prior knowledge from earlier grades.
Indicator 1g
In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.