3rd-5th Grade - Gateway 3
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Teacher and Student Supports
Gateway 3 - Partially Meets Expectations | 81% |
|---|---|
Criterion 3.1: Teacher Supports | 9 / 10 |
Criterion 3.2: Student Supports | 4 / 6 |
Criterion 3.3: Intentional Design |
The materials reviewed for Takeoff by IXL Grades 3 through Grade 5 partially meet expectations for Teacher & Student Supports. The materials meet expectations for Criterion 1, Teacher Supports, and Criterion 3, Intentional Design, but partially meets Criterion 2, Student Supports.
Criterion 3.1: Teacher Supports
Information on Multilingual Learner (MLL) Supports in This Criterion
For some indicators in this criterion, we also display evidence and scores for pair MLL indicators.
While MLL indicators are scored, these scores are reported separately from core content scores. MLL scores do not currently impact core content scores at any level—whether indicator, criterion, gateway, or series.
To view all MLL evidence and scores for this grade band or grade level, select the "Multilingual Learner Supports" view from the left navigation panel.
Materials include opportunities for teachers to effectively plan and utilize with integrity to further develop their own understanding of the content.
The materials reviewed for Takeoff by IXL Grades 3 through Grade 5 meet expectations for Teacher Supports. The materials provide clear guidance through useful annotations and suggestions for enacting both student and ancillary materials. A year-long scope and sequence is provided, along with standards correlation information. Additionally, the materials explain the program’s instructional approaches, identify research-based strategies, and clarify the role of the standards. The materials provide strategies for communicating with stakeholders and suggestions to support student progress. A comprehensive list of required supplies is included, as well as multiple opportunities for assessing student learning, guidance for interpreting performance, and suggestions for follow-up instruction. The materials partially include explanations and examples of grade-level concepts and standards, along with how these connect to prior and future grade levels, supporting teacher content knowledge.
Indicator 3a
Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in engaging students to guide their mathematical development.
The materials reviewed for Takeoff by IXL Grades 3 through 5 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.
The materials offer teacher support digitally on IXL. The landing pages organize resources for planning, prepping, and teaching. These resources include instructional support for each lesson part, i.e., Instruction, Guided practice, and Independent practice. The materials also include ancillary resources, i.e., New activities; Online games; Spiral review skills; Spiral review activities; Student self-reflection activity, and a Daily planner. These resources appear in the Additional Resources section of each unit with guidance on how and when to use them. The Grade level Additional resources include a grade level at a glance: Planning and materials document. This document includes a Pacing guide that identifies the suggested time for each unit; a Manipulatives and materials section that lists manipulatives and materials needed in each unit; and a unit and lessons outline.
The materials provide annotations and suggestions connected to specific learning objectives in the lesson guides. In each Lesson, the Goals tab lists the Objective, Let’s discover, and standards addressed. The Objective identifies what students will do by the end of the lesson, and the Let’s discover section identifies the lesson’s main takeaway in student-friendly language. The Instructional context tab explains how the lesson fits into the broader sequence by connecting to content in earlier and later lessons and grade levels. Select lessons include a Concept review tab that offers a teacher-level refresher on the mathematical concepts. The Additional Supports tab includes Readiness skills that help students access the content and tips for teaching multilingual learners. The Materials section provides links to printable materials and lists any physical objects or manipulatives needed for the lesson.
Annotations within lessons provide guidance for engaging students in mathematical development. Teacher support appears in the Teacher notes, Student book screenshots with answer key, Tips for support, and Ideas for extension. Examples include:
Grade 3, Unit 4: Area, Lesson 4.4, Instruction: Relate area and the distributive property. Teacher notes state, “For #3, start by asking students why Troy needs to find 4\times13. (The rectangle has 4 rows of 13 foam mats.) Then guide students to complete the equations and find the area. Be sure they recognize that this is faster than skip counting all of the squares! The blue rectangle is 4 feet by 10 feet, so find 4\times10. Consider reminding students that they can use parentheses to group this product together. The yellow rectangle is 4 feet by 3 feet, so find 4\times3. Add the areas of the blue and yellow rectangles to find the total area. Ask students whether this strategy reminds them of something they've seen before, and surface that this is another application of the distributive property.”
Grade 4, Unit 6: Divide by 1-digit numbers, Lesson 6.4, Guided Practice, Divide using an area model, Teacher notes, Tip for support states, “If students struggle to write an equation, have them focus on the individual parts of the rectangle first. Once they find the missing parts of each rectangle, then ask them what each part of the larger rectangle represents in the division equation.”
Grade 5, Unit 6: Multiply Fractions, Lesson 6.4, Guided Practice, Multiply Fractions, Teacher notes, Idea for extension states, “For #5, encourage students to find the distance Tina ran in more than one way. For example, students could subtract the total distance and the distance Tina walked. Students could also count the sections that were shaded just once in the model. Those sections are part of the \frac{4}{5} of a mile but not part of the \frac{2}{3} that Tina walked.”
Indicator 3b
Materials contain explanations and examples of grade-level/course-level concepts and/or standards and how the concepts and/or standards align to other grade/course levels so that teachers can improve their own knowledge of the subject.
The materials reviewed for Takeoff by IXL Grades 3 through 5 partially meet expectations for containing explanations and examples of grade-level/course-level concepts and/or standards and how the concepts and/or standards align to other grade/course levels so that teachers can improve their own knowledge of the subject.
The materials provide adult-level explanations and examples of grade-level concepts so that teachers can improve their own knowledge.
Concept reviews are available in select lessons. Concept reviews provide adult-level explanations and examples of mathematical concepts. Examples include:
Grade 3, Unit 9: Time, volume, and mass, Lesson 9.8, Concept review provides teachers with adult-level information about mass and weight. “Mass and weight are often confused! They are two different measures, but they are closely related. Mass is the amount of matter in an object. The mass of any given object is constant, no matter where in the universe it is. Weight is the force that acts upon an object due to gravity. It depends on the location of the object when it is measured. This is why the same object will weigh a different amount on the moon than on Earth, but has the same mass in both locations. Grams and kilograms are metric units of mass. Colloquially, they are often also used to describe weight, but that is technically inaccurate. In third grade, students are not expected to differentiate between mass and weight, so it is not necessary to belabor the distinction. Simply keep in mind that when talking about grams and kilograms, it's best to mention mass, not weight, when you can.”
Grade 4, Unit 5: Factors, multiples, and patterns, Lesson 5.9, Concept review provides teachers with adult-level information about number patterns. “Number patterns can be described in two ways. Some number patterns, like those in Lessons 5.5 and 5.6, are described by stating the rule that you use to find the next number in the pattern. For example, you can write a pattern that starts at 1 and adds 5 every time: Some number patterns, like those in this lesson, are described by stating the rule that you use to find a number based on its position in the pattern sequence. For example, you can write a pattern whose rule is to multiply the position number by 2: It can be described by saying that the starting number is 5 and the rule is to add 5. It can also be described by saying that the rule is to multiply the position number (the input) by 5. It isn't important for students to switch between both of these ways to describe number patterns at this point, but it is important that students are able to work with both types of descriptions.”
Grade 5, Unit 2: Whole number division, Lesson 2.6, Concept review provides teachers with adult-level information about using the standard algorithm. “Dividing using the standard algorithm is conceptually and procedurally similar to dividing using partial quotients. The standard algorithm is more compact, however, allowing students to divide more efficiently. For example, consider finding 276\div12. With both the partial quotients method and the standard algorithm, you find a multiple of the divisor, subtract it from the dividend, and repeat this process by subtracting a multiple of the divisor from the remainder. In other words, you divide in stages. With the partial quotients method, you can choose to start by subtracting 12\times10=120 as many times as possible (twice). You can record the 2 groups of 120 separately. For each group, you subtract 120, write its factors on the side, and record the remainder underneath. With the standard algorithm, you use place value to help you record both groups of 120 in one step. Think about 120 as 12 tens, and notice that 276 has 27 tens in it. So you can start by subtracting 2 groups of 12 tens, or 24 tens. Record a 2 in the tens column at the top and the 24 tens at the bottom. Subtract to see how many tens are left, and then bring down the 6 ones to find the remainder. Now divide 36 into as many groups of 12 as possible. Notice that with both methods, you can record your work in one step. With the partial quotients method, you record the 3 groups by subtracting 36, writing its factors on the side, and recording the remainder of 0 at the bottom. With the standard algorithm, you record a 3 in the ones place above 276, and subtract 3\times12=36 from 36 to show that the remainder is 0. Last, find the quotient. With the partial quotients method, add the factors on the right to get 23 and record it above 276. With the standard algorithm, the quotient of 23 is already written above 276.”
Materials contain explanations and examples of how the concepts and/or standards align to prior grade/course levels so that teachers can improve their own knowledge of the subject. The materials do not contain adult-level explanations for how the concepts and/or standards align to future concepts and/or standards.
In each Unit outline and within each lesson under Instructional context, Look back, This unit, and Look forward show connections to future grade levels but do not provide adult-level explanations that link learning from the current grade to the next grade. Examples include:
Grade 3, Unit 4: Area, Unit outline, Instructional context, Look forward, “In later grades, students will use area models to represent multi-digit multiplication. Later this year, students will solve problems involving perimeter, and in fifth grade, students will learn about volume.”
Grade 4, Unit 9: Add and subtract fractions, Lesson 9.4, Instructional context, Look forward, “In the next lesson, students will subtract fractions with like denominators without the support of models. In fifth grade, students will learn to subtract fractions with unlike denominators.”
Grade 5, Unit 2: Whole number division, Unit outline, Instructional context, Look forward, “In the next unit, students will learn to interpret and evaluate expressions. In later units, students will learn to divide fractions and decimals.”
Indicator 3c
Materials include a year-long scope and sequence with standards correlation information.
The materials reviewed for Takeoff by IXL Grades 3 through 5 meet expectations for including a year-long scope and sequence with standards correlation information.
The program contains multiple documents that teachers use to guide instruction for the year. Examples include:
Each grade level’s landing page shows the sequence of topics covered in the grade and provides a summary of each unit.
Each grade level’s Additional Resources include a Grade level at-a-glance: Standards and materials document. This document includes a pacing guide that identifies the number of days needed for each unit.
Each grade level’s Additional Resources include a Grade level at-a-glance: Standards document. This document includes a standards chart that identifies which lessons address which standards. It also includes a chart that identifies which lessons address which standards for mathematical practice.
Each unit’s Additional Resources include a Daily Planner. This document shows the progression of lesson objectives and standards across the unit.
Indicator 3d
Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.
Indicator 3e
Materials explain the program’s instructional approaches, identify research-based strategies, and explain the role of the standards.
The materials reviewed for Takeoff by IXL Grades 3 through 5 meet expectations for explaining the program’s instructional approaches, identify research-based strategies, and explain the role of the standards.
The Instructional design PDF explains the program’s instructional approaches. The document includes sections titled A balanced approach to rigor, A Coherent Path to Growth, Differentiation, Solved Mathematical Discourse, Standards for Mathematical Practice, and Research Summary. The objectives tab within each unit connects the unit objectives to standards and states how the program aligns its teaching and learning goals to those standards. Each unit and lesson includes a tab titled Instructional context that identifies how the unit or lesson addresses grade-level expectations and how the expectations relate to previous and subsequent grades.
Examples of materials explaining the instructional approaches of the program include:
Grade 3, Additional Resources, Instructional Design, A Balanced Approach to Rigor, Real-world Applications, Example 1, “In Lesson 1.9, students use expanded form to add three-digit numbers one place at a time when solving a real-world problem. In Lesson 1.10, students continue to add one place at a time in place value charts.”
Grade 4 landing Page, Additional Resources, Instructional Design, A Balanced Approach to Rigor, Procedural Fluency, Example, “Later in Lesson 11.3, students multiply fractions by whole numbers without model support. They use the efficient procedure of multiplying the numerator by the whole number and keeping the denominator the same.”
Grade 5 landing page, Additional Resources, Instructional Design, A Balanced Approach to Rigor, Conceptual Understanding, Example 2, “In Lesson 6.5: Multiply Fractions, students use their conceptual understanding to discover a more efficient procedure when multiplying fractions. They use a model they created in the previous activity to explain why the product makes sense, recognizing that the denominator represents the number of equal parts the whole square is divided into and the numerator represents the number of overlapping shaded parts.”
Examples of materials including and referencing research-based strategies:
Grade 3, Additional resources, Instructional Design, Research Summary, Rigor, “Rigorous mathematics instruction deepens students; knowledge of mathematical concepts by building their conceptual understanding, procedural fluency and ability to strategically approach applications. Takeoff intentionally develops conceptual knowledge that leads to procedural fluency, ensuring algorithms and strategies are always rooted in thorough understanding. Students leverage both conceptual understanding and procedural ability to confidently tackle a wide range of applications, from relevant real-world scenarios to complex mathematical challenges. (NRC 2001) There is growing evidence that students learn best when they are presented with academically challenging work that focuses on sense making and problem solving as well as skill building. (NRC 2001, 335).”
Grade 4, Additional Resources, Instructional Design, Research Summary, Mathematical Discourse, “Discourse in mathematics classroom enhances students’ learning by providing opportunities for them to make conjectures, explain their thinking, and construct logical arguments. These opportunities help students see mathematics as more than just getting right answers quickly. By talking about the math they’re learning in intentional and meaningful ways, students not only solidify their understanding but also come to know their own problem solving abilities more completely. Takeoff seamlessly integrates multiple opportunities for mathematical discourse throughout each lesson. Designated Think and talk activities spark rich classroom discussions, enabling students to work collaboratively to explore new math concepts and uncover new strategies. And frequent writing activities challenge students to articulate their thoughts using sound reasoning and precise terminology, further enhancing their ability to effectively communicate about math. (Lampert 1990; NCTM 2000)”
Grade 5, Additional Resources, Instructional Design, Research Summary, Coherence, “A coherent, focused curriculum, where topics are logically structured and connected within and across grade levels, cultivates deeper understanding, improved retention, and enhanced problem-solving abilities. By reinforcing and building on key concepts over time and in different contexts, a coherent curriculum helps students develop a strong mathematical foundation that supports long-term success in using mathematics both in the classroom and their everyday lives. Takeoff’s coherent design is clearly outlined for teachers in every unit and lesson. This not only helps teachers strengthen their understanding of mathematical connections but also enables them to consistently foster these connections in students’ everyday learning. Takeoff also helps students make connections to previous learning with warm-up activities in every lesson, enabling students to activate prior knowledge before diving into new material, and by using the same models and representations across grade levels to ensure students are always building on their conceptual understandings. (NCTM 2000, NRC 2001) In a coherent curriculum, mathematical ideas are linked to and build on one another so that students’ understanding and knowledge deepens and their ability to apply mathematics expands (NCTM 2000, 16).”
Examples of materials including and referencing the role of the standards in the program:
Grade 3, Unit 7: Applications of multiplication and division, Unit outline, Objectives, Major unit objectives connects objective 1 “Solve two-step word problems involving addition, subtraction, multiplication, or division” to 3.OA.8. and objective 2 “Multiply one-digit numbers by multiples of ten” to 3.NBT.3.
Grade 4, Unit 2: Add and subtract whole numbers, Lesson 2.2, connects the lesson objective “Add multi-digit numbers using the standard algorithm” to 4.NBT.4, MP.3, MP.8.
Grade 5, Unit 8: Decimal place value, Unit outline, Objectives, Major unit objectives connects objective 2 “Compare decimals to thousandths using place value” to 5.NBT.3b.
Indicator 3f
Materials provide a comprehensive list of supplies needed to support instructional activities.
The materials reviewed for Takeoff by IXL Grades 3 through 5 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.
Each grade level includes an at-a-glance PDF titled Planning and materials that lists the manipulatives and other materials needed for the curriculum. The document organizes the manipulatives by unit. Each lesson includes a materials section that identifies the manipulatives and resources teachers prepare before teaching the lesson.
Examples include:
Grade 3, Unit 6: Division Fluency, Lesson 6.6, Materials, Instruction and Guided practice, “Student book lesson 6.6, Instructional slides for lesson 6.6, Game time, Counters and printed copies of game sheets and division cards from Swap 'n' freeze: Division, Independent practice, Independent practice 6.6, Independent practice 6.6 answer key.”
Grade 4, Additional Resources, Fourth grade at-a-glance: Planning and materials, includes a Manipulatives and Materials chart that lists protractors for Unit 14. The chart also identifies materials used throughout the year, including colored pencils, dominoes, counters in a variety of colors, number cards, paper clips, toothpicks, and dice.
Grade 5, Unit 4: Volume, Lesson 4.1, Materials, Instruction and Guided practice, “Student book lesson 4.1 Instructional slides for lesson 4.1, Two different-shaped glasses with the same volume, scissors, tape, inch cubes, and printed copies of Build a box: Inch grid paper, Independent practice, Independent practice 4.1, Independent practice 4.1 answer key.”
Indicator 3g
The assessment system provides consistent opportunities to determine student learning throughout the school year. The assessment system provides sufficient teacher guidance for evaluating student performance and determining instructional next steps.
The materials reviewed for Takeoff by IXL Grades 3 through 5 meet expectations for providing consistent opportunities to determine student learning throughout the school year. The assessment system provides sufficient teacher guidance for evaluating student performance and determining instructional next steps.
The grade-level landing page under Additional resources in the Unleashing the power of IXL PDF, IXL Assessment Suite, describes the assessment system and outlines the types of assessments available throughout the program.
Unit assessments, “Takeoff's Mid-unit check-ins and End-of-unit tests don't just assess understanding - they help you provide differentiated support to each student… Available in both digital and paper formats, they offer the flexibility to vet any classroom set up while providing clear insights to guide instruction.”
Build Your Own Quizzes, “Whether you need an exit ticket or a short quiz on a specific lesson, you can use IXL quizzes to pull questions from IXL skills in the what you need in minutes.”
Real-time Assessment, “With IXL’s diagnostic in real-time mode, you can understand your students’ overall grade-level proficiency and get a personalized action plan for each learner.”
Benchmark Assessment, “With IXL’s diagnostic in benchmark mode, your school can swiftly and precisely measure students' overall grade-level proficiency in math.”
Universal Screener, “IXL's universal math screener quickly flags students who are at risk of not meeting grade-level standards, so that you and your administrators can plan for intervention accordingly.”
The assessment system provides sufficient teacher guidance for evaluating student performance. The program provides digital and print answer keys for Unit Quizzes and Unit Tests. On the grade-level landing page, Unit 1, Quiz or Test, Get started with Takeoff unit assessments PDF, Insightful assessments, provides teachers with information on how to evaluate student performance. “Every Takeoff unit includes tech-enhanced, standards-aligned assessments, effectively measuring students' mastery of the unit’s content.” After the assessment section lists the components for analyzing the assessments, the guidance for teachers includes:
Grade open response questions, “When students take an assessment digitally, you can enter scores for open response items directly into Takeoff.”
Score Printed Assessments, “You can also enter scores here for every question when assessments are taken on paper. The printable answer key and intuitive navigation between students makes grading quick and easy.”
The Quiz Analysis report provides information about students’ performance on the assessment. The Student scores chart includes a student performance graph that shows how students performed on the assessment.
Student Scores Chart, “You can see a more detailed breakdown of students’ scores and mastery levels in this chart, making it easy to group students at similar performance levels for further differentiated instruction.”
Question Review, “The Question review details how the class performed on each question and objective in the assessment. You can use the colors on the bars to gauge which questions were missed the most and review them as a class.”
The assessment system provides sufficient teacher guidance for interpreting student performance and determining next instructional steps. Grade level landing page, Unit 1, Personalization day, Get started with Takeoff personalization days PDF, Dedicated personalization days, guides teachers on how to interpret student performance and determine next instructional steps. The materials state, “Personalization days transform unit assessment data into exact content each and every student needs to fill knowledge gaps or extend their learning. With Takeoff's Personalization days, students always get the support or enrichment they need based on their performance, unlocking each student's potential to learn and grow from where they are.” Components of the personalization report include:
Analytics Reports, “Easily navigate to the Quiz Analysis report for additional insights into students’ assessment results, including a breakdown of students’ responses to each question. Visit the Score Grid report to track students’ progress on their Personalization day skills.”
Personalized Skill Recommendations, “The Personalization day report identifies the exact skills each student should work on to address the objectives they haven’t met yet.”
Start a Group Jam, “For small-group reteaching, click the icon to start a Group Jam with the targeted students.”
Assign Skills, “Click the icon to assign all of this objective’s skills to every recommended student.”
Skills for Enrichment, “The Personalization day report suggests enrichment skills for students who are ready to take their learning to the next level.”
Indicator 3h
This is not an assessed indicator in Mathematics.
Indicator 3i
This is not an assessed indicator in Mathematics.
Criterion 3.2: Student Supports
Information on Multilingual Learner (MLL) Supports in This Criterion
For some indicators in this criterion, we also display evidence and scores for pair MLL indicators.
While MLL indicators are scored, these scores are reported separately from core content scores. MLL scores do not currently impact core content scores at any level—whether indicator, criterion, gateway, or series.
To view all MLL evidence and scores for this grade band or grade level, select the "Multilingual Learner Supports" view from the left navigation panel.
Materials are designed for each child’s regular and active participation in grade-level/grade-band/series content.
The materials reviewed for Takeoff by IXL Grade 3 through Grade 5 partially meet expectations for Student Supports. The materials include varied approaches to learning tasks and offer multiple ways for students to demonstrate their understanding, along with opportunities for self-monitoring across the series. Teachers are supported with strategies for using varied grouping methods. Supports are included for varying reading levels to ensure accessibility, and manipulatives, both virtual and physical, accurately represent mathematical concepts and, when appropriate, are connected to written methods. The materials partially offer assessment accommodations that allow students to demonstrate their knowledge without altering the content and include a range of representations of people, along with guidance and support for educators to incorporate and build upon students’ cultural, social, and community backgrounds to enrich learning experiences. The materials partially provide strategies to ensure that students in special populations can access grade-level content and meet or exceed grade-level standards. The materials partially provide regular extensions and opportunities for advanced students to engage with mathematics at greater depth. The materials partially offer assessments that include accommodations that allow students to demonstrate their knowledge without altering the content. The materials provide a range of representations of people, but do not consistently include detailed instructions to effectively incorporate and draw upon students’ cultural, social, and community backgrounds to enrich learning experiences.
Indicator 3j
Materials provide strategies and support for students in special populations to work with grade-level content and meet or exceed grade-level standards, which support their regular and active participation in learning.
The materials reviewed for Takeoff by IXL Grades 3 through 5 partially meet expectations for providing strategies and support for students in special populations to work with grade-level content and meet or exceed grade-level standards, which support their regular and active participation in learning.
Each lesson includes an Additional Supports tab that provides teachers with readiness skills and language supports. Readiness skills consist of links to the IXL platform for online practice. The materials do not include teacher-facing guidance for addressing readiness skills within Takeoff lessons. For example, Grade 3, Unit 2: Understand multiplication, Lesson 2.3, Additional supports, Readiness skills, “Identify multiplication expressions for equal groups (9AE).” Language tips, “If you made an anchor chart in Lesson 1.6 with properties of addition, consider revisiting it and adding examples with properties of multiplication as they're introduced over the next two units, starting with the identity and zero properties of multiplication in this lesson. You can also add the new multiplication properties to your vocabulary list. All of these references can help language learners use academic vocabulary throughout the lesson.”
Lessons include Tips for Support that provide guidance for supporting students with lesson content. For example, Grade 4, Unit 5: Factors, multiples, and patterns, Lesson 5.6, Instruction, Learn to describe features of number patterns, Teacher notes, Tip for support, “For #4, if students struggle to complete the sentences, encourage them to do the following: Underline the digit in the ones place of each number and look for a pattern. Circle the digit in the tens place of each number and look for a pattern.” Guided practice, Practice describing number patterns, Teacher notes, Tips for Support, “If students struggle to write a statement that describes every number in the pattern, consider giving some sentence starters they can use: Every number is a multiple of . Every number is (even/odd). The digit in the ones place is always __.”
Each lesson includes an Independent Practice section with a Support subsection for students who need additional support. Support skills consist of links to the IXL platform for online practice. The materials do not include teacher-facing guidance for addressing support skills within Takeoff lessons. For example, Grade 5, Unit 10: Multiply decimals, Lesson 10.3, Independent practice, Skills, Practice, Multiply a decimal by one-digit whole number using the distributive property (9BA), Support, “Multiply a decimal by a one-digit whole number using blocks (U5Q).”
Indicator 3k
Materials regularly provide extensions and/or opportunities for advanced students to engage with grade-level/course-level mathematics at greater depth.
The materials reviewed for Takeoff by IXL Grades 3 through 5 partially meet expectations for regularly providing extensions and/or opportunities for advanced students to engage with grade-level/course-level mathematics at greater depth.
The materials include some extensions and opportunities that engage advanced students with grade-level mathematics at greater depth. For example:
Grade 3, Additional Resources, Instructional Design, Differentiation, Solved, Teacher-led Differentiation, “Ideas for extension offer challenging follow-up questions and enrichment activities to stretch students’ knowledge.”
Grade 5, Additional Resources, Instructional Design, Differentiation, Solved, Automatic Differentiation, “After students take one of Takeoff’s built-in assessments, the Personalization day will suggest the just-right skills to provide differentiated support for students based on their assessment performance. And for students who excelled across objectives on the assessment, IXL will suggest challenge or extension skills.” On Personalization days, students engage in IXL skills tasks selected based on their assessment performance.
Lessons include Optional Challenge Problems. For example, Grade 4, Unit 4: Multiply by 2-digit numbers, Lesson 4.2, Independent practice 4.2, Question 8, “Mandy wrote a multiplication equation. The first factor is the number of hours in a day. The second factor is the number of days in December. Write and solve Mandy’s equation. What does the product tell you about the month of December?”
However, there are also instances in which advanced students are assigned additional tasks beyond those required of their classmates that extend the workload without substantially deepening the mathematical thinking. For example:
Grade 3, Unit 4: Area, Lesson 4.3, Guided Practice, Use Multiplication to Find Areas, Teacher Notes, Question 17: Students, “shade the grid to show a rectangle that has an area of 18 square units.” As an extension, students “find all of the rectangles that have an area of 18 square units: 2\times9, 3\times6, 6\times3, and 9\times2” and analyze that these representations identify “all of the factors of 18 that are 10 or less.” This extension requires students to complete multiple additional representations after completing the original task.
Grade 4, Unit 6: Divide by 1-Digit Numbers, Lesson 6.1, Guided Practice, Divide Multiples of 10, 100, and 1,000, Question 19: students, “follow the quotients to find the correct path through the maze.” As an extension, students “make their own maze with division equations, then trade with a partner.” This extension adds a new task that students complete after finishing the original maze.
Grade 5, Unit 5: Add and Subtract Fractions, Lesson 5.10, Instruction, Warm Up, students fill in the missing numbers in Ian’s pattern. Question 1: “Ian came up with a number pattern. He added 1\frac{2}{5} to get from one number to the next. Fill in the missing numbers in Ian’s pattern. _____, 4\frac{9}{10}, _____, 7\frac{7}{10}, _____.” As an extension, students “predict whether any number in Ian's pattern would be a whole number if he extended the pattern,” and justify that “no numbers in Ian's pattern will be whole numbers.” This extension requires students to complete an additional task beyond filling in the missing values.
Taken together, the materials provide some opportunities for advanced students to engage with grade-level mathematics at greater depth. However, the extensions are inconsistent, and in some cases they add additional work rather than consistently deepening the mathematical thinking.
Indicator 3l
Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
Indicator 3m
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3n
Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
Indicator 3o
Materials provide a range of representation of people and include detailed instructions and support for educators to effectively incorporate and draw upon students’ different cultural, social, and community backgrounds to enrich learning experiences.
Indicator 3p
Materials provide supports for different reading levels to ensure accessibility for students.
Indicator 3q
Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
The materials reviewed for Takeoff by IXL Grades 3 through 5 meet expectations for providing manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
Each grade level includes a Grade-At-A-Glance document that lists manipulatives and materials required for the grade level. Grade 3, Additional resources, Third grade at-a-glance: Planning and Materials, Manipulatives and Materials state, “Takeoff by IXL invites students to explore math hands-on using a variety of manipulatives, concrete objects, and mathematical tools. By interweaving manipulatives throughout the curriculum, Takeoff makes math come to life for students while deepening their understanding and retention of key math concepts. Takeoff is intentionally designed to use manipulatives and tools that you probably already have in your classroom! These are the manipulatives you’ll need as you soar through third grade with Takeoff: Counters, Inch tiles, Place value blocks, Scales and measuring cups, Containers of various sizes, objects of various weights, Fraction strips (Takeoff provides printable fraction strips and number cards in case you don’t have classroom sets), Pattern blocks, Rulers. Additionally, these materials will come in handy throughout the year: Colored pencils, Dice, Paper clips, Index cards.”
Students use manipulatives during lesson activities across all grade levels. Examples include:
Grade 3, Unit 11: Compare fractions, Lesson 11.6, Instruction: Learn to Compare Fractions with the Same Numerator, students use fraction strips to compare fractions. The Teacher Notes state, “For #2, consider having students work in pairs or small groups. Provide each group with a set of fraction strips. Withhold the thirds and sixths to avoid giving away the answer to #3. Start by having students line up fraction strips that show \frac{1}{4}, \frac{1}{2}, and \frac{1}{8} from shortest to longest. Then have them write the fractions from least to greatest. Because it has the shortest strip, \frac{1}{8} is the least. Because it has the longest strip, \frac{1}{2} is the greatest. Before moving on, discuss why the fraction strips are ordered this way. For example, surface these ideas when comparing \frac{1}{8} and \frac{1}{2}: One of the strips is made by splitting the whole into 8 equal parts. The other strip is made by splitting the whole into only 2 equal parts. Since the wholes are the same size, the strip that is split into more equal parts has smaller parts.”
Grade 4, Unit 8: Equivalent fractions and comparing, Lesson 8.1, Instruction, Learn to Use Models to Find Equivalent Fractions, students fold and shade paper to model equivalent fractions. The Teacher Notes state, “Give each student a sheet of paper they can use to model equivalent fractions. Have them fold it down the middle into two equal parts. (Throughout the activity, students can fold the paper either lengthwise or widthwise.) Then have them unfold the paper, trace the crease with a pencil, and shade one of the equal parts. Discuss the fraction the shaded area represents. Students should note that they shaded \frac{1}{2} of the paper. Next, have students fold the paper into fourths and then unfold it, again tracing the creases they made. Discuss how the \frac{1}{2} that was shaded is now two of the four total parts, or \frac{2}{4} of the page. Make sure students understand that \frac{1}{2} and \frac{2}{4} are equivalent because they represent the same shaded area. Have students repeat the activity to find how many eighths \frac{1}{2} is equivalent to. (It's equivalent to \frac{4}{8}.)” Question 2, “What equivalent fractions does your paper show?”
Grade 5, Unit 8: Decimal place value, Lesson 8.2, Instruction: Investigate Place Value Relationships, students use place value blocks to model decimal values. The Teacher Notes state, “Provide each student or small group with place value blocks to use throughout the lesson. Include 1 large cube, 10 flats, 10 rods, and 10 small cubes. For #3, discuss how changing the block that represents one whole changes the value of the other blocks. For example, if students choose the rod to represent one whole, the flat is now a ten because it is 10 times as much as a rod. Similarly, the large cube is now a hundred, not a thousand. Students will likely need help determining the value of the small cube. Prompt them by asking how it relates to the rod. Students should recognize that the small cube is \frac{1}{10} of a rod, so it is now a tenth. So when the rod is the whole, Antonia's model represents 161.8… For #4, have students start by labeling the value of each block. Then have them fill out the place value chart to identify the number the model shows. Discuss how to find the value of the digit 3 in 15.34. Point out that since 3 is in the tenths place, it is worth 3 tenths. You can also see that there are 3 tenths (rods) in the model.”
Mid-unit check-ins and end-of-unit assessments require students to use virtual manipulatives that are accurate representations of physical tools. Examples include:
Grade 3, Unit 4: Area, Unit 4 Test, Question 2, “Use the square tiles to find the area of the rectangle. Each square tile has an area of 1 square unit. Write a multiplication equation that shows how to find the area of the rectangle.” Students drag virtual square tiles into the rectangle to determine the area.
Grade 4, Unit 14: Angles, Unit 14 Test, Question 13, “Use the protractor to draw an 80\degree angle.” Students drag one arm of the angle along a virtual protractor to measure 80 degrees.
Grade 5, Unit 14: Classify 2D figures, Unit 14 Test, Question 3, “Sort the polygons.” Students sort five polygons into the categories “octogons” and “not octogons” using virtual representations.
Criterion 3.3: Intentional Design
Materials include a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.
Indicator 3r
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic software in ways that engage students in the grade-level/series standards, when applicable.
Indicator 3s
Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
Indicator 3t
The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
Indicator 3u
Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.