Alignment: Overall Summary

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for alignment to the Common Core State Standards (CCSS). ​The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards. The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor. The materials meet expectations for meaningfully connecting the Standards for Mathematical Content and the Cluster Standards for Mathematical Practice (MPs).

See Rating Scale Understanding Gateways

Alignment

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Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
14
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
17
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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Meets Expectations

Not Rated

Gateway 3:

Usability

0
22
31
38
36
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

​The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for not assessing topics before the grade level in which the topic should be introduced. The materials assess grade-level content and, if applicable, content from earlier grades.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for assessing grade-level content.

Assessments are located in the Assessment Guide book. Assessments consist of a Prerequisite Skills Inventory, Middle-of-Year Test, End-of-Year Test, 20 Module Tests, and 5 Unit Performance Tasks. Each Module Assessment consists of a printable and interactive Form A and Form B.

The Interactive Middle of Year Test assesses the standards taught in approximately the first half of the year, and the Interactive End of Year Test assesses the full year of standards. Examples include:

  • End of Year Test, Item, 18 "Mica builds this shape. Which shapes could Mica have used to build his shape?" (K.G.6)
  • End-of-Year Test, Item 6, "Cal uses trucks to show one way to make 6. Which equation shows another way to make 6?" The item shows a group of 3 trucks and a group of three more trucks. (K.OA.3)

Module Tests are available digitally and in the Assessment Guide. Examples include:

  • Module 4 Test, Forms A and B, Items 4-6, students classify objects into given categories. Form A, Item 4, instructs students to, “draw lines from the cats to the words to show if they are big or small. You will draw lines to all the cats.” (K.MD.3) 
  • Module 8 Test, Forms A Items 5, students are instructed to count, “How many turtles? Fill in the blank with the correct number.” (K.CC.3)
  • Module 12 Test, Forms A and B, Items 1-3, students are read a word problem and given a picture. Then students select the equation that matches the word Item and the picture. In Form A, Item 3, “Carl has five plants. He has one plant that is big. Carl has four plants that are small. Which equation tells about Carl's big and small plants?" Form B, Item 2, “There are seven sports balls. Four of them are soccer balls and the rest are tennis balls. Which equation shows how many are tennis balls?” (K.OA.1) 
  • Module 12 Test, Forms A and B, Items 5 and 7, students represent subtraction with objects, drawings, or equations by writing a subtraction equation to match a picture representation. In Form B, Item 7, “ Lisa has ten shapes. Two shapes are gray and the rest are white. How can an equation be used to model how the groups are put together? Fill in the blanks with the correct numbers.” (K.OA.1)
  • Module 16 Test, Forms A and B, Items 1 and 3, students identify shapes by selecting the matching shape. In Form A, Item 1, “Tom sees this shape (triangle). Which is the same shape as Tom’s?” (K.G.4)
  • Module 16 Test, Forms A and B, Items 2, 5, and 7 students analyze shapes to identify the correct number of sides or vertices and whether the shapes are 2 dimensional or 3 dimensional. In Form B, Item 5, “Which shows a two-dimensional shape?” (K.G.4)
  • Module 20 Test, Form A, Items 1-2, students identify objects that are heavier or lighter. Form A, Item 2, “Stacy has this tennis ball. Which object has less weight than Stacy’s tennis ball?” (K.MD.2)
  • Performance Assessments with multiple tasks for each unit are provided in the Assessment Guide. Module 4 Task 3, “Yoshi and Neela are picking flowers. They pick more than 10 flowers but no more than 19 flowers. Write a number that could be the number of flowers they pick.” (K.CC.3)

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for spending a majority of instructional time on major work of the grade. 

  • The approximate number of Modules devoted to major work of the grade (including assessments and supporting work connected to the major work) is 15 out of 20, which is approximately 75%. 
  • The approximate number of Lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 77 out of 96, which is approximately 80%.
  • The approximate number of days devoted to major work (including assessments and supporting work connected to the major work) is 128 out of 162, which is approximately 79%.

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 module. As a result, approximately 80% of the instructional materials focus on major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
8/8
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade and content designated for one grade level that is viable for one school year. The instructional materials are also consistent with the progressions in the standards and foster coherence through connections at a single grade.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meets the expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

Throughout the instructional materials, supporting work of the grade is connected to major work. Examples of how the materials connect supporting work to the major work of the grade include:

  • In Module 4, Lesson 1, Step It Out, the supporting work of K.MD.3 is connected to the major work of K.CC.5 as students classify objects into given categories and count to answer "how many?" questions. In Problem 2, “Pat has seven cubes. She classifies the cubes by color. How many cubes does Pat have of each color?”
  • Module 4, Lesson 4, On Your Own, Problem 4, the supporting work of K.MD.3 (Classify objects into given categories; count and sort the objects) is connected to the major work of K.CC.5 (Count to answer “how many?”) as students solve “Amelia has 8 buttons in 3 colors to classify. She wants to know how many buttons are in each category. Then she wants to sort each category by count.” 
  • In Module 14, Lesson 5, the supporting work of K.G.4 (Analyze and compare two- and three-dimensional shapes) is connected to the major work of K.CC.5 (Count to answer “how many?”) as students answer “Does the shape have any flat surfaces? If so, how many?”  "Does the shape have flat or curved surfaces? What do you notice about the surfaces?" 
  • Module 15, Lesson 1, Step It Out, the supporting work of K.G.1 (Describe objects in the environment using names of shapes) is connected to the major work of K.CC.5 (Count to answer “how many?”) as students solve "How many objects shaped like a sphere are in the picture? How many objects shaped like a cube are in the picture?”
  • Module 16, Lesson 2, Spark Your Learning, Persevere, the supporting work of K.G.2 (Correctly name shapes) and K.G.4 (Analyze and compare two- and three-dimensional shapes) is connected to the major work of K.CC.5 (Count to answer “how many?”) as students count the number of sides of shapes to answer: "Which plate has four sides? Which plate has four corners? Which plate has four equal sides?; Build Understanding, sample guided discussion "How many sides are there?"
  • Module 16, Lesson 3, Build Understanding,  the supporting work of K.G.4 (Analyze and compare two- and three-dimensional shapes) is connected to the major work of K.CC.5 (Count to answer “how many?”) in the Sample Guided Discussion: "How many vertices does it have? How many triangles do you see in Task 4? Are the triangles similar or different?"

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations that the amount of content designated for one grade-level is viable for one year. 

As designed, the instructional materials can be completed in 162 days. The suggested amount of time and expectations for teachers and students in the materials are viable for one school year as written and would not require significant modifications.

  • The provided scope and sequence found in the Planning and Pacing Guide includes materials for 114 instructional days.
  • There are 3 days per year for the Growth Measure Assessments.
  • There are 5 Units. There is 1 day per Unit for the Performance Task, for a total of 5 days. 
  • There are 20 Modules, with 1 day for each Module Opener, Are You Ready?, and 1 day for each Module Review and Module Test, for a total of 40 days.

The suggested pacing from the publisher is 1 day per lesson for most lessons. However, some lessons are listed for 2 days. There are no lessons that require more than 2 instructional days to complete. 

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for being consistent with the progressions in the Standards, providing all students with extensive work of the grade, and explicitly identifying prior knowledge needed for grade level work.

In the Planning and Pacing Guide, there is a Correlations Chart where all grade-level standards are represented. Tasks are aligned to grade-level work and are connected to prior knowledge..

The instructional materials clearly identify for each module Teaching for Success that shows the progressions of the standards from “Prior Learning”, to “Current Development,” and to “Future Connections,” respectively. In the beginning of each lesson, Mathematical Progressions include the same progressions with “Future Connections” explicit to the lesson. Examples of “Future Connections” include:

  • Module 5, Lesson 1, Mathematical Progressions, Future Connections, “Children will make connections among a variety of representations to explain addition situations (Grade 1, Lessons 1.1 - 1.7). Children will relate counting to addition (Grade 1, Lesson 1.2).”
  • Module 11, Lesson, 3, Mathematical Progressions, Future Learning, “Children will use addition within 20 to solve word problems involving situations of adding to and putting together with unknowns in all positions (Grade 1, Lessons 5.1-5.4).”
  • Module 19, Teaching for Success, Mathematical Progressions Across the Grades, Future Connections, “Children will order three objects by length (Grade 1, Lesson 17.1); and, compare the lengths of two objects using a third object (Grade 1, Lesson 17.2).”

 A typical lesson includes multiple opportunities for students to engage with extensive work of the grade. Build Understanding, Step It Out, and Connect Concepts and Skills are intended to engage students with new grade-level content. During On Your Own (independent practice), and More Practice/Homework, students work with grade-level problems. For example:

  • Unit 1 introduces the counting sequence and numbers to 5. In Modules 1 through 4, students identify, compare, classify, sort, add, and subtract within 5. Modules 5-6 introduce word problems involving addition and subtraction. 
    • Module 4, Lesson 3, On Your Own, Problem 3, “Classify the peppers by size and draw the peppers in each category. Mosi has six peppers in her garden. Some peppers are big and the rest are small. __ peppers (big). __ peppers (small).”
    • Module 5, Lesson 7, Step It Out, “Draw to show the total number of children riding their bikes on the trail. Write an equation to model the problem. ‘Three children are riding their bikes on a trail. Two more children join them. How many total children are riding?”
    • Module 6, Lesson 7, On Your Own, Problem 8, “Three brown butterflies and two orange butterflies are flying. How many total butterflies are flying?” 
  • Unit 4, Number and Operation in Base Ten consists of Module 17, Place Value Foundations: Represent Numbers to 20, and Module 18, Place Value Foundations: Represent Numbers to 20 with a written numeral. In Module 17, students compose ten and some more ones to make 14, 15, 19, and 20. In Module 18, students count and write from 11 to 20. 
    • Module 17, Lesson 3, Build Understanding, Problem 1, “The ten cubes at the top of the page represent ten ones. How can you use those cubes and draw some more ones to show the number? Write the numbers to show ten ones and some more ones. 16, __ones and __ones.”

In addition to including Mathematical Progressions identifying prior learning for each lesson, the beginning of each module explicitly identifies and engages prior learning during the "Are You Ready?" activities designed to diagnose mastery, inform grouping and differentiation. Warm-Up Options in all lessons, and Spark Your Learning activities in Build Understanding and Connect Concepts and Skills lessons are intended to assist with activating prior knowledge. Examples include: 

  • In Module 1, Lesson 4, Mathematical Progressions, Prior Learning is identified as “Children used counting and numbers to determine quantities up to 5.” 
  • In Module 3, Teaching for Success, Mathematical Progressions, prior Grade K skills address K.CC.4 and K.CC.5, when children counted and ordered numbers to represent numbers zero to five. 
  • Module 5, Lesson 3, Mathematical Progressions, Prior Learning: "Children represented addition by acting out situations, Grade K Lesson 5.1," 
  • In Module 11, Lesson 5, Prior Learning: “Children wrote addition equations within 10." This addressed standard K.OA.1 in Grade K, Lesson 5.5.
  • Module 13, Lesson 4 , Mathematical Progressions, identify prior learning as "Children learned about ways to make numbers to 9. (Grade K, Lessons 1.5, 13.1–13.3) Children used objects and drawings to represent addition problems within 10. (Grade K, Lesson 12.1) Children wrote addition equations within 10. (Grade K, Lesson 11.5) Children solved word problems within 10 (Grade K, 12.5)." This learning connects to the current development lessons which target K.OA.3 and K.CC.4b. In these lessons, children decompose the number 10 and use objects, drawing, and equations to find and represent different ways to make 10. From these lessons, future connections will be made with 1.OA.1, found in lessons 5.1-5.4, 6.1-6.3, 6.6-6.7, 7.1-7.3, and 7.7, where students represent and solve addition and subtraction problems.
  • Module 15, Lesson 2, Mathematical Progressions, identify prior learning from Grade K Lessons 14.1 - 14.4 (K.G.3 and K.G.1- describing three-dimensional shapes and using positional words like above or below). This learning connects to the current development lessons which target K.G.1. In these lessons, students begin to use the positional words next and beside. From these lessons, future connections will be made with 1.G.1, found in Grade 1 Lessons 14.1 - 14.2, where students distinguish between defining attributes and build and draw shapes to possess defining attributes.
  • Module 6, Lesson 1, Are You Ready?, includes writing numbers to make 5 (K.OA.5 ) that builds to students representing addition with objects, fingers, images, or equations (K.OA.1). 
  • Module 12, Lesson 4, Activate Prior Knowledge, reviews prior learning of subtraction problems within 10 (K.OA.2 ). Based on this Math Routine , students participate in Interactive Reteach, Grade K, Lesson 2.2, or complete a prerequisite skills activity.
  • Module 20, Lesson 3, Spiral Review,, includes review questions that will help determine if students have retained information taught in the past. This Spiral Review assesses whether children will identify a hexagon from a group of shapes (K.G.A.2 ). These Spiral Reviews are located in the More Practice/Homework section of the student materials.

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

The materials include learning objectives that are visibly shaped by CCSSM cluster headings, including:

  • In Module 12, Lesson 4, the Learning Objective, “Use objects, drawings, and equations to solve take apart problems within 10,” is shaped by K.OA.A, (Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from).
  • In Module 17, Lesson 3, the Learning Objective, “Understand the numbers 16 to 19 by decomposing the numbers into ten ones and some more ones using objects,” is shaped by K.NBT.A, (Work with numbers 11–19 to gain foundations for place value).
  • In Module 19, Lesson 2, the Learning Objective, “Understand how to compare the lengths of two objects,” is shaped by K.MD.A, (Describe and compare measurable attributes).

The materials include problems and activities connecting two or more clusters in a domain or two or more domains in a grade, in cases where these connections are natural and important, and examples of this include:

  • In Module 2, Lesson 5, connects K.CC.B and K.CC.C as students count how many counters are in each group. Students point to the counter as they count, trace, and write the corresponding numbers. “How many counters will you need to show for the number that comes after 2?” Students then place 3 counters, counting aloud as they place each one, and then write the number.  
  • In Module 11, Lesson 6, Step It Out, connects K.CC.A  and K.OA.A as students count groups of objects or animals and represent each number counted to create and solve subtraction equations. Problem 2, “Listen to the subtraction word problem. Mark an X on the campers that are leaving. Write an equation to model the problem. Explain what each number represents. Eight campers are in a campground. Two campers are driven away. How many campers are there now?”
  • In Module 17, Lesson 2, connects K.NBT.A  and K.CC.C as students build the numbers 14 and 15. On Your Own, Problem 4, “Circle ten pears. Circle some more pairs to show the number 15. Write the numbers to represent the number of pears.”

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

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Gateway Two Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and they meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
8/8
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications. The instructional materials also do not always treat the aspects of rigor separately or together.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. 

Each module contains two types of lessons specifically designed to engage students with conceptual understanding, Spark Your Learning and Bridging Lessons. The instructional materials present multiple opportunities for students to develop conceptual understanding, examples include:

  • Module 2, Lesson 3, Read and Write 4 and 5, Spark Your Learning, the teacher models the number 3 with counters and asks students "What number is one larger than three?" During Learn together, students build understanding with counting, one to one correspondence, identify four and five, and write the corresponding numerals. In independent practice, students show what they know about the numbers four and five and how the two numbers are different from each other. Students count and circle the picture that represents 5 swimmers and draw what they know about 4 and 5. (K.CC.3)
  • Module 11, Lesson 3, students solve addition problems within 10 by counting the number of objects in the picture. Spark Your Learning questions develop student understanding by showing different representations and highlighting common errors. (K.OA.1)

The instructional materials present multiple opportunities for students to develop conceptual understanding, examples include:

  • Module 11, Lesson 5, students count how many objects are in each group in a picture and write a corresponding addition equation. (K.OA.1)
  • Module 12, Lesson 3, Small Group, includes three options to develop students’ conceptual understanding of put together problems within 10. Students use two color counters and crayons to create word problems putting together two groups and writing an equation. (K.OA.1)
  • Module 17, Lesson 1, Problem 1, students use 10 cubes and draw some more ones to show the number. (K.OA.3)

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

Students develop procedural skills and fluencies throughout the grade level. Each module contains Procedural lessons that help students develop the steps in a procedure and determine when the procedure should be used. Module and Lesson components that specifically attend to student’s developing and independently demonstrating procedural skill and fluency include:

  • In Module Planning: Teaching for Success, Teacher to Teacher notes include advice for teachers on how to question the student in order to build procedural fluency. For example, in Module 12, Teacher to Teacher suggests having students visualize 6, draw 6, and then talk about a part-part-whole relationship to make the connections about part-whole relationships. (K.OA.5)
  • Activating Prior Knowledge is included in lessons. Lesson 5.1, the activity states: "Have children identify the number shown in each five frame." This supports fluency with addition within 5. (K.OA.5)  

Students develop fluency with K.OA.5 in Modules 5 and 6. Specific lesson components, Step it Out and More Practice/Homework, include opportunities for students to engage in procedural skill and fluency. In addition, Reteach opportunities provide additional fluency practice. For example:

  • Module 5, Lesson 3, ReTeach, includes independent practice for students to build fluency of addition within 5. Additionally, the More Practice/Homework and Test Prep sections provide students with independent practice of adding within 5.
  • Module 5, Lesson 4, Step It Out, On Your Own, and More Practice/Homework, students independently practice take from problems within 5. Test Prep extends independent practice by having students use pictures to demonstrate fluency of take from problems within 5.
  • Module 5, Lesson 6, Step It Out, students use pictures to create matching subtraction equations to practice fluency within 5. During On Your Own, students independently practice within 5. The More Practice/Homework provides students with additional practice opportunities to build subtraction skills.
  • Module 6, Lesson 2, Practice and Homework Journal, students write subtraction equations to solve, “Molly has five cars. Two of the cars are yellow. The rest are blue. How many cars are blue?” 

In addition, every lesson has an optional Sharpen Skills activity to build procedural skill and fluency. For example, in Module 5, Lesson 3, students use different color connecting cubes to articulate sentences that include addition vocabulary. For example, “I am joining 3 blue and 2 red. The total number is 5. I am adding 2 red cubes to 3 blue cubes. Three plus 2 is equal to 5.” (K.OA.5)

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for teachers and students spending sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

Students engage in routine application problems throughout the grade level. In Independent Practice and On Your Own, students apply what they have learned to solve real world problems independently. For example:

  • In Module 5, Lesson 1, students solve, “How can you act out an addition problem to match the picture? Write the numbers that represent the children in each group.” Guided questions throughout the activity prompt students to apply their understanding of addition to find a total unknown. “How many children are sitting on the rug? How many children come? What happens to the group when one child joins them? How can you find the total number of children there now? How many children join them? What happens to the group of children when one child joins them? What groups are you adding?” (K.OA.2).
  • In Module 5, Test Form A, Item 5, students apply mathematics to a real-world context: “Ben and Lisa are playing in the park. Their friends Matt and Kate join them. How many friends are in the park now?” (K.OA.2)
  • In Module 12, Lesson 5, Step It Out and On Your Own, students create picture models and equations to solve addition and subtraction word problems, and in More Practice/Homework, students solve word problems within 10 in a variety of contexts. (K.OA.2)

Students engage with non-routine application of the mathematics when they create story problems for pictures and number sentences. For example:

  • In Module 5, Lesson 6, students “Tell a subtraction word problem about taking from a group using numbers within 5. Use drawings to solve the problem. Write the equation to model the problem.” (K.OA.2)
  • In Module 6, Lesson 1, students represent addition problems within 5 using objects and drawings. During Spark Your Learning, students respond to, “Look at the picture. What addition word problem can you tell about the cat and the dogs? Write how many total pets?” Students create their own story problem based on the picture of 4 pets. (K.OA.2)
  • In Module 6, Lesson 7, students “Tell your own addition word problem within 5. Draw to solve the problem. Write the equation to model your story.” (K.OA.2)
  • In Module 12, Lesson 1, Spark Your Learning, students look at a picture of dogs. “How can you represent the brown dogs and the white dogs? Complete the equation to model the groups and the total number of dogs.” Students count the small dogs and place a red counter on them while counting aloud. Students count the large dogs and place a yellow counter on them while counting aloud and then are asked, “How can you decide how many dogs there are in all?” (By counting all the counters). Students add the brown (red counters) and white dogs (yellow counters) and write a corresponding equation. Throughout the lesson, students model a story problem with counters, write a corresponding addition sentence using the correct numbers, plus sign, and equal sign, and find the total sum. (K.OA.1)

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for the three aspects of rigor not always being treated together and not always being treated separately. Overall, two or all three of the aspects of rigor are interwoven throughout each module.

All three aspects of rigor are present independently throughout the program materials. Examples include:

  • Module 1, Lessons 1-3 address developing conceptual understanding of numbers to 5 as students use counters to represent numbers. Students listen to stories and show the number using counters. Lesson 3, Build Understanding, Task 3, “Listen to the story. Draw counters to represent the number of objects in the story. Say each number as you draw the counters. Circle the number you represented. “Shana sees five beach balls.”
  • In Module 2, Lesson 4, Step It Out, students develop procedural skill and fluency as they count the flowers in each vase to count and write the number. (K.CC.3)
  • In Module 5, Lesson 2, students use pictorial representations to demonstrate story problems to show subtraction within 5. (K.OA.5) 

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

  • In Module 9, Lesson 3, Step It Out, Task 1, students apply what they know about counting to understand how to count on from any given number in a counting sequence. “There are five pumpkins in the crate. Beginning at 5, count forward. Mark an X on each pumpkin as you count. Tell a classmate how many total pumpkins there are.” (K.CC.2)
  • In Module 10, Lesson 1, On Your Own, Problem 4, students develop conceptual understanding by using counters, pictures, or connecting cubes to compare two groups of objects within 10. Students practice procedural skill by drawing lines to match the objects in each group. “Use matching to identify which group has a greater number of objects that the other group. Circle the group that has a greater number of balloons. There are two groups of hot air balloons.” (K.CC.6)

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
9/10
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified and clearly labeled throughout the materials, and the instructional materials support the standards’ emphasis on mathematical reasoning.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
1/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten partially meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout the grade-level.

All MPs are identified throughout the materials. There are some over identifications of MP1 and MP5 as they are identified as being present in every lesson. MP8 is underidentified in the materials. For example:

  • MPs are identified in both the Planning and Pacing Guide and the Teacher Edition.
  • In the Teacher Edition, MPs are identified by using headings such as Persevere, Reason, Attend to Precision, Use Repeated Reasoning, Use Tools, Use Structure, and Model with Mathematics.
  • The Planning and Pacing Guide explains each MP and provides a correlation to specific lessons. All Spark Your Learning lessons are labeled as Persevere (MP1). Planning and Pacing Guide, page PG64, says “Included in every lesson.” According to the Planning and Pacing Guide, Use Tools (MP5) is “In every Spark Your Learning and Module Review.”
  • The Planning and Pacing Guide indicates that the following lessons provide an opportunity to work with “MP8: 3.6, 9.2, 12.1, 13.4”.

In each lesson, Focus and Coherence identifies the MPs within the lesson, and the MPs are also identified throughout the lesson before a task. Because the identification is associated with a task, there are connections to grade level content. For example:

  • In Module 17, Lesson 2, Spark Your Learning, MP1 is identified in the Planning and Pacing Guide. Students “Listen to the story. What do you know about the total number of apples? Luke has apples on some plates. How can you represent the number of apples on each plate?” The Teacher Edition provides questions if children need support, to guide them by asking, “What do you need to do to solve the problem?” 
  • Module 5, Lesson 2, Task 3, page 107, identifies MP2 “Reason- Have children act out what they see in the picture in different ways, such as with classmates, objects, and drawings, and reason about how they all represent the same problem.”
  • Module 12, Lesson 1, Build Understanding, Task 1, identifies MP4. “Kyle sees the five red kites in the sky. He also sees three blue kites in the sky. How many kites does Kyle see?” The Teacher Edition notes, “Children will model addition with equations. Ask children to describe the groups for each problem. Help children decide which tool to use. The discussion below uses counters.” (Page 310)
  • Module 9, Lesson 2, Build Understanding, Task 1, identifies MP7, “Use Structure- Encourage children to look at the last column of the hundreds chart and find ways the numbers are alike. Have children listen as you read the problem aloud. Ask children to describe the problem in their own words. Invite children to describe the different ways they could solve the problem.”

MPs are often identified and explained in the Teacher Edition: Professional Learning to explain how to use the Mathematical Practices. The Planning and Pacing Guide, pages PG17-PG19, also provides additional details and clarity about each MP. These pages include “Questions to Ask” with each Mathematical Practice. For example: 

  • The Planning and Pacing Guide, includes “Questions to Ask” for MP4, Model with mathematics: “Why is that a good model for this problem? How can you use a simpler problem to help you find the answer? What conclusions can you make from your model?” 
  • Module 2, Lesson 1: Count and Write 0 and 1, Teacher Edition: Professional Learning identifies MP 2: “Reason abstractly and quantitatively. Mathematically proficient children make use of quantities and their relationships in problem situations. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. In this lesson, children identify and write the numbers 0 and 1. This will help them in the identification of larger numbers.” 
  • Module 8, Lesson 4: Count and Order to 10, Step It out, Task 1, page 215, identifies MP5, “Count the flowers in each picture. Write the numbers as you count. Then write the number in counting order.” In Turn and Talk, teachers are prompted to, “Have children talk about whether they think cubes or counters are more effective for modeling this problem and why.”

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for carefully attending to the full meaning of each practice standard (MP). 

The materials attend to the full intent of the MPs. Examples of the instructional materials attending to the full meaning of the MPs include:

  • MP1: In Module 11, Lesson 1, students listen to a story, act it out, and then write an equation to match. “There are six butterflies in the meadow. Four more butterflies join them. How many butterflies are in the meadow now?”
  • MP2: In Module 12, Lesson 2, students solve “There are ten plates on the picnic table. Six are blue. The rest are red. How many are red?” Teachers are instructed to ask “What kind of equation will you write? What does 10 represent? What number will you write next? What does 6 represent? What number will you write next? What does 4 represent? What signs will you write?”
  • MP4: In Module 6, Lesson 4, On Your Own , students “Tell a subtraction word problem about a group being taken apart using numbers within 5. Use drawings to solve the problem. Write the equation to model the problem.”
  • MP5: In Module 7, Lesson 3, Spark your Learning, students listen to the story “Zoe is at the carnival with her family. She needs ten tickets to ride the carousel.” Teachers are encouraged to ask “Which tool could you use to solve the problem? Why is the tool you chose the one that works for you?
  • MP6: In Module 9, Lesson 3, Learn Together, “There are five pumpkins in the crate. Beginning at 5, count forward. Mark an X on each pumpkin as you count. Tell a classmate how many total pumpkins there are.” 
  • MP7: In Module 7, Lesson 4, Ways to Make Ten, students use two color counters to represent 10, color the ten frame on the page to match their counters, and write in the addition sentence to match.
  • MP8: In Module 9, Lesson 2, Step It Out, Task 2, “Point to the yellow box. Count to 100 by tens. Color each number as you count. What number should you start with if you want to count by tens? Start with 10 and count ten more. What number is ten more than 10? Point to the number on the hundred chart. Ten more is 20. The 1 in the number 10 changes to a 2, and the 0 stays the same. Now count ten more. What number is ten more than 20? How has the number changed? What are the other numbers you will say to count to 100 by tens?”

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

Students have opportunities to construct viable arguments through activities where they explain their thinking or justify, and the materials prompt them to analyze the arguments of others. Examples include:

  • In Module 5, Lesson 4, Build Shared Understanding, students explain how they solved a problem and discuss why they chose a specific strategy or tool.
  • In Module 9, Lesson 2, On Your Own, students “place rows of numbers as you count by tens to 100. Tell a classmate about counting by tens to 100. How are the numbers you count alike? How are the numbers you count different?” 
  • In Module 12, Lesson 5, students draw representations of word problems and write an equation to model the problem. Students “compare their drawings and talk about how they knew how many objects to draw and how they can use their drawings to help them solve the problem.” 
  • In Module 19, Lesson 2, On Your Own, Problem 3, “Look at the rugs. Compare the lengths of the two rugs. Use the words longer than or shorter than to describe the lengths. Circle the longer rug. Mark an X on the shorter rug. Explain why the two rugs must be at the same starting point to compare the lengths.” 
  • In Module 19, Lesson 3, Learning Mindset, Bounce Back, students discuss that other perspectives are valuable and not everyone sees things in the same way.

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

The materials provide teachers with Sample Guided Discussions, Turn and Talks, and Leveled Questions to assist teachers in engaging students in discourse. There is also some teacher guidance on how to lead discussions beyond the provided questions. Examples include:

  • In Module 4, Lesson 1, Build Understanding, Connect Math Ideas, Reasoning, and Language, Compare and Connect, states, “Before beginning the task, have children describe and give examples in their own words of the meaning of the words classify and category. Have students discuss their examples. Prompt discussion by asking, Do you agree or disagree? Why?”
  • In Module 7, Lesson 2, Turn and Talk, “Have children explain to partners how they chose what color or colors of counters to use. Did they use all red or all yellow? Did they use one color for each number? Why?”
  • In Module 19, Lesson 3, Turn and Talk, “Have children talk about what would happen if the birdbath on the right were placed in a hole instead of on the same surface as the one on the left. What would be different about how children could or could not compare the heights?”

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for attending to the specialized language of mathematics. The materials provide explicit instruction on communicating mathematical thinking with words, diagrams, and symbols. The materials use precise, accurate terminology and definitions when describing mathematics and support students in using them.

The Planning and Pacing Guide has a section for Language Development that states HMH Into Math is built upon 4 design principles to promote the use and development of language:

  • Principal 1: Support Sense Making;
  • Principal 2: Optimize Output to help students describe their mathematical reasoning and understanding;
  • Principal 3: Cultivate Conversations to facilitate mathematical conversations among students; and,
  • Principal 4: Maximize Linguistic and Cognitive Meta-Awareness to help students evaluate their use of language and see how mathematical ideas, reasoning and language are connected.

Language Routines and new/review vocabulary are summarized on the Language Development page for each Module, and includes Key Academic Vocabulary for Prior Learning, Review Vocabulary and Current Development, and New Vocabulary with definitions. Also in Language Development, Linguistic Notes provide teachers help with possible misconceptions relating to academic language. For example:

  • Module 3 identifies and defines review vocabulary, larger, and Current Development, greater than, count, less than, equal to, compare, and match.
  • In Module 5, the Linguistic Note states, “Listen for children who mix up the language between addition and subtraction. For example, children should say that when two groups are joined together, the result is the total.” When a group is taken apart, children should say the number that is “left.” Help children use the correct terms throughout each lesson.”
  • Module 6 includes Key Academic Vocabulary such as put together and take apart.
  • In Module 8, the Linguistic Note states, “Point out the difference between an amount of something and a number of objects. Discuss this idea in terms of ‘how much’ versus ‘how many.’ To help children understand the difference, provide examples from a variety of contexts. For example, ‘how much’ can be used to describe a value of a coin or an amount of liquid in a jar. On the other hand, ‘how many’ could be used to describe the number of coins or the number of ice cubes in a jar.”

The Guided Student Discussion often provides prompts related to understanding vocabulary such as: Module 14, Lesson 4, Task 1, states, “What does a cone look like? Which objects in the picture have curved surfaces? Which of the objects are cones? Why is the garbage can not a cone?”

Student pages include vocabulary boxes defining content vocabulary. Vocabulary is highlighted and italicized within each lesson in the materials. The vocabulary review at the end of each Module requires students to match new vocabulary terms with their meaning and/or examples provided, fill-in-the-blank with definitions or examples, or create a graphic organizer to help make sense of terms. Some lessons include Vocabulary Review. Connect Math Ideas, Reasoning, and Language Compare and Connect encourage students to use vocabulary terms to discuss mathematics with correct terminology. For example:

  • In Module 3, Lesson 2, Connect Math Ideas, Reasoning, and Language Compare and Connect states, “Review the vocabulary term greater than. Have children compare the meanings of the terms greater than and less than. Ask questions to help clarify their understanding.”
  • In Module 4, Lesson 2, Build Understanding, Connect Math Ideas, Reasoning, and Language Compare and Connect states, “Before beginning the task, have children describe and give examples in their own words of the meaning of the word shape. Have children discuss their examples. Prompt discussion by asking: Do you agree or disagree? Why?”
  • In Module 5, Lesson 7, students use visual models and equations to help review the module’s vocabulary for addition and subtraction.
  • In Module 16, Lesson 1, students use graphic organizers with the terms, circle, square, rectangle, and triangle. Students draw a picture to illustrate each term and give an example of a real world object of that shape.

Vocabulary cards can be used with vocabulary games. The eGlossary includes vocabulary terms and definitions translated into ten different languages. The Interactive Glossary provides the definition and a visual (diagrams, symbols, etc.) is provided for each vocabulary word.The Interactive Glossary also provides space for students to make graphic organizers or drawings for each new vocabulary term. In the student materials, the instructions state, “As you learn about each new term, add notes, drawings, or sentences in the space next to the definition. Doing so will help you remember what each term means.”

Gateway Three

Usability

Meets Expectations

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials include an underlying design that distinguishes between problems and exercises, assignments that are not haphazard with exercises given in intentional sequences, variety in what students are asked to produce, and manipulatives that are faithful representations of the mathematical objects they represent.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations that there is a clear distinction between problems and exercises in the materials.

The materials distinguish between problems and exercises within each lesson. Lessons include Spark Your Learning or Step it Out, Turn and Talk, Build Understanding, Check Understanding, and On Your Own, and More Practice/Homework. Spark Your Learning Problems activate prior knowledge and introduce new mathematics to students. Build Understanding includes problems that help students build conceptual understanding of the mathematics topic being taught. Check Understanding and On My Own sections include exercises that ask students to use the newly learned mathematics in each lesson. Additional practice and Homework is available in a separate Student Edition, providing more exercises for students to solve.

Each Module presents lessons with a consistent structure. During Build Conceptual Understanding, and Connect Concepts and Skills, students have opportunities to learn new content through problems and examples in guided instruction, step-by step procedures, and problem solving.

At the end of the lesson, On Your Own, More Practice/Homework, and Additional Practice provides a variety of exercises which allow students to independently show their understanding of the material. Exercises are designed for students to demonstrate understanding and skills in application and non-application settings. Test Prep and Spiral Review also include exercises.

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations that the design of assignments is intentional and not haphazard.

Overall, lessons are intentionally sequenced and scaffolded so students develop their understanding of mathematical concepts and skills. The structure of a lesson provides students with the opportunity to activate prior learning, build procedural skills, and engage with multiple activities that utilize concrete and abstract representations and increase in complexity.

Exercises are given in intentional sequences. In general, lessons are designed to begin with activating prior knowledge and build toward conceptual development and procedural skill. In Spark Your Learning, students use manipulatives and/or visual models to engage with the mathematical content, developing a concrete or representational understanding. This is followed by a Turn and Talk with a partner where students process the connections they have found. Throughout the lessons, students are provided scaffolding with new content in Build Understanding and Step It Out, where the abstract concept is broken down into smaller steps with additional Turn and Talks, and students complete independent exercises to build understanding and mastery. Check Understanding provides a mid-lesson check in and can be used to indicate the need to differentiate learning for students. Students solve and practice concepts in On Your Own, and More Practice/Homework.

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for having a variety in what students are asked to produce.

In Spark Your Learning, Build Understanding, and Step It Out, students use visuals to show their thinking. In Turn and Talks, students frequently construct arguments, and explain why. There are opportunities for students to produce answers and solutions in On Your Own, while also providing opportunities for students to provide written explanations. Throughout the materials, students represent mathematics using equations.

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The Planning and Pacing Guide, Manipulatives and Tools, explains how manipulatives are used in each module.  The materials identify the manipulatives needed at the beginning of each lesson, and on student pages there is a picture of the manipulative they will use. Examples of manipulatives for Kindergarten include: connecting cubes, pattern blocks, and counters.

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0
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Indicator Rating Details

The visual design of HMH Into Math Kindergarten is not distracting or chaotic. The printed and digital materials follow a consistent format. Teacher editions provide information for teachers to be able to access digital resources. There is room for students to record answers and show their thinking.

Features of the materials are consistently presented, and the use of colored fonts supports identification of lesson components. Components of the lesson are labeled in the Teacher Edition as Part 1: Spark Your Learning, Part 2:  Learn Together, Part 3: Check Understanding, Part 4: Differentiation Options, and Part 5: Wrap Up.  For example, Turn and Talks are highlighted in yellow, and Check for Understandings are always in orange font. Visual images mirror the situation in the problem or can be used by students as they solve the problem.

Tasks within a lesson are numbered to match the module and lesson numbers. Student practice problem pages include enough space for students to write their answers and provide explanations.

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
7/8
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for supporting teacher learning and understanding of the CCSSM. The instructional materials include: quality questions to support teachers in planning and providing effective learning experiences, a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials, a teacher edition that partially contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons, and explanations of the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for providing quality questions to help guide students’ mathematical development. 

Throughout the Teacher Edition, questions are posted to help support teachers with questions to guide students’ mathematical development. Activate Prior Knowledge, Spark Your Learning, Build Understanding, On Your Own, and Turn & Talk consistently provide questions to drive student discussion. 

  • Module 2, Lesson 3, Build Understanding provides the following questions for teachers: “When counting baseballs, how do you know how many baseballs are in the group? How can you check if your answer to how many baseballs are in each group is correct?”
  • Module 4, Lesson 4, Learn Together provides the following questions for teachers: “How many different colors of crayons should you use? Which colors do you want to use? After you draw the crayons, how can you find the number of crayons in each category? Do any of the boxes of crayons have the same number of crayons? How can you sort the categories by count?”

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for containing ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials.

In the Module planning pages, there is a variety of information that can help teachers understand the materials in order to present the content. Each lesson identifies the relevant content standards and Mathematical Practices, an I Can Statement, Learning Objective, Language Objective, materials needed, and Mathematical Progressions that contain prior learning, current development, and future connections. 

Unpacking the Standards provides further explanations of the standards’ connections. This section gives an explanation of the content standard contained in the lesson and Professional Learning, which sometimes contains information about the practice standard contained in that lesson. Teaching for Depth provides teachers with information regarding the content and how this relates to student learning.There are additional suggestions about activating prior knowledge or identifying skills in Warm-up Options, activities to Sharpen Skills, Small-Group Options, and Math Centers for differentiation.

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
1/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten partially meet the expectations for containing adult-level explanations so that teachers can improve their own knowledge of the subject. 

The materials include adult-level explanations of the grade-level content, but the materials do not include adult-level explanations of advanced mathematics concepts so that teachers can improve their own knowledge of the subject.

The materials include explanations and examples of the course-level mathematics specifically for teachers that can improve their own knowledge of the subject. In the Teacher Edition modules, there are examples and support for the adult in the math classroom as it relates to grade-level standards. For example: 

  • The Mathematical Progressions table in each module and lesson, highlights Prior Learning, Current Development and Future Connections.
  • Planning and Pacing includes a correlation chart for the math practices that defines each math practice in full.
  • Every Module introductory pages include Teacher for Depth and Teacher to Teacher. Every lesson includes either Professional Learning (About the Math, Using Mathematical Practices and Processes, and Visualizing the Math) and/or Unpacking Math Standards. 
  • Professional Learning videos are available online on Ed: Your Friend in Learning. This is noted on each Module Planning Page A of the Teacher Edition.

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for explaining the role of grade-level mathematics in the context of the overall mathematics curriculum.

Each module in the Teacher Edition includes Mathematical Progressions which lists prior learning, current development, and future connections. Similarly, the beginning of each lesson in the Teacher Edition includes Mathematical Progressions that show connections to prior and future grades’ standards, as well as other lessons within the program.

In the Planning and Pacing Guide, Progressions and Algebra Readiness notes “Algebra as a course of study today is integrated around four progressions of elementary and middle school content leading to the Algebra course: Number and Operations, Operations and Algebraic Thinking, Statistics and Probability, and Functions” and includes a table that shows how the domains in Grades K-5, 6-7, and Grade 8 / Algebra fit into these progressions.

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten provide a list of lessons in the teacher's edition, cross-­referencing the standards addressed, and a pacing guide. 

The Planning and Pacing Guide includes the standards and pacing (number of days) for each lesson. There is another standards chart in the Planning and Pacing Guide that lists each standard and correlation to Student Edition Lessons. In the Teacher Edition, pacing is provided in the module planning pages, with written descriptions of the standards, as well as listed under Current Development in the Mathematical Progressions chart.

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten include strategies for parents to support their students progress. The Family Resources tab includes several resources for parents:

  • “School Home Letters  inform families about the skills, strategies, and topics students are encountering at school.” Each module includes a letter, found online in 4 languages, providing vocabulary, a home activity, and discussion prompts. This letter is available in English, Spanish, Haitian-Creole, and Portuguese.
  • Math on the Spot videos are available for specific lessons within a module.

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten explain instructional approaches used and how they are research based.

The Planning and Pacing Guide contains Teacher Support Pages that include a section on Supporting Best Practices. “Into Math Florida was designed around research-based, effective teaching practices such as those described in Principles to Actions (NCTM 2014).” These include:

  • Establish mathematics goals to focus learning.
  • Implement tasks that promote reasoning and problem solving.
  • Use and connect mathematical representations.
  • Facilitate meaningful mathematical discourse.
  • Pose purposeful questions.
  • Build procedural fluency from conceptual understanding.
  • Support productive struggle in learning mathematics.
  • Elicit and use evidence of student thinking.

The Planning and Pacing Guide describes four design principles from the Stanford Center for Assessment, Learning, and Equity (SCALE) that “Into Math classrooms maximize student growth by helping teachers deliver high quality instruction while monitoring every student’s success.” These principles are: Support sense-making; Optimize output; Cultivate conversation; and Maximize linguistic and cognitive meta-awareness. To address this, the instructional materials include language routines that “help teachers promote the design principles during instruction.” Each module contains a Language Development page in the Teacher Edition that states where the language routines should be used. On the lesson pages of the Teacher Edition, there are Support-Sense Making boxes that describe how the language routine can be used. Also, there are notes in the margin of the teacher’s edition providing connections from the strategy to the principle.

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
9/10
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge, strategies for teachers to identify and address common student errors and misconceptions, and assessments that clearly denote which standards are being emphasized.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels.

  • At the beginning of the year, students’ prior knowledge is gathered through a Prerequisite Skills Inventory. “This short-answer test assesses core precursor skills that are most associated with on-grade success.” (Assessment Guide)
  • Each module begins with Are You Ready, a diagnostic assessment of prior learning related to the current grade-level standards. Intervention materials are provided to assist students not able to demonstrate the necessary skills. Commentary for each standard explains how the prior learning is relevant to the current module’s content. 
  • Prior learning is identified in the Mathematical Progressions section at the beginning of each module and lesson in the Teacher Edition.

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

  • The module overview in the Teacher Edition contains Common Errors as students engage in an introductory task and provides questioning strategies intended to build student understanding.
  • The Spark Your Learning planning page for each lesson in the Teacher Edition includes Common Errors related to the content of the lesson that identifies where students may make a mistake or exhibit misunderstanding. There is a rationale that explains the likely misunderstanding and suggests instructional adjustments or steps to help address the misconceptions. 
  • There are also Watch Fors and question prompts that highlight areas of potential student misconceptions.

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
1/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten partially meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The materials provide support for ongoing review and practice.

  • Within each lesson there are activities to Activate Prior Knowledge. The Math Routine is a review problem from prior units/lessons. Make Connections provides teacher support on next steps based on the students’ responses.
  • Sharpen Skills provides ongoing fluency practice.
  • Test Prep questions “provided are intended to assess the child’s ability to extend understanding…”
  • In Homework/Practice, Spiral Review is designed to “help determine if children have retained information taught in the past.” 
  • Online interactive lessons and homework practice provide students with immediate notification if their answers are correct/incorrect.

There is no specific feedback to students or guidance for teachers on how to interpret and give feedback to students for the Sharpen Skills, Test Prep, and Spiral Review.

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations that assessments clearly denote which standards are being emphasized. 

The Lesson Focus and Coherence page indicates the CCSSM that will be addressed within the Lesson. Throughout the lesson, there are formative assessments in Check for Understanding, On Your Own, and More Practice/Homework. Each lesson has a diagnostic assessment, Are You Ready, correlated to standards.

Each Module has an End of Module Test, and the standards associated with each problem on this test can be found on the Individual Record Form within the Assessment Guide Book. In addition, Assessment Preparation includes Standards-Based Practice for most lessons.

Each Unit has a summative Performance Task that includes the content focus in the teacher pages of the Assessment Guide.

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
2/2
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Indicator Rating Details

The instructional materials for reviewed HMH Into Math Kindergarten meet the expectations that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Each lesson has a diagnostic assessment, Are You Ready, and the materials state that teachers can use Online Ed, to assign the Digital Are You Ready? to power actionable reports including proficiency by standards item analysis.

The Planning and Pacing Guide notes, “Check Understanding is a quick formative assessment in every lesson. Teachers use data to determine which students need additional small-group support and which students can continue on to independent practice or math center challenges.” 

Each performance task includes a task-specific rubric indicating a level 0 response through a level 3 response. The structure of the rubrics is the same, but specific words are changed to reflect the mathematical content of the module. Level 3 indicates that the student made sense of the task, has complete and correct answers, and checked their work or provided full explanations. Level 2 indicates that the student made sense of the problem, made minor errors in computation or didn’t fully explain answers. Level 1 indicates that the students made sense of some components of the task but had significant errors in their solution strategies. Level 0 shows little evidence that the student has made sense of the task, addressed specific components,and does not complete the problem. The Planning and Pacing Guide indicates a content focus for each of the items on the Unit Performance Tasks.  Each content area is identified with a depth of knowledge as well as one or more Reteach pages for follow-up with students. 

The Individual Record Forms in the Assessment Guide suggest Reteach Lessons that teachers can use for follow-up based on the Module assessments and Performance Assessments.

The Individual Record Forms for the Prerequisite Skills Inventory, Beginning-of-Year, Middle-of-Year Test, and End-of-Year Tests do not suggest Reteach Lessons or provide other guidance that teachers can use for follow-up with students.

Indicator 3q

Materials encourage students to monitor their own progress.
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten include Scales to Track Learning Goals at the end of each lesson. The Teacher Edition introduction states, “The scales below can help you and your students understand their progress on a learning goal. Scales are also available in Module Resources.” 

Each lesson contains “I can” scales with four levels of “I Can” statements written in increased difficulty. While there is a note saying, “The scale below can help you and your students understand their progress on a learning goal.” There is no explicit indication of how to use these scales. 

At the end of On Your Own, there is Learning Mindset where students write a response to reflect on the lesson.

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
12/12
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials partially embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations, and they provide opportunities for advanced students to investigate mathematics content at greater depth. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. 

Throughout the materials, strategies are present, with guidance in the beginning of each module and lesson for both teachers and students. Examples include: 

  • Teaching for Depth provides information on strategies to use when teaching the concept. Represent and Explain focuses on ways for students to describe and picture a concept. Make Connections helps students understand a new idea by connecting it to previous knowledge.
  • Mathematical Progressions make connections to both prior and future skills and standards to scaffold instruction.
  • Diagnostic Assessment, Are You Ready?, allows teachers to “diagnose prerequisite mastery, identify intervention needs, and modify or set up leveled groups.”
  • Each lesson provides Warm-up Options to activate prior knowledge such as Math Routines and Make Connections.
  • Throughout the lessons, there are notes, strategies, sample guided-discussion questions, and possible misconceptions that provide teachers structure in making content accessible to all learners.
  • In each lesson, Check for Understanding problems provide information on student understanding of the lesson content, before they begin independent work during On Your Own.

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

  • There are Reteach and Challenge activities for each lesson.
  • Each lesson includes Plan for Differentiated Instruction that provides teachers with teacher-guided, Small-Group Options and self-directed Math Center Options based on student need: “On Track, Almost There (RtI), and Ready for More.”
  • Each lesson provides Leveled Questions identified as DOK 1, 2, and 3 with an explanation of the knowledge those questions uncover about student understanding.
  • In the Teacher Edition, Spark Your Learning provides two possible strategies and a common error. Each section describes student actions and has teachers either describe and practice or remind them of important strategies to support learning and how to intervene..

There are four “Language Routines to Develop Understanding” used throughout the materials: 

  • “Three Reads: Students read a problem three times with a specific focus each time.” 
  • “Stronger and Clearer Each Time: Students write their reasoning to a problem, share, explain their reasoning, listen to and respond to feedback, and then write again to refine their reasoning.”  
  • “Compare and Connect: Students listen to a partner’s solution strategy and then identify, compare, and contrast this mathematical strategy.” 
  • “Critique, Correct and Clarify: Students correct work that is not their own with a flawed explanation, argument, or solution method and share with a partner to reflect and then refine the sample work.”

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

STEM Tasks are provided at the beginning of every instructional unit and include cross-curricular tasks which allow multiple entry-points and various solution strategies or representations. For example:

  • In Unit 4, STEM Task: “Have children work in a group. Give each group three pieces of construction paper. Ask them to use their senses as they think about physical education class. On one piece of paper, have them draw things they might see in a gym. On another piece of paper, have them draw things they might hear in the gym. On the last piece of paper, have them draw things they might feel or touch in the gym. Have the groups share and discuss their work.”

Turn and Talks throughout each lesson provide opportunities for students to share a variety of ways to solve the problem, for example:

  • In Module 6, Lesson 1, Turn and Talk: “Have partners tell each other their word problems and compare them. Guide children to discuss how, even though their problems might not be the same, they all should have added one cat and three dogs to get a total of four pets because those are the numbers in the picture..”

In the Planning and Pacing Guide, Spark Your Learning tasks are “designed as ‘low-floor/high ceiling’ tasks that all students can access but that can also be extended to provide challenge.” Teachers are provided guidance on how to assist various levels of learners, depending on how they respond to the problem.

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for suggesting support and accommodations for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

In each module, Language Development provides support for ELLs including linguistic notes that provide strategies intended to help students struggling with key academic vocabulary such as: “Speak with students about words that can have multiple meanings….”, and “Visual cues help students…” Language Development also includes information about the Language Routines embedded in the instructional materials: Three Reads; Stronger and Clearer Each Time; Compare and Contrast; Critique, Correct, and Clarify. These are identified by a pink box throughout lessons with a speech bubble that identifies the Language Routine to be used. In addition, there are supports for special populations including:

  • Language Objectives are included in every lesson.
  • Reteach and RtI worksheets can be assigned online or printed.
  • Turn and Talk prompts designed to support students, for example, “Go back and reread the problem and break it into pieces. For example: What do you know? What do you need to find?”
  • A multilingual glossary is available online.

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

Supports for advanced students include:

  • Each lesson has a corresponding Challenge page, provided in print or online, addressing the same concepts and standards where students further extend their understanding. 
  • In the beginning of each module, Extend the Task provides suggestions for deeper exploration of the tasks.

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

Pictures of adults and children in the materials show a variety of demographics and personal characteristics. There are a variety of names used in word problems throughout the materials. The lessons contain a variety of tasks and situations in the story problems that interest students of various demographic and personal characteristics. There is a balanced approach to the use of gender identification. Examples include:

  • The materials reference roles instead of pronouns (e.g., the players, book fair, sailboats, collection of toy cars, piggy banks, carton of eggs).
  • The materials include a set number of names used throughout the problems and examples (e.g., Janette, Anton, Zed, Ari, Tai, Nick, Sam). These names are presented in a way that does not stereotype characters by gender, race, or ethnicity.

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten provide opportunities for teachers to use a variety of grouping strategies.

In the Planning and Pacing Guide there is a section titled, “Grouping and Recommendations. This section states, “One of the most valuable and time-saving tools for teachers is the online Recommend Groups feature. It synthesizes data from assessments and places students into leveled groups. You can easily modify the recommended groups yourself as needed.” 

  • Each lesson provides teachers with a differentiated plan that includes small-group options. 
  • The materials provide students with self-directed activities at math centers.
  • Throughout the materials, there are ample opportunities for students to Turn and Talk with a partner. 
  • Using the Check for Understanding, the teacher is directed to pull students into small groups and use the Teacher Tabletop Flipchart.

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten encourage teachers to draw upon home language and culture to facilitate learning.

The student Interactive Glossary is available in both English and Spanish, and  School-Home Letters are available in English, Spanish, Haitian-Creole, and Portuguese. Examples of home language connections and connections to assist in embracing the culture of students are present to assist in facilitating student learning.

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten: integrate some technology in ways that engage students in the Mathematical Practices; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; are intended to be easily customized for individual learners; and do not include technology that provides opportunities for teachers and/or students to collaborate with each other.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten include interactive lessons that can be found in online practice. The interactive lessons include drag and drop options, multiple choice questions, and click-on-the-correct item questions. Students are able to submit their completed assignment for teacher feedback via the digital platform.

Interactive Lessons are provided online for each lesson. Audio is provided to read each page. Students can draw pictures. (Note: Students using a computer must use the mouse to draw.) For example, in Lesson 5.3, Interactive Lessons, students draw or add shapes to solve the word problem. The problem can be read aloud to them. Some interactive tasks provide in-time feedback to students as they answer questions telling them “Great effort!”, if given a correct answer.

No virtual manipulatives were found in the online lessons. Some lessons do include the draw or add a shape interactive tools.

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten are web-based and compatible with multiple Internet browsers.

  • The materials are platform-neutral and compatible with Chrome, ChromeOS, Safari, and Mozilla Firefox.
  • Materials are compatible with iPads, laptops, Chromebooks, and other devices that connect to the internet with an applicable browser. Online use was difficult on a Chromebook with scrolling and loading issues as well as difficulty seeing all pieces of the interactive editions.
  • The materials are not compatible with an Android device (using Chrome browser). Although the website can be reached, it is not possible to zoom in or out, nor can one move the screen, so a student cannot access the entire screen.

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten include opportunities to assess student mathematical understanding and knowledge of procedural skills using technology through a website called Online ED, which parallels the print textbook. Only one module per grade is currently available in the digital format, so some of the evidence is stated in the materials but has not actually been observed.

  • Lesson problems from the Student Edition, assessments, and unit performance tasks are provided to be completed and scored using technology, providing students with feedback on whether the answers are correct or incorrect.
  • Online Ed is designed to make recommendations for differentiation after auto-scoring of Check Understanding problems within each lesson. 
  • Growth monitoring assessments are “designed to be administered in 40 minutes, 3 times per year. The system utilizes a secure bank of assessments to adapt to each student’s ability and maps progress on the Quantile Framework.” (Pacing Guide)
  • Dynamic Reporting allows teachers to drill down into data for deeper insights into student performance. Assignment reports show detailed results for each assignment. Standard reports show progress towards mastery of each standard. Interim growth measure reports help identify intervention needs and link to recommendations and groupings. 
  • Assessments can be created using a question bank that repeats the questions presented throughout the interactive lessons. However, teachers cannot modify questions nor add new questions.
  • The online system has dynamic reporting by assignment or standards. If teachers are using the online system, they can view student progress for interim growth, module readiness, and lesson practice and homework.

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten are intended to include opportunities for teachers to personalize learning for all students. Full functionality of online materials is not accessible at the time of this review.

  • Teachers can assign lesson problems and assessments, as well as view assessment analytics. 
  • Teachers can group students according to individual needs. The online component has Recommended Groups that “synthesizes data from assessments and places students into leveled groups.” (Pacing Guide) Recommended lesson resources can be assigned to each group.
  • Teachers can create assessments using a bank of items.

The instructional materials reviewed for HMH Into Math Kindergarten provide minimal opportunities to be adapted for local use. Full functionality of online materials is not accessible at the time of this review.

  • Pieces of a lesson can be assigned directly to students or groups of students. 
  • There is a question bank for teachers to create assessments. The bank repeats the questions that are already included in each lesson, and these questions cannot be modified.

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Kindergarten do not incorporate technology that provides opportunities for multiple students to collaborate with the teacher or one another.

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Additional Publication Details

Report Published Date: 05/21/2020

Report Edition: 2020

Title ISBN Edition Publisher Year
Into Math Comprehensive Student Resource Print/Digital Package 6 Year 9780358155539 Houghton Mifflin Harcourt 2020

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

The publisher has not submitted a response.

Please note: Beginning in spring 2020, reports developed by EdReports.org will be using an updated version of our review tools. View draft versions of our revised review criteria here.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
  • Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways. 

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. 

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.

Math K-8

Math High School

ELA K-2

ELA 3-5

ELA 6-8


ELA High School

Science Middle School

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