1st Grade - Gateway 1

The instructional materials reviewed for Math Expressions Grade 1 partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting standards/clusters are connected to the major work of the grade in the lessons devoted to these standards, however, only Units 6 and 7 address supporting work standards. In the Teacher Edition, the Day at a Glance for each lesson contains a bubble identifying the mathematical content standards and mathematical practices addressed in the lesson, and can include connections between supporting and major work.

Examples include, but are not limited to:

• In Unit 6, Lesson 1, students count the animal data in each of two groups and determine how many animals there are in all. This connects supporting standard represent and interpret data (1.MD.4) to the major work of add and subtract within 20 (1.OA.6 ).
• In Unit 6, Lesson 4, students use data representations with three categories to compare most, fewest, and answer questions such as, “How many fewer eggs did Vanilla lay than Daisy? How many eggs did they lay altogether?” This connects supporting standard represent and interpret data (1.MD.4) to major work of solve addition/subtraction/comparing story problems within 20 (1.OA.1).
• In Unit 7, Lesson 2, students “walk their fingers around a clock” while reading together the hour numbers from one through 12 as they touch them. This connects the supporting standard tell and write time in hours and half-hours (1.MD.3) to the major work of count to 120 starting with any number through natural connections (1.NBT.1).
• In Unit 7, Lesson 8, students have to cut out shapes and fold them in half and then determine how many different ways they could fold the shape to make a half. This connects the supporting standard of partitioning shapes (1.G.3) with the major work of adding within 20 (1.OA.6).

The instructional materials for Math Expressions Grade 1 partially meet expectations for the materials being consistent with the progressions in the Standards. The instructional materials follow the progressions of the standards, and identify prior knowledge, however, there are grade-level standards that are not fully met.

The instructional materials clearly identify content from prior and future grade-levels and use it to support the progressions of the grade-level standards. The Teacher Edition (page I19) states, “Standards are designed around coherent progressions from grade to grade. Standards are not stand alone events; they form cohesive links to major work within and across grade levels,” in the Teacher Edition (page I12) there is a chart, A Path to Fluency: Kindergarten through Grade 6 to “help students achieve fluency as described in the Common Core State Standards.” Each unit contains a Math Background section referencing the standards progressions in text boxes, and how they relate to work of the grade. Each Unit Overview lays out how the progression of the grade moves towards standards in future grades. Examples of grade level progressions include, but are not limited to:

• Teacher Edition, Unit 4, Unit Overview, the text box states, “In Grade 1, children will represent 2-digit numbers using concrete objects, place value cards, or drawings. In Grade 2, children will represent 2 and 3-digit numbers using math drawings.”
• Teacher Edition, Path to Fluency, (page I12), the chart notes in Grade 1 students, “Fluently add and subtract within 20 demonstrating fluency for addition and subtraction within 10 (1.OA.6)” and in Grade 2 students, “Fluently add and subtract within 20 using mental strategies. By end of Grade 2 know from memory all sums of two one-digit numbers (2.OA.2).”
• In Unit 6, Lesson 6, students solve comparison story problems using comparison bars to represent the problem. Compare situations are initially introduced in first grade. In a compare situation, two quantities are compared to find ‘How many more’ or ‘How many less.’

The instructional materials attend to the full intent of many grade-level standards by giving all students extensive work with grade-level problems, however, instances where the full intent of the grade-level standards are not met is evident as students have limited opportunities to engage in extensive work. The structure of the Math Expressions program provides a variety of learning opportunities for students to master the grade-level curriculum and provide extensive work with grade-level problems. Knead Knowledge through Practice ensures students gain understanding and fluency with desired methods. Daily Routines, Quick Practice, Student Practice pages, Homework practice, Remembering pages, and Math Activity Centers support the classroom learning in every lesson. Some instances are evident where the full intent of the standard is not met, and there are some lessons that would need to be omitted as they attend to future grade standards.

Examples of materials meeting full intent of the standards include, but are not limited to:

• Unit 3, Lessons 3 through 12, Quick Practice, students count on to find the unknown partner in addition equations. For example, “2 + ? = 4” (1.OA.8).
• Unit 4, Lesson 12, Math Activity Center for on-level, challenge, and intervention work. On-Level Resources include Activity Card 4-12 which has students write two 2-digit numbers, model the numbers with a drawing, and compare the numbers. Challenge Resources include Activity Card 4-12 which has students create four 2-digit numbers and determine which has the greatest value and which has the least value. Students needing intervention complete Activity Card 4-12 which has students represent two 2-digit numbers using base ten blocks and compare the numbers using >, <, or = (1.NBT.3).
• Unit 6, Daily Routines, Example 83, the student leader shows the class a number with one Demonstration Secret Code Card tens card and a ones card. Then asks the students, “What is this number? How many tens and ones? What is ten more than 83? Why?” (1.NBT.2)

Instances where full intent of the standard is not met:

• Three lessons in Unit 7 (Lessons 12, 13, 14) address standard 1.MD.1, measure lengths indirectly and by iterating length units which is major work of the grade. Within the three lessons, students measure two real objects and 13 pictures of objects with paper clips. Students are not given the opportunity to measure with different objects or to compare how the measurements are different if different measuring tools, other than paper clips are used. Supplemental work may need to be provided to meet the full intent of this standard.
• Four lessons in Unit 4 (Lessons 3, 12, 16, 18) address standard 1.NBT.3, compare two-digit numbers using symbols. An additional comparing numbers lesson appears in Unit 8, Lesson 6, however no symbols are used for the comparisons.

One example of an above grade level lesson needing to be omitted:

• Unit 8, Lessons 1 and 2, students are introduced to the “New Group Below” and “New Group Above” methods for vertical addition. The “New Group Above Method” is the standard algorithm which is a Grade 4 standard (4.NBT.4) and is not clearly identified as future grade level content. Throughout the Unit, students are not required to use the “New Group Above” method.

The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Learning paths are identified at the beginning of each unit relating grade-level concepts to prior knowledge from earlier lessons. Examples where content is connected to prior grades includes, but is not limited to:

• Teacher Edition, Unit 1, Learning Path in the Common Core Standards, states, “Unit 1 emphasizes the 1-more and 1-less pattern, first with counting numbers, then with finding partners, and finally with addition and subtraction. The repeated experiences in Unit 1 are a bridge from Kindergarten experiences to the embedded addends required in Unit 2 for counting on...Later in Units 2 and 3, children will extend their thinking to using strategies for adding and subtracting within 10.”
• Teacher Edition, Unit 4, Learning Path in the Common Core Standards, the author states, “This unit builds on the work with teen numbers that began in Kindergarten. Children explore tens and ones using physical groupings and math drawings. Activities provide repeated experience in building 2-digit numbers with strong visual support. Children extend these place value concepts to adding with 1- and 2-digit numbers.”
• Teacher Edition, Unit 7, Learning Path in the Common Core Standards, the author states, “This unit builds on the geometry and measurement concepts and knowledge that children bring from Kindergarten.”