Materials considered for review for this indicator were STEM projects. The instructional materials reviewed for Grade 5 do not meet the expectations for this indicator. The review team found that the instructional materials assess grade level content beyond the scope of the grade. The out of grade level standards assessed are not Mathematically reasonable for this grade level.

STEM materials that assess grade level content beyond Grade 5 include:

• M-Class Hydroplane Racing STEM project on pages 55 – 78 of the teacher STEM project edition.
  • This project asks students to address surface area. This is not to be addressed until Grade 6 according to 6.G.A.4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
  • This project, on page 37 of the student STEM project edition, asks students to find the percent of a number. This is not to be addressed until Grade 6 according to 6.RP.3.C.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
    

• Engines STEM project on pages 15 – 38 of the teacher STEM project edition:
  • This project asks students to find the area of a circle. This is not to be addressed until Grade 7 according to 7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
  • The project asks students to find the volume of a cylinder. This is not to be addressed until Grade 8 according to 8.G.C.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
• Fractional playground STEM project on pages 39 – 54 of the teacher STEM project edition:
  • This project asks students to find the average. This is not to be addressed until Grade 6 according to 6.SP.B.5.C Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
    

Review Team Note: A separate supplemental digital assessment database is available for an additional purchase cost. The review team did not analyze this supplemental digital assessment database as evidence for indicator 1a due to the fact that this additional component is not provided as part of the core materials.

*Evidence updated 10/27/15

The instructional materials reviewed for Grade 5 do not meet expectations for focus. The materials do not spend the majority of class time on the major cluster of each grade. A total of 74 activities/lessons are provided between the three resources, and some may be repeated or take additional class periods. However, only 47 of the 74 lessons are aligned to major work at the grade according to teacher edition, ART and STEM table of contents. If the 47 lessons were fully aligned, 63.5% of the time is spent on the major work. In looking more closely, the percent of time spent on major work would be below 63.5%. These lessons are labeled as aligned to major work of the grade but the activities in the lessons do not actually align and some of the lessons include content that is beyond the scope of the grade. Examples of these misalignments include:

• The ART lesson on page 14 is about factors and prime factorization which can connect to expressions, but the activity does not follow the full meaning of the standard.
• The 5.NF.A.2 lesson beginning on teacher edition page 233 limits use of visual fraction models, no use of benchmark fractions and few experiences with adding/subtracting fractions in word problems.
• The STEM project "M-Class Hydroplane Racing" does not include work of counting unit cubes or include a jump to surface area.
• The teacher edition lesson on pages 35-47 only addresses one-step numerical patterns and students are not generalizing patterns themselves.
• Most of the pages in teacher edition pages 48-62 are limited to writing numbers, identifying the value of digit in a number and comparing numbers, which is not what is meant in the standard 5.NBT.A.1.
• In the lessons on pages 95-106, the >, = and < symbols are mentioned on page 97 and one student exercise on page 105 uses the symbols, but the rest of the lesson does not use the symbols to compare decimals to thousandths. The lesson doesn't show students how to place numbers together to demonstrate comparing each digit on both sides of a decimal to determine if the numbers are greater than, equal to, or less than. It also waters down the symbols by referring to the numbers as merely bigger or smaller rather than the vocabulary of the grade level (5.NBT.A.3.B).
• In the teacher edition on pages 113-121, all the problems round to exactly one place to the left of the last digit in the number; e.g., numbers in the hundredths always rounded to tenths, thousandths always rounded to hundredths (5.NBT.A.4).
• Teacher edition pages 263-299 are supposed to build on student understanding of fractions and use visual fraction models, but they merely have students perform a procedure to solve the problems (5.NF.B.4).
• Teacher edition pages 300-316 provide additional multiplication practice with no real connection to scaling or comparing product to factor size (5.NF.B.5.A).
• Teacher edition pages 317-337 provide no opportunities to have students explain why multiplying a number by a fraction less than one results in a smaller product (5.NF.B.5.B).
• Teacher edition pages 338-350 instructs students to always turn a mixed number into a fraction to perform an operation on it, even when that is not the most efficient strategy (5.NF.B.6).
• Teacher edition pages 351-360 do not have students use visual fraction models or create story context to solve problems (5.NF.B.7.A).

Therefore, the percentage would be considerably less than 63%, making the content connections to major work less focused.

The instructional materials for Grade 5 do not meet the expectation for coherence so that supporting content would enhance the major work of the grade. Examples of missed opportunities for coherence include:

• The STEM lesson "Cryptology," which does not support the major work of 5.NBT.
• The ART lesson on page 146 does not support the major work of 5.NF fully at the grade level; all fraction calculation has been done for students, additional units could have been added so that students had to use conversion and the connection to 5.NBT.

The Grade 5 instructional materials reviewed for school year viability do not meet expectations for the indicator. The amount of content is not viable for one school year for the following reasons:

• Between the three resources, 63.5% of the time is spent on major work. Beyond that, the lessons do not all align with major work. There would be gaps in understanding with only one lesson in the teacher edition on page 122 specifically on fluency (5.NBT.B.5), and little to no connection made to multi-digit multiplication in other lessons in the teacher edition, STEM or ART resources.
• The liquid volume example in ART, page 157, with the cylinder is a Grade 8 example. "Cube nets" on two ART lessons, pages 162 and 167, are aligned with 6.G.
• The examples show that the amount of time on major work in the Grade 5 instructional materials decreases, meaning less time is spent on major work connecting to prior and future grade levels.

The materials reviewed for Grade 5 do not meet expectations for consistency with the progressions in the standards.

• All three resources are void of a tape diagram model, which is an essential representation in the coherent development of whole number and fraction understanding in the standards progressions.
• The ART lesson on page 54 on fluency has a problem with an array model, a great strategy that was not fully developed in prior grades. At this point, students should move to an open area model and partial products methods in connecting with other standards in the 5.NBT domain, which allow student work to reach fluency.
• Considering 5.NBT is major work in Grade 5 and division is a large portion of the standards in 5.NBT, it is not enough to have three lessons on 5.NBT.B.6.
• Teacher edition page 134, ART page 60 and the STEM project "Engines" connect to 5.MD, but are not labeled as such.
• Connections between multiplication and multiplication with fractions misses groups of fractional amounts or fraction-sized parts to multiply by a whole group or situation. This is evidenced in ART lesson page 94. Additionally, ART lesson page 100 should allow for students to tile fractional units, and see the overlap in the product on the area model, not just the shaded product.
• The classroom activity on pages 519-530 on the standards 5.G.B.3 and 5.G.B.4 requires students to classify two-dimensional figures in a hierarchy based on properties and understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. However, the student exercises focus on using equations to find the missing angles instead of classifying or organizing shapes by categories.
• Mathematical practices are not indicated nor aligned throughout lessons and instead are provided their own set of activities at the end of the book. This exact same set of activities appears in all teacher editions, Grades 3-5.

There are further examples where content from future grades is inconsistently identified as such:

• Teacher editions pages 155-157 (5.NBT).
• Teacher editions pages 351-373, beyond grade fraction work (5.NF.B.7).
• ART pages 125, 128 and 134, beyond grade level fraction work (5.NF.B.7.A and 5.NF.B.7.B).
• Teacher editions page 409, Grade 2 level line plot (5.MD.B.2).
• Teacher editions page 453, lacking real world problems, beyond grade level.

The instructional materials reviewed for Grade 5 do not meet expectations for fostering coherence through connections at a single grade level. Learning objectives are written and either address learning at the individual standard level, or they restate the cluster. Although standards and objectives are listed for each lesson, it does not always cohesively connect together in the following examples:

• STEM project "Planetary Exploration"
• ART lesson, page 44
• Teacher edition lesson, page 1
• Teacher edition, page 210
• Teacher edition, page 388
• STEM project "Cryptology"

Each lesson is taught in isolation, as a standard or a cluster of standards within the same domain. There are missed opportunities for connections including:

• Missing 5.OA and 5.NBT connections in teacher edition pages 2-47, mostly whole number smaller numbers.
• Missing coherence between 5.MD.B and 5.NF.A with use of fractions within line plots for real-world problems.

With the exception of the ART lessons having a family theme (21st Century Families), there is no mathematical connection from one lesson to the next within a domain and materials do not make connections between domains or clusters when appropriate. Connections between concepts are not clearly articulated for teachers and therefore the criteria is not met.