3rd-5th Grade - Gateway 1

The materials reviewed for Experience Math Grades 3 through Grade 5 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The formal assessments follow a consistent structure across grades, including Diagnostic Tasks, Topic Assessments, Online Topic Assessments (autoscorable), Parallel Topic Assessments, and Performance Tasks. Grade 3 includes seventeen Diagnostic Tasks, seventeen Topic Assessments, seventeen Online Topic Assessments (autoscorable), four Parallel Topic Assessments, and ten Performance Tasks. Grade 4 includes twenty-one Diagnostic Tasks, twenty-one Topic Assessments, twenty-one Online Topic Assessments (autoscorable), nine Parallel Topic Assessments, and sixteen Performance Tasks. Grade 5 includes fourteen Diagnostic Tasks, fourteen Topic Assessments, fourteen Online Topic Assessments (autoscorable), nine Parallel Topic Assessments, and nine Performance Tasks.

Examples include:

• Grade 3, Topic 12: Algebra, End of Topic Resources, Topic Assessment, Question 12, “For Questions 11 to 14, model each equation using counting rods or a pan balance and cubes. 12. 4\times7=3\times7+1\times7.” (3.OA.3)

• Grade 4, Topic 2: Representing, Comparing, and Ordering Fractions, End of Topic Resources, Topic Assessment, Question 12, “How do you know that \frac{2}{5} is less than \frac{7}{10} by just looking at the fractions?” (4.NF.2)

• Grade 5, Topic 4: Whole Number and Fraction Operations, Planning and Resources, Diagnostic Task, Question 4, “Use the numbers above to do the following. You may use a number more than once. Write two fractions with the same denominator, and then subtract one fraction from the other.” Students are provided with the numbers 2, 3, 4, 5, 8, 25, and 50. (4.NF.3a)

The materials reviewed for Experience Math Grades 3 through Grade 5 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

Assessment Item Correlations documents include item analysis charts for all formal assessments in the program (Diagnostic Tasks, Topic Assessments, and Performance Tasks). Each chart contains several key components: the item number for reference, a brief description of the mathematical content assessed (“Math Content” column), the aligned Common Core State Standard (“CCSS” column) with its cluster designation, the Depth of Knowledge (“DOK” column) level indicating the required cognitive complexity (Levels 1–3), and the Standards for Mathematical Practice (“SMPs” column) that students engage in while solving the problem.

Examples include:

• Grade 3, Topic 14: Geometry, End of Topic Resources, Topic Assessment, Question 6, "What are all the different names you could give to this shape?" A picture of a square is provided. The Assessment Item Correlations to CCSS states that the standards addressed are 3.G.1, MP3, MP6, MP7.

• Grade 4, Topic 2: Representing, Comparing, and Ordering Fractions, Planning and Resources, Diagnostic Task, Questions 3 and 4, “3. Show your fraction as part of a set of counters. Explain how you created your counter model. 4. Write a fraction that is equivalent to your fraction. How do you know it’s equivalent?” The fractions provided are \frac{4}{6}, \frac{4}{8}, and \frac{4}{10}. The Assessment Item Correlations to CCSS states that the standards addressed are 3.NF.A.1, 4.NF.1, MP1, MP3, MP4, MP6, MP7.

• Grade 5, Topic 10: Representing Decimals, End of Topic Resources, Performance Task, Question 1, “Create a game for two players that involves representations of decimals to thousandths. Part of the game should involve representing fractions, decimals, to tenths, or decimals to hundredths as decimal thousandths.” The Assessment Item Correlations to CCSS states that the standards addressed are 5.NBT.3, MP1, MP4.

There is no standard identification provided within the assessments themselves or in the Teacher Experience Guide for each topic.

The materials for Experience Math Grade 3 through Grade 5 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Each lesson follows a consistent three-part structure that engages students in extensive work with grade-level problems. The three parts include Minds On, Action Task (which provides open-ended problem-solving prompts that require collaboration and critical thinking), and Consolidate Questions. Each topic includes various games and activities that may feature Academic Vocabulary, Brain Benders, Data Tasks, Making Connections Tasks, Math Talks (including Number Talks and Data Talks), and Wonder Tasks, as well as Your Turn and Additional Practice. Across the materials, students have multiple opportunities to demonstrate understanding of the full intent of the grade-level standards. The materials provide extensive opportunities for students to engage with grade-level work aligned to the standards, with limited opportunities for extensive work with 3.MD.1.

Examples include:

• Grade 3, Topic 4: Representing Fractions, Lesson 1, and Topic 14: Geometry, Lesson 2 engage students with the full intent of 3.G.2 (Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole). Topic 4, Lesson 1, Minds On Activity, Question 1 states, “What foods might you eat half of at a time? Explain your thinking.” Students use pictures of whole foods and sets of foods, such as a whole chicken or four pieces of sushi to name and represent fractions in different ways, including showing fractions of an area. Question 2 states, “When might you eat a fraction of a food that is not a half? What fraction do you eat? Explain your thinking.” Teacher Guidance, After the Minds On Activity states, “Introduce standard fractional notation. Let students know that we can write one half as \frac{1}{2}. Show one or two different representations of \frac{1}{2}. Make sure students understand that the 2 in \frac{1}{2} tells how many equal sections the whole has been partitioned into. Use the term ‘denominator’ to name that value. Let students know that the 1 in \frac{1}{2} tells that we are talking about one of those sections. Then ask students what \frac{1}{3} might mean. Help them see that the whole is divided into 3 equal sections and the unit is 1 third. Then introduce \frac{2}{3} (read as two thirds) and ask students what they think that might mean. Help them learn that it means there are two \frac{1}{3}s, that is, \frac{1}{3} and another \frac{1}{3} . The ‘numerator’ (the top number) tells how many of the units we’re talking about…” Action Task, Teacher Guidance, In This Task … states, “Students create wholes that allow them to display given fractions.” Action Task, Question 1 states, “Use tiles for a-c. a. Draw a sketch or take a picture. Show 26 . b. Which part is 26? c. What other fractions do you see?” Question 2 states, “Use tiles for a-d. a. Draw a sketch or take a picture. Show \frac{2}{8} . b. Which part is \frac{2}{8}? c. What fraction describes the whole? d. What other fractions do you see?” Teacher Guidance, And the Point Is … states, “This Action Task provides an opportunity to create a whole when given a fraction of a whole; focuses on the respective roles of the numerator and denominator of the fraction; addresses the fact that when you have one fraction (Sample response: 26), you always have another one: the other part of the whole is there (Sample response: 46), as well as the whole itself (Sample response: 66). Consolidate Questions, Question 1 states, “Suppose you use tiles to show \frac{2}{6}. What does the 2 in the fraction tell you? What does the 6, or ‘sixths,’ tell you?" Question 2 states, “If 2 red tiles show \frac{2}{6}, do they have to be next to each other? Explain.?” Question 3 states, “When you see a fraction like \frac{2}{8}, what other fractions can you see? Explain.” A picture showing two red and six blue squares, with two squares on top and six on the bottom, is provided. Question 4 states, “How can a trapezoid represent \frac{1}{2} in one situation and \frac{1}{4} in another situation?” A picture of a red trapezoid is provided. Topic 14, Lesson 2, Action Task states, “In Questions 1 and 2, fold the shapes or use a ruler and pencil to partition the shapes.” Question 1 states, “Start with a rectangle. a. Partition the rectangle into 4 equal parts. b. What shape are the parts? c. What fraction of the big rectangle is each part?” Question 3 states, “How can you know that the parts that you made for Question 1 are the same size as the parts you made for Question 2?” Question 4 states, “Decompose a square into 8 smaller parts. The parts should not all be the same size. Is each part \frac{1}{8} of the big square?”

• Grade 4, Topic 14: Dividing Whole Numbers, Lesson 3, engages students with the full intent of 4.OA.3 (Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies, including rounding). Action Task, Question 1 states, “Ryan and Kyle served 249 meals at the community kitchen. Ryan served twice as many meals as Kyle. How many meals did each person serve? Show all your work.” Question 3 states, “A meal program in a large city served three times as many meals in a week as a meal program in a smaller city. Altogether, both programs served 8,320 meals in a week. How many meals did each program serve?” Your Turn, Question 8 states, ”Lync and his brother Lionel collect seashells. Lync has collected 4 times as many seashells as Lionel. They have 520 shells altogether. How many shells does each person have?”

• Grade 5, Topic 12: Adding and Subtracting with Decimals, Lessons 1, 2, 3, 4, and 5 engage students with the full intent of 5.NBT.7 (Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used). Lesson 1, Action Task, Question 3 states, “Carson and Anika put their pencils together. Carson has 2. \squarepacks. (2 and \square tenths). Anika has 1. \square packs. (1 and \square tenths). Together, they have enough pencils to fill more than 4 packs. How many packs might each student have? List all the possibilities you can. Explain your reasoning. Write a few answers using equations.” Teacher Guidance, And the Point Is… states, “This Action Task involves a model for 1 that obviously shows 10 tenths (i.e., a pack of 10 pencils). These types of models are helpful for students as they start adding decimals. The first two questions should give you a sense of whether students are comfortable representing decimals to tenths. As students work on the task in Action Question 3, some will think of whole numbers (i.e., 2\square pencils and 1\square pencils have a sum of 4\square pencils), whereas others will work with decimals. The former approach is good scaffolding for students who need it, but it’s important in the Consolidate discussion to make the connection to decimals.” Your Turn, Question 5 states, “Think about adding 4.2 and 3.8. a. Show or describe two or three strategies for calculating the sum.” Lesson 2, Action Task states, “Families made 9 pans of lasagna for a school event. Each pan of lasagna was cut into 10 equal pieces. After the event, there were: a few full pans of lasagna left over; 3 pieces of another pan of lasagna left over. 1. How much lasagna might have been eaten? List lots of different possible answers. Write your answers in the following form using decimals: \square.\square pans of lasagna. Show or explain how you figured out your answers.” Your Turn, Question 6 states, “Think about subtracting 2.9 from 6.1. Show or describe two or three strategies for calculating the difference. How would you estimate the difference?” Lesson 3, Action Task, Question 1 states, “Choose three of the containers above. If you put the contents of all three containers you chose together, what size container would fit that amount exactly? Estimate to show that your answer makes sense.” Teacher Guidance, And the Point Is… states, “This Action Task requires the addition of decimals to tenths and decimals to hundredths. Students often find this kind of situation challenging. If they use a conventional algorithm, they might line up the digits incorrectly. Students are given a choice in selecting containers so that they have some ownership of the problem they’re solving. There are 10 possible combinations of 3, so there is a lot of choice for students. They are asked to repeat the problem with other combinations to provide more practice.” Your Turn states, “For Questions 2 and 3, use a model to show each addition.” Question 2 states, “4.5 + 3.82”, Question 3 states, “3.17 + 2.89.” Lesson 4, Action Task, Question 1 states, “Think about how far you walk in a week. a. What is a reasonable value for the number of miles you walked last week (7 days)? b. Explain why your value is reasonable. For Questions 2 to 4, calculate each difference. Show your thinking using words and models or pictures. 2. Kendra walked 24.25 miles. Is your value more or less than that? How much more or less? 3. Zayden walked 21.38 miles. Is your value more or less than that? How much more or less. 4. Wyatt walked 15.23 miles. Is your value more or less than that? How much more or less? 5. If you walk 3.29 fewer miles next week, how many miles would that be? Explain how you know.” Your Turn states, “For Questions 2 and 3, calculate each difference. Use models to show how to subtract.” Question 2 states, “4.5 - 0.82.” Question 3 states, “8.17 - 2.89” Lesson 5, Action Task states, “Fruit cups come in packs of 10. Some full packs and part of a pack are in one cupboard. Some more full packs and part of another pack are in another cupboard. Vince served some of the fruit cups at a party. There are 2 full packs and 2 fruit cups left. 1. How many packs of fruit cups might have been in each cupboard? Fill in the chart, using decimals to represent packs of fruit cups. Write an equation to describe each row. 2. Use one of your equations from Question 1. Make up a different word problem that could be solved using that equation.” Teacher Guidance, And the Point Is… states, “The problem in this Action Task involves both addition and subtraction and has many possible solutions. Because the solutions are related, it will be possible to discuss these relationships. Using the relationships among solutions is an important math skill for students to practice. It is also important for students to see that the same equation describes myriad situations. Asking students to think of something other than fruit cups in Action Question 2 requires them to think of other circumstances where using decimals to tenths would make sense.”

Materials do not present all students with extensive work of 3.MD.1. Examples include:

• Students have limited opportunities to engage in extensive work of 3.MD.1 (Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram). This is the only lesson that addresses 3.MD.1. In this lesson, students read both analog and digital clocks to the nearest minute and apply those times to solve problems involving elapsed time. Topic 7: Length and Time, Lesson 1, Minds On Activity, Question 1 states, “The hands of a clock are about as far apart as they are when the time is 5:55, but the time is closer to 10:00. What time might it be?” Question 2 states, “What if the hands of the clock are about as far apart as they are at when the time is 3:35, but the time is close to 9 o’clock? What time might it be?” Teacher Guidance, After the Minds On Activity states, “Review skip counting by 5s from 0 to 60 to remind students about reading times to the nearest 5 minutes. Introduce telling time to the nearest minute by showing the distinction between 1:50 and 1:51 or 2:10 and 2:12. Show a few more examples on the clock, and have students read time to the nearest minute. Remind students about digital clocks and what they look like. Provide a few examples of showing digital time on an analog clock and vice versa. Students will likely need to practice this over time, not only in this lesson. Model how a number line can be used to measure how much time has passed.” Action Task, Teacher Guidance, In This Task … states, “Students choose pairs of times that meet given criteria, represent the times on analog and digital clocks, and estimate and calculate how much time will pass from one time to the next.” Action Task states, “For Questions 1–3, think of two times when both hands of an analog clock are pretty close together.” Question 1 states, “Show each time as it would appear on both an analog clock and a digital clock.” Students are provided with black analog and digital clocks to fill in. Question 2 states, “About how much time will pass between the 2 times? Explain your estimate." Question 3 states, “Exactly how many minutes have passed? How did you calculate your answer?” Question 4 states, “What time is it if it’s 42 minutes after 2:43? Show both times on both an analog clock and digital clock. Explain how you figured out the time.” Question 5 states, “Think of 2 different times that are 100 minutes apart. Make sure neither time is exactly on an hour, such as 1 o’clock or 2 o’clock. Show both times on both a digital and analog clock. How did you figure out the times?” Consolidate Questions, Question 1 states, “Why is the minute hand very important for reading time to the nearest minute but not as important for reading time to the nearest half hour?” Question 2 states: “Describe how you would use a number line to tell how much time has passed from 3:21 to 4:18. How else could you figure out that length of time?” Question 5 states, “When figuring out the time from 3:52 to 5:15, why does it make sense to use a number line instead of subtracting 352 from 515?” The Exit Ticket and Additional Practice are the only portions of the lesson where students tell time on analog clocks. The Minds On Activity states, “Students will likely need to practice this over time, not only in this lesson.” There are no additional lessons that provide opportunities for students to continue practicing this standard. Based on this single lesson, students are not provided opportunities to engage in extensive work with telling time or using number lines to determine elapsed time.

The materials for Experience Math Grades 3 through Grade 5 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. 

The pacing guide outlines that instruction time varies by grade. In Grade 3 and Grade 5, most lessons span about two days, totaling approximately 90 to 130 minutes when differentiation is included. In Grade 4, most lessons are designed to take one day, about 45 to 65 minutes each, with a few identified for two-day instruction. Each grade level also includes additional days for review, assessment, and connecting or extension tasks. Overall, the program dedicates at least sixty-five percent of instructional time to the major work of the grade.

In Grade 3:

• The number of topics devoted to the major work of the grade (including assessments and related supporting work) is 12 out of 17, approximately 71%.

• The number of lessons devoted to the major work of the grade (including assessments and related supporting work) is 43 out of 58, approximately 74%

• The number of days devoted to major work of the grade (including assessments and related supporting work, but excluding a review day) is 93 out of 150, approximately 62%.

• The number of days devoted to major work of the grade (including assessments and related supporting work) is 105 out of 150, approximately 70%.

In Grade 4:

• The number of topics devoted to the major work of the grade (including assessments and related supporting work) is 15 out of 21, approximately 71%.

• The number of lessons devoted to the major work of the grade (including assessments and related supporting work) is 72 out of 86, approximately 84%

• The number of days devoted to major work of the grade (including assessments and related supporting work, but excluding a review day) is 98 out of 162, approximately 60%.

• The number of days devoted to the major work of the grade (including assessments and related supporting work) is 113 out of 162, approximately 70%.

In Grade 5:

• The number of topics devoted to the major work of the grade (including assessments and related supporting work) is 11 out of 14, approximately 79%.

• The number of lessons devoted to the major work of the grade (including assessments and related supporting work) is 40 out of 53, approximately 75%

• The number of days devoted to the major work of the grade (including assessments and related supporting work, but excluding a review day) is 98 out of 148, approximately 66%.

• The number of days devoted to major work of the grade (including assessments and related supporting work) is 109 out of 148, approximately 74%.

An instructional day analysis across Grades 3 through 5 is most representative of the instructional materials as the days include major work, supporting work connected to major work, and the assessments embedded within each topic. Approximately 70% of the materials in Grade 3, 70% of the materials in Grade 4, and 74% of the materials in Grade 5 focus on the major work of the grade.

The materials reviewed for Experience Math Grades 3 through 5 meet expectations that supporting content simultaneously enhances focus and coherence by engaging students in the major work of the grade. 

Materials are designed so that supporting standards/clusters are connected to the major standards/ clusters of the grade. These connections are found within Topics and Lessons. 

An example of a connection in Grade 3 includes:

• Topic 7: Length and Time, Student Experience Book, Lesson 3, connects the supporting work of 3.MD.4 (Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters) to the major work of 3.NF.2 (Understand a fraction as a number on the number line; represent fractions on a number line diagram). Students measure objects to the nearest quarter inch, apply their understanding of fractional units in a concrete context, and record these measurements on a number line as line plots, reinforcing fractions as specific numerical locations. The Minds On Activity has students measure lengths and then create line plots to display fractional measurement data. Student Experience Book, Action Task states, “Start with 6 straws. Cut 2 of your straws into 2 pieces that are not equal in length. Cut 2 of your straws into 3 pieces that are not all equal in length. Cut 2 of your straws into 4 pieces that are not all equal in length. 1. Measure each of your straw pieces to the nearest quarter inch. 2. Create a line plot to display the lengths of the straw pieces. Label the tick marks using quarter-inch intervals. Plot your straw piece lengths. Make sure to create a title and label the line plot. 3. Tell 3 things you know from your line plot.” 

An example of a connection in Grade 4 includes:

• Topic 16: Weight and Mass, Student Experience Book, Lesson 2, connects the supporting work of 4.MD.2 (Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale) to the major work of 4.OA.3 (Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies, including rounding). Students solve multistep word problems using the four operations that focus on weight and mass measurement units. In the Minds On activity, students create a word problem that has a solution of 3\frac{1}{2}. In the Action Task, students search the internet to find data to help solve word problems involving weight and mass as well as converting units of measure. Student Experience Book, Action Task states, “1. Choose three types of animals. Find out how heavy they usually are at birth and as adults. Use ounces, pounds, or tons as units. Which one grows the most? 2. Choose a big vehicle that weighs a lot and a smaller one that does not weigh as much. Use kilograms or tons as units. How many of the small vehicle would it take to have the same weight as the big vehicle? 3. Suppose you had eaten 4\frac{1}{2} ounces of a snack and then ate another 2\frac{1}{4} ounces. How many ounces will you have eaten? 4. Fill in the blanks to make this statement true. Explain your thinking. 5\frac{1}{2} tons - ____ pounds = ____ ounces.”

An example of a connection in Grade 5 includes:

• Topic 14: Solving Measurement Problems, Student Experience Book, Lesson 6, connects the supporting work of 5.MD.2 (Make a line plot to display a data set of measurements in fractions of a unit (\frac{1}{2}, \frac{1}{4}, \frac{1}{8}). Use operations on fractions for this grade to solve problems involving information presented in line plots) to the major work of 5.NF.2 (Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers). Students use line plots with fractional units to represent data and then solve addition and subtraction word problems with fractions. In the Minds On activity, students solve simple addition and subtraction problems using data from a line plot with fractional units. In the Action Task, students create line plots and then solve addition and subtraction problems. Student Experience Book, Action Task states, “1. Choose about 20 books on a bookshelf in the library. a. Measure the height of each book to the nearest eighth of an inch. Record the measurements in eighths, fourths, and halves of an inch. b. Create a line plot to show your measurements. c. Pose and answer three questions that require adding and subtracting fractions with different denominators, using the information in your line plot.”

The materials reviewed for Experience Math Grades 3 through 5 meet expectations for including problems and activities that connect two or more clusters in a domain, or two or more domains in a grade. 

Connections among the major work of the grade are present throughout the materials where appropriate. These connections are within Topics and Lessons.

An example of a connection in Grade 3 includes:

• Topic 13: Mass, Lesson 3, Student Experience Book, connects the major work of 3.MD.A (Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects) to the major work of 3.NF.A (Develop understanding of fractions as numbers). Students interpret 13 of a kilogram as a quantity of mass and use the fractional unit to find the total mass. Teacher Experience Guide, Action Task states, “Varies between questions involving fractions and questions involving whole numbers.” Student Experience Book, Action Task states, “5. A pair of children’s sneakers has a mass of about \frac{1}{3} of a kilogram. What would the mass of all our sneakers be?”

An example of a connection in Grade 4 includes:

• Topic 9: Representing Decimals, Lesson 6, Student Experience Book, connects the major work of 4.NF.A (Extend understanding of fraction equivalence and ordering)to the major work of 4.NF.C (Understand decimal notation for fractions, and compare decimal fractions). Students solve a word problem converting fractions to decimals and decimals to fractions to solve. Student Experience Book, Action Task states, “Rosi’s school has exactly 100 students in Grade 4. Groups of students at the school can be described using fractions or decimals. 1. Choose two of these fractions. \frac{1}{2}, \frac{3}{4}, \frac{2}{5} Describe what each fraction might represent about the Grade 4 students. Use a model to show each fraction. Write each fraction as a decimal. 3. Choose two of these decimals. 0.11, 0.16, 0.4. Describe what each decimal might represent about the Grade 4 students. Use a model to show each decimal. Write each decimal as a fraction.”

An example of a connection in Grade 5 includes:

• Topic 12: Adding and Subtracting Decimals, Lesson 1, Student Experience Book, connects the major work of 5.NBT.A (Understand the place value system) to the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths). Students use models to represent whole numbers as decimals (tenths) and solve addition problems. Student Experience Book, Action Task states, “1. What does 0.3 of a pack of pencils look like? 2. What do 1.2 packs of pencils look like?” Students see two packs of 10 pencils and one pack with 3 pencils. For question 3, students see that Carson has two packs of 10 pencils and another pack that is covered. Annika has one full pack of 10 pencils showing and another pack that is covered. “3. Carson and Anika put their pencils together. Carson has 2. \square packs (2 and \square tenths) Anika has 1. \square packs (1 and \square tenths) Together they have enough pencils to fill more than 4 packs. How many packs might each student have? List all the possibilities you can. Explain your reasoning. Write a few answers using equations.”

The materials reviewed for Experience Math Grades 3 through 5 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. 

The materials provide multiple features to support coherence across grade levels. Connecting to Concepts Beyond the Grade notes at each grade and topic guide teachers to see how current instruction fits within the broader K-8 progression of learning. These notes identify how current instruction prepares students for future standards and clarify the significance of these connections by sharing the progression of mathematical understanding. For example: 

• In Grade 3, Teachers Experience Guide, Connecting to Concepts Beyond the Grade links the work in Grade 3 to related concepts in later grades, including Grades 5, 6, 8, and high school. Estimating Whole Numbers (Topic 9) states, ​“In Grade 3 Topic 9, students focus on making sense of numbers through estimation using place value concepts, with particular emphasis on rounding to the nearest ten and hundred. This work with estimation establishes foundational skills that extend to increasingly complex contexts in later grades. As students progress to Grade 5, they apply these estimation principles to decimals. In Grade 6, they extend their estimation skills to larger numbers. In Grade 8, the skills developed in Grade 3 help students estimate large numbers like 1,034,044,121 as approximately 10^9 or round decimals like 4.234158 to 4.2 or 4.23 depending on the required precision. The distinction between rounding to the nearest ten versus the nearest hundred introduces students to the important concept of precision, which becomes increasingly significant in Grade 8 scientific notation work. Students will understand that a measurement of 4.23 inches is more precise than 4.2 inches because the range of possible values is smaller-only measurements from 4.225 to 4.235 (a range of \frac{1}{100}) round to 4.23, while measurements from 4.15 to 4.25 (a range of \frac{1}{10}) round to 4.2. This understanding of estimation and precision supports students’ work across mathematical domains as they progress through middle school and high school.”

Going Back notes emphasize prior knowledge and skills that form the foundation for grade-level learning, while Going Forward notes describe how current concepts will be extended and applied in later grades. Together, these supports strengthen coherence across grade levels by helping teachers make explicit links between prior, current, and future learning. 

An example of a connection to future grades in Grade 3 includes:

• Topic 4: Representing Fractions, Teachers' Experience Guide, Planning and Resources, Topic 4: Planning connects the fraction work of Grade 3 to the future work in Grade 4, where students represent, compare, and order fractions. Teachers' Experience Guide, Going Forward states, “In moving from Grade 3 to Grade 4, students extend their understanding of representing, comparing, and ordering fractions, as well as finding equivalent fractions and performing fraction operations.”

An example of a connection to prior knowledge in Grade 3 includes:

• Topic 10: Adding and Subtracting Whole Numbers, Teachers' Experience Guide, Planning and Resources, Topic 10: Planning connects the adding and subtracting whole numbers work of Grade 3 to the prior work in Grade 2, where students added and subtracted within 20, subtracted from two-digit numbers, added and subtracted numbers less than 100, and solved addition and subtraction problems. Teachers' Experience Guide, Going Back states, “Students gain more fluency and approach addition and subtraction more symbolically in Grade 3 than Grade 2. That said, the standard algorithms are not required until Grade 4. The problems solved in Grade 3 tend to involve more three-digit numbers and may be somewhat more complex than problems solved in Grade 2.”

An example of a connection to future grades in Grade 4 includes:

• Topic 3: Representing Four-Digit Whole Numbers, Teachers' Experience Guide, Planning and Resources, Topic 3: Planning connects the Grade 4 work of representing four-digit whole numbers using words and numbers to the future work in Grade 5, where students extend their understanding to numbers in the millions and beyond. Teachers' Experience Guide, Going Forward states, “In moving from Grade 4 to Grade 5, students extend what they learn about four-, five-, and six-digit whole numbers to work with greater whole numbers.”

An example of a connection to prior knowledge in Grade 4 includes:

• Topic 10: Shapes and Lines, Teachers' Experience Guide, Planning and Resources, Topic 10: Planning connects the Grade 4 work of identifying lines of symmetry, parallel and perpendicular lines, and classifying triangles by angles to the prior work in Grade 3, where students developed knowledge of shapes to support classification. Teachers' Experience Guide, Going Back states, “In Grade 3, students develop the skills that will help them identify, create, and classify triangles and quadrilaterals in Grade 4.”

An example of a connection to future grades in Grade 5 includes:

• Topic 4: Whole Numbers and Fraction Operations, Teachers' Experience Guide, Planning and Resources Topic 4: Planning connects the multiplying and dividing of fractions and whole numbers of Grade 5 to the future work of Grade 6, where students divide two fractions. Teachers' Experience Guide, Going Forward states, “In Grade 6, students extend their work with dividing whole numbers by unit fractions or dividing unit fractions by whole numbers to dividing any pair of fractions.”

An example of a connection to prior knowledge in Grade 5 includes:

• Topic 11: Rounding, Estimating, and Comparing Decimals, Teachers' Experience Guide, Planning and Resources, Topic 11: Planning connects the Grade 5 work with decimals to the thousandths place to the prior Grade 4 work, where students rounded, estimated, and compared decimals to the tenths and hundredths place. Teachers Experience Guide, Going Back states, “In Grade 4, students work with decimals to tenths and to hundredths in terms of representing, rounding, estimating, and comparing them. They move to thousandths in Grade 5.”