3rd-5th Grade - Gateway 1

The materials reviewed for Takeoff by IXL Grades 3 through 5 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The assessments align with grade-level standards and avoid content from future grades. In Grades 3 through 5, each unit provides an Unit Test, and longer units also incorporate Unit Quiz.

Examples include: 

• Grade 3, Unit 7: Applications of multiplication and division, Unit 7 Test, Question 3, “Brendan is preparing lunch for 9 third graders. Each third grader will get 2 boxes of raisins. The boxes of raisins are sold in packages of 6. How many packages should Brendan buy? _____ packages” (3.OA.8)

• Grade 4, Unit 9: Add and subtract fractions, Unit 9 Quiz, Question 6, “Which number line shows \frac{4}{6}+\frac{7}{6}?” Two number lines are shown. One number line begins at \frac{4}{6} and includes a jump to 1\frac{5}{6}. The second number line also begins at \frac{4}{6} and includes a jump to 1\frac{1}{6}. “What is \frac{4}{6}+\frac{7}{6}?” (4.NF.3a)

• Grade 5, Unit 4: Volume, Unit 4 Test, Question 2, “Each side of a cube is 4 feet long, What is the volume of the cube?” (5.MD.5)

The materials reviewed for Takeoff by IXL Grades 3 through 5 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

The online platform, teacher landing pages, Unit Quizzes, and Unit Tests display grade-level standards and Standards for Mathematical Practice for each assessment item. On the digital assessments, grade-level standards appear as objectives with a brief narrative, and the full standard is available when users hover over the objective. Standards for Mathematical Practice are listed as MPs, with the full descriptions also accessible through hover features. Printable versions of these assessments do not include standards. The standards and mathematical practices are also listed in the unit overview, at the beginning of each assessment under the objectives, and alongside each assessment question.

Examples include:

• Grade 3, Unit 8: Perimeter, Unit 8 Test, Question 6, “Katie is setting up an outdoor space for her pet turtle. She has 22 feet of fencing. She wants to use all of the fencing to make a rectangular space with an area of less than 25 square feet. What could the length and width of the turtle's outdoor space be? Select all that apply. 7 feet by 4 feet, 9 feet by 2 feet, 6 feet by 4 feet, 8 feet by 3 feet” (3.MD.7b, 3.MD.7d, 3.MD.8, MP1)

• Grade 4, Unit 10: Line plots, Unit 10 Test, Question 1, “Josh is caring for a litter of newborn kittens. He weighed each kitten and used the data to make a line plot. What is the most common weight?” A line plot displays kitten weights in ounces. (4.MD.4, MP2)

Grade 5, Unit 5: Add and subtract fractions, Unit 5 Quiz, Question 3, “What is \frac{5}{12}+\frac{3}{8}?” (5.NF.1)

The materials reviewed for Takoff by IXL Grades 3 through 5 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

Formal assessments include Mid-unit check-ins and End-of-unit tests. Teachers can print digital assessments, allowing both online and paper-pencil administration. Performance Tasks appear in the Personalization section of four units. The assessments evaluate procedural skills and conceptual understanding and require students to engage with mathematical reasoning, problem-solving strategies, and communication skills. Online assessments offer students opportunities to demonstrate their understanding of grade-level content standards through item types such as Drop Down, Drag and Drop, Fill-in-the-Blank, Multi-Select, Short Response, and Single Select. The teacher notes provide additional information when a print version of the assessment is used.

Examples include:

• Grade 3, Unit 10: Understand fractions, End-of-unit test, Question 11 states, “Christine drew a number line to show \frac{1}{3}. She made a mistake. What fraction did Christine actually show? Explain Christine's mistake.” A number line is shown from 0-1 with four sections. The materials assess the full intent of 3.NF.2 as students interpret the partitioning of the number line, determine the fraction represented by the point, and explain how the incorrect partitioning leads to a different fraction.

• Grade 4, Unit 9: Add and subtract fractions, End-of-unit test, Question 17 states, “Marcy tried to find 4\frac{2}{5}-2\frac{3}{5} but she made a mistake. Explain Marcy's mistake and how to fix it. What should her answer be?” 4\frac{2}{5}-2\frac{3}{5}=2\frac{1}{5} is shown as Marcy’s solution. The materials assess the full intent of MP3 as students analyze Marcy’s work, identify and explain the error in her reasoning, and justify the correct solution. 

• Grade 5, Unit 12: Measurement and data, End-of-unit test, Question 2 states, “Alvin measured how much snow fell each hour for 12 hours during a snowstorm. Use Alvin's data to complete the line plot. Click to select the X's. To clear a column, click on the number line below it.” The table shows the following measurements: \frac{1}{4},0,\frac{1}{4},\frac{1}{2},\frac{3}{4},1,1,\frac{3}{4},\frac{1}{2},\frac{1}{2},\frac{1}{4},\frac{1}{4}. Question 8 states, “Look at the line plot again. Complete the sentence. Jen caught ___ bass weighing 3\frac{1}{2} pounds. How much did those bass weigh in all? Write your answer as a whole or mixed number.” A line plot from Question 7 is provided. The materials assess the full intent of 5.MD.2 as students create a line plot using fractional measurement data and use operations on fractions to solve problems based on information shown in the plot.

In Grades 3–5, the materials assess MP8 only through Performance tasks. The materials include four Performance tasks per year, which the publisher describes as optional and intended for personalization, stating, “For a dynamic approach to student assessment, consider assigning this performance task.” The materials do not include MP8-aligned items in assessments or quizzes.

The materials reviewed for Takeoff by IXL Grades 3 through 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 structure that engages students with grade-level problems. Lessons include Instruction, Guided practice, Game time, and Independent practice. Units also include Personalization days that provide activities for small-group practice. Across the materials, students regularly demonstrate understanding of the full intent of the grade-level standards through engagement with grade-level work aligned to those standards.

Examples include:

• Grade 3, Unit 2: Understand multiplication engages students with the full intent of 3.OA.1 (Interpret products of whole numbers, e.g., interpret 5\times7 as the total number of objects in 5 groups of 7 objects each). Lesson 2.1, Instruction, Relate repeated addition, skip counting, and equal groups, Teacher notes, “For #3, guide students to draw an equal groups model using a large circle to represent each paw and a dot to represent each toe. Students could draw five dots four times and then circle each group. Or they could draw four circles and then draw five dots in each circle. Then guide students in writing a repeated addition sentence and a skip-counting list. For the repeated addition sentence, look out for students who write four + symbols, and thus five addends, rather than four addends. Remind them that since there are four 5s in the model, they should see four 5s in the addition sentence. Similarly, students should list four numbers when they skip count by 5s because there are four 5s in the model.” Question 3, “A bear has 4 paws. Each paw has 5 toes. How many toes does a bear have in all? Show three ways to find the total. Draw an equal groups model.” Lesson 2.2, Guided practice, Practice multiplying to find the total number of objects, Question 8, “There are 5 bunches of bananas with 3 bananas in each bunch. Show two ways to find the total number of bananas. Use skip counting. Use multiplication. ______ \times ______ = ______ There are bananas in all.” Lesson 2.4, Guided Practice, Represent arrays with multiplication, Question 10, “Oscar set up chairs for the fall play. He put the chairs in 6 rows. He put 3 chairs in each row. How many chairs did Oscar set up in all? Draw an array. Write a multiplication equation. ___ \times _____ = _____ Oscar set up __ chairs in all.”

• Grade 4, Unit 9: Add and subtract fractions engages students with the full intent of 4.NF.3 (Understand a fraction a/b with a > 1 as a sum of fractions 1/b). Lesson 9.1, Instruction, Learn to decompose fractions in different ways, Teacher notes, “Consider having students work in pairs or small groups. Provide each student or group of students with a set of fraction strips to use throughout the lesson. For #2, remind students that when you decompose a number, you break it into smaller parts. Explain that you can decompose fractions just as you can whole numbers. Have students use fraction strips to model \frac{4}{5}. Ask which unit fraction they used for their model. Then have students decompose \frac{4}{5} into unit fractions by separating the fraction strips into four individual \frac{1}{5} strips. Make sure they understand that the new model still represents \frac{4}{5} because there are still four strips that are each \frac{1}{5}. Guide students to record how they decomposed \frac{4}{5} by drawing lines on the fraction strip model in their books. Then have them complete the equation to represent the model.” Guided Practice, Decompose fractions, Question 8, “Decompose \frac{5}{8} in three ways. Use unit fractions. \frac{5}{8}=___ Use two fractions. \frac{5}{8}=___ Use three fractions. \frac{5}{8}=___.” Lesson 9.2, Guided practice, Use models to add fractions with like denominators, Teacher notes, “For #12, make sure students understand that to find how many gallons of pink paint Maria made, they need to find \frac{7}{8}+\frac{4}{8}. Have them use a model or number line to find the sum. Consider pointing out that for many word problems, it makes more sense to give the answer as a mixed number than as a fraction greater than 1. For example, a recipe would call for 1\frac{1}{2} cups of flour, not \frac{3}{2}cups. Similarly, it's more common to give an amount of paint as a mixed number.” Lesson 9.5, Instruction, Learn to subtract fractions without models, Teacher notes, “For #8, make sure students understand that to find the amount of fabric Brian has left, they need to find \frac{7}{12}-\frac{3}{12}-\frac{1}{12}. Highlight that even though this difference involves subtracting three fractions, the strategy they've learned to subtract without a model will work because they are still just finding the number of same-sized fractional parts left over. Consider using this problem as an opportunity to remind students that for many word problems, it makes more sense to give the answer in simplest form. In this case, it is more common to say the length is \frac{1}{4} of a yard than to say it's \frac{3}{12} of a yard.” Guided Practice, Subtract fractions, Question 9, “Subtract. \frac{3}{5}-\frac{2}{5}=.”

• Grade 5, Unit 12: Measurement and data engages students with the full intent 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). Lesson 12.8, Instruction, Learn to represent data on a line plot, Teacher notes, “For #4, discuss the meaning of each column in the table. Students used data in tables to make line plots in third and fourth grades, so they should know that this table tells the number of times each weight occurs: the first column shows 1 clam weighed 1 pound, the second column shows 3 clams weighed 1\frac{1}{4} pounds, and so on. You can continue to call these data tables throughout this lesson, but introduce the term frequency chart so students are familiar with it as well. Explain that you can use a line plot to show the same data in a different way. The number line will represent the weights, and the number of Xs above each mark on the number line will represent the number of clams with that weight. Have students write a title for the line plot and label the number line to describe the data shown. Remind them to include a measurement unit in the label. Guide students through marking the number line. Note that all of the data is between 1 and 3, so the number line is already marked with the whole numbers 1, 2, and 3. Then divide the number line into equal sections. Point out that the data includes halves and fourths, and ask students how they think they should divide the number line. Surface that since \frac{1}{2} is equal to \frac{2}{4}, they can represent all of the data on a number line divided into fourths. Consider discussing strategies for neatly dividing the number line. Students can divide each whole into fourths by cutting it in half and cutting each half in half again. After students divide the number line into fourths, have them plot the data by drawing one X on the line plot for each clam.” Guided practice, Create line plots, Teacher notes, “For #9, make sure students understand that since halves and fourths can be written using eighths, they should divide the number line to show eight equal parts between each pair of whole numbers.” Lesson 12.9, Guided practice, Interpret and solve problems using line plots, Teacher notes, “For #8, consider discussing how students can use the number line to help them answer the second question. Students can start with the most yards jumped and count back (or subtract) 2\frac{2}{3}, or they can start with the fewest yards jumped and count up (or add) 2\frac{2}{3}.” Question 8, “The Springfield Zoo had a frog jumping competition. The line plot shows how far the first 8 frogs jumped. How far, in feet, was the longest jump? After the zookeeper added the next frog’s jump to her line plot, the difference between the longest jump and the shortest jump was 2\frac{2}{3}yards. How many yards did that frog jump?” Lesson 12.10, Guided Practice, Solve multi-step problems using line plots with fractions and decimals, Question 4, “Candice went to Penning Farms to buy cherries for her bakery. She recorded the weights of the cherry baskets she bought. Candice needs \frac{}{2} of a pound of cherries for each batch of her famous cherry compote. How many batches can she make?”

The materials reviewed for Takeoff by IXL Grades 3 through 5 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade as included in the following grade-level breakdowns.

The materials present unit-level pacing and planning information in the Online Platform under Teacher, Additional Resources, Grade at a Glance: Planning and materials (page two). This section lists each unit by name and specifies the number of instructional days per unit. The Pacing Guide states, “Pacing includes one school day for each lesson, Review day, Mid-unit check in, End-of-unit test, and Personalization day.” The materials also identify the number of lessons, assessments, review days, and personalization days included in each unit. Lessons marked as optional by the publisher are excluded from the calculations.

Grade 3:

• The approximate number of units devoted to the major work of the grade is 10 out of 13, approximately 77%.

• The approximate number of lessons devoted to the major work of the grade is 67.5 out of 94, approximately 72%. 

• The approximate number of instructional days devoted to major work of the grade (including assessments and related supporting work) is 101.5 out of 139, approximately 73%. 

Grade 4:

• The approximate number of units devoted to the major work of the grade is 12.5 out of 15, approximately 83%.

• The approximate number of lessons devoted to the major work of the grade is 74 out of 105, approximately 70%.

• The approximate number of instructional days devoted to major work of the grade (including assessments and related supporting work) is 116.5 out of 153, approximately 76%.

Grade 5:

• The approximate number of units devoted to the major work of the grade is 11 out of 14, approximately 79%.

• The approximate number of lessons devoted to the major work of the grade is 81 out of 103, approximately 79%.

• The approximate number of instructional days devoted to major work of the grade (including assessments and related supporting work) is 120.5 out of 155, approximately 78%.

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 chapter. Approximately 73% of the materials in Grade 3, 76% of the materials in Grade 4, and 78% of the materials in Grade 5 focus on the major work of the grade

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

The materials connect supporting standards and clusters to the major standards and clusters of the grade. These connections appear within Units and Lessons.

Examples include:

• Grade 3, Unit 12: Data, Lesson 12.3, Instruction, Learn to solve two-step word problems involving scaled graphs connects the supporting work of 3.MD.3 (Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs) to the major work of 3.OA.8 (Solve two-step word problems using the four operations. 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 use data in a bar graph to determine the unknown quantity and solve comparison problems involving subtraction. Teacher notes state, “For #3, to find the number of pots sold, students will need to find the number of each item type given on the graph and then subtract the sum from 200. Then they can complete the graph by drawing a bar to represent the number of pots sold (40). To answer the second question, students will need to identify the number of plants sold and the combined number of fertilizer and garden decor items sold. Once they determine which Bright Blooms sold more of, they can subtract to find the difference.” Student book states, “3. Bright Blooms recorded the number of garden items they sold one day. They sold 200 items in all, but they forgot to record the number of pots they sold. How many pots did they sell? Complete the graph. Did they sell more of the most popular item type or the two least popular types combined? How much more?” Students view a bar graph titled Items Sold. The left side is labeled Total Sold, and the bottom is labeled Type of Item. The graph shows plants (60), pots (blank), fertilizer (20), seeds (50), and garden decor (30). Students complete the graph by drawing a bar to represent 40 pots sold.

• Grade 4, Unit 12: Measurement, Lesson 12.6, Instruction, Learn to solve problems involving unit conversions 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 use a number line to determine the start time, finish time, and duration in a multi-step problem involving two events. Teacher notes state, “For #6, discuss with students how to use an open number line to find the total distance Harmony ran. Surface that since her distance on the trail is in kilometers and her distance in laps is in meters, students should start by converting 2 kilometers to meters. Then they can draw all of their jumps on the number line in meters.” Student book states, “6. For cross-country practice, Harmony runs 2 kilometers on a trail. Then she runs 4 laps around the track. Each lap is 400 meters. How far does Harmony run in all? Use the number line to solve the problem.” Students use an open number line as a visual model to support problem solving.

• Grade 5, Unit 12: Measurement and data, Lesson 12.9, Guided practice, Interpret and solve problems using line plots 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.6 (Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem). Students use data represented in a line plot to solve addition, subtraction, and multiplication problems involving fractions. Teacher notes state, “For #6, consider pointing out that the questions ask about fourths even though the number line is divided into eighths, so it could be helpful to start by labeling fourths on the number line. Note that the last question requires students to use information from the previous questions. You know that Ellie bought 7 ribbons and Parker bought 1. Since there are 13 ribbons in all, there are 5 ribbons left for Kyle.” Student book states, “6. Jessica works at Cloth Corner. She measured and labeled the lengths of the ribbons to be sold out of the scrap bin. The line plot shows her data. Ellie bought all of the ribbons that were less than \frac{3}{4} of yard long. How many ribbons did Ellie buy? What is the difference between the longest and shortest ribbons that Ellie bought? Ellie cut each ribbon that was \frac{1}{4} of a yard long into 3 pieces. How long was each piece? Parker bought the longest ribbon. If he cut his ribbon into pieces that were \frac{1}{4} of a yard long, how many pieces did he cut?” Students view a line plot titled Ribbon Scraps. The line is labeled Length (yards) and shows marks for each eighth of a yard.

The instructional materials for Takeoff by IXL 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. 

The materials show connections among the major work of the grade where appropriate. The teacher guides identify lessons addressing specific standards in Grade at a glance, in each unit’s Additional Resources within the Daily Planner, and within individual lessons.

Examples include:

• Grade 3, Unit 9: Time, Volume, and Mass, Lesson 9.9, Instruction: Learn to solve problems involving mass and volume, connects the major work of 3.OA.D (Solve problems involving the four operations, and identify and explain patterns in arithmetic) to the major work of 3.MD.A (Solve problems involving measurement and estimation of intervals of time, liquid, volumes, and masses of objects). Students use the four operations to solve word problems involving different measurement quantities. Teacher notes state, “For #4, have students draw a strip model to represent the problem. As in earlier lessons, they can first identify what they know (the total number of milliliters of glue and the number of batches) and represent that information. Then they can use a letter to represent what they need to find (the amount of glue in each batch). Students can then use division or multiplication to determine that there are 8 milliliters of glue in each batch of slime. For #5, students must consider which measuring tool will help them answer each question. The milkshake and the measuring cup each have their own mass. The first question asks for the mass of both, and students can read it on the scale. The second question asks for the mass of only the milkshake. Point out that Shawna doesn't need to pour the liquid on the scale to find its mass. Since the mass of the empty measuring cup is known, students can find the difference between that amount and the total mass. The third and fourth questions focus on volume, so students can use the measuring cup to find the information needed to answer them.” Student book states, “4. Patrick has 40 milliliters of glue. He can make 5 batches of slime with it. How many milliliters of glue are in each batch of slime? Draw a strip model to show the problem. Use a letter for the unknown number. There are ____ milliliters of glue in each batch of slime.” Students construct a strip model in the space provided. “5. Shawna makes a milkshake and puts it in a measuring cup. What is the mass of the measuring cup and the milkshake inside of it? The mass of the empty measuring cup is 191 grams. What is the mass of the milkshake? What is the volume of the milkshake? How much milkshake would be left if Shawna poured 230 mL in a cup?” Students examine a graphic showing a measuring cup on a scale. The milkshake reaches the 300-mL line, and the scale displays a mass of 525 grams.

• Grade 4, Unit 13: Decimals, Lesson 13.4, Instruction, Learn to compare decimal numbers, 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 use their understanding of equivalent fractions to compare and order decimals using a number line and by finding a common denominator. Teacher notes state, “For #6, have students compare 0.4 to 0.68 in two ways. Consider discussing the advantages and disadvantages of each method. For example, it's easy to shade models, but they are better for comparing decimals that are less than 1. It's also easy to compare distances from 0 on a number line, but it can be hard to accurately draw some decimals on a number line. For #7, discuss Anna's idea. Point out that writing decimal numbers as mixed numbers to compare them can be faster than using models or number lines. Then have students use Anna's strategy. Point out that 9.4 and 9.25 will have different denominators when you write them as equivalent mixed numbers. That means you should rename \frac{4}{10} as \frac{40}{100}  before you compare. Students may also notice an even faster way—they can rewrite 9.4 as 9.40, which is equivalent to 9\frac{40}{100}.” Guided practice, Compare decimals, Teacher notes state, “For #11, have students show each number on the number line and then order them from greatest to least. Make sure they understand that the greatest number is the one farthest to the right on the number line, and the smallest is the one farthest to the left.” Student book states, “6. Show two ways to compare 0.4 and 0.68. One way: Use Models. Another way: Use a number line.” Students view fraction grids for the first method and a number line labeled from 0 to 1 for the second method. “7. Anna wants to compare 2.85 and 2.82 without drawing a model. Use Anna’s strategy to compare. 4.6____4.8, 9.4___9.25.” Students observe that Anna’s strategy is to rewrite both decimals as mixed numbers with the same denominator. “11. Show and label 10.8, 10.35, and 10.62 on the number line. Then write the numbers in order from greatest to least. ____>____>____>” Students use a number line labeled 10 on the left and 11 on the right.

• Grade 5, Unit 10: Multiply decimals, Lesson 10.1, Instruction, Use patterns and place value to multiply whole numbers by decimal numbers, 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 place-value patterns and decimal place value to solve multiplication problems. Teacher notes state, “For #9, start by making sure that students see how Javon got his three answers. In particular, point out that you can find 0.3\times0.1 by finding \frac{1}{10} of 0.3 since 0.1 and \frac{1}{10} are equal. Then, discuss patterns that students see to help them finish Javon's equations. Surface that the digit 3 moves one place to the left as you go down the list of equations (or one place to the right as you go up), and guide students to use this pattern to complete the remaining equations. For example, you can find that 0.3 × 0.01=0.003 by moving the 3 in 0.03 one place to the right. Finally, discuss why this idea works. Highlight that each equation has a factor of 0.3, and the other factor increases by a factor of 10 as you go down the list of equations. For example, 100 is 10 times as much as 10, so 0.3\times100 is 10 times as much as 0.3\times10=3. That means 0.3\times100=30. Similarly, 0.1 is 10 times as much as 0.01, so 0.3\times0.1 is 10 times as much as 0.3\times0.1. For #10, discuss Javon's and Melanie's ideas. Highlight that Javon's idea uses the pattern from the equations in #9. That is, each time you multiply a number by 10, you move the digits in the number one place to the left. You can think of multiplying 0.5 by 100 as multiplying by 10 twice, so you can move the digit 5 two places to the left instead of just one. Then ask students how Melanie's idea relates to Javon's idea. After the digit 5 moves two places to the left, the decimal point is two places to the right of where it started. That means Melanie's idea is just another way to think about Javon's idea. Discuss whether their ideas always work when multiplying by powers of 10. Highlight that anytime you multiply by a power of 10, it's the same as multiplying by 10 several times. The exponent or number of zeros in standard form tells you how many times to multiply by 10. For example, both 10³ and 1,000 are equivalent to multiplying by 10 three times, so you can move the digits three places to the left or move the decimal point three places to the right to find 0.5\times10^3 or 0.5\times1,000.” Student book states, “9. Javon found 10 times and \frac{1}{10} of 0.3 using place value. After writing his equations together, he wonders if there is a pattern. Help him finish the rest of the equations. Javon: My answers all have a 3, but it’s in different places. How can I tell where to put it in the other products? 0.3\times0.0=1____, 0.3\times0.1=0.03, 0.3\times1=0.3, 0.3\times10=3, 0.3\times100=____, 0.3\times1,000=____. 10. Javon and Melanie have ideas to find 0.5\times100 without finding 0.5\times10 first. Javon: I know 100 is 10\times10, so I bet I can move the 5 two places to the left. Melanie: I’m going to move the decimal point two places to the right instead. How are Javon’s and Melanie’s ideas related? Do they always work to multiply the powers of 10? Explain why or why not.”

The instructional materials reviewed for Takeoff by IXL 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 Teacher’s Guide includes Unit and Lesson overviews that identify content standard connections. Each Unit and Lesson features an Instructional Context section with Look Back and Look Forward components that illustrate how current concepts connect to prior learning and prepare for future standards across grades. At the lesson level, Warm-Up activities in Grades 1–5 introduce new concepts by drawing on students’ prior knowledge.

Examples of connections to prior knowledge and future learning in Grade 3 include:

• Unit 1: Addition and subtraction within 1,000, Lesson 1.6, Instructional context, Look back states, “In previous grades, students learned that they can add in any order and the sum stays the same. They used this property to add three or four numbers with sums within 100.”

• Unit 7: Applications of multiplication and division, Unit outline, Instructional context, Look Forward states, “In fourth grade, students will solve more complicated problems by writing multi-operation equations. They will also generate and extend number patterns and explore input/output tables.”

Examples of connections to prior knowledge and future learning in Grade 4 include:

• Unit 2: Add and subtract whole numbers, Unit outline, Instructional context, Look back states, “In third grade, students developed addition and subtraction strategies based on place value to fluently add and subtract numbers within 1,000. They focused on strategies that emphasize recording work numerically, including the standard algorithms for addition and subtraction. Students represented one- and two-step problems using strip models. They also learned to write and solve corresponding equations that use a letter to represent the unknown number.”

• Unit 5: Factors, multiples, and patterns, Unit outline, Instructional context, Look forward states, “In the next unit, students will use divisibility rules to predict whether division problems will have remainders. Understanding factors and multiples will help students write equivalent fractions and compare fractions in later units. In fifth grade, students will begin to explore functions as they relate the terms of two numerical patterns and use them to form ordered pairs.”

Examples of connections to prior knowledge and future learning in Grade 5 include:

• Unit 3: Expression, Unit outline, Instructional context, Look back states, “In previous grades, students represented multi-step problems using sequences of numerical expressions. They learned that they could use parentheses to indicate which operations to do first in expressions with multiple operations.”

• Unit 12: Measurement and data, Lesson 12.10, Instructional context, Look forward states, “In sixth grade, students will learn how to describe the center, spread, and shape of data using line plots. They will also learn to calculate and interpret measures of center and variation in datasets.”