enVision, Mathematics, Grade 4

In this Grade 4 enVision Mathematics lesson from Chapter 1, students learn to read and write numbers through one million using expanded form, standard numerals, and number names. The lesson introduces place value concepts including periods, place-value charts, and how commas separate periods in large numbers up to the millions. Students practice skills like writing 356,039 as 300,000 + 50,000 + 6,000 + 30 + 9 and identifying the value of specific digits within multi-digit numbers.

In this Grade 4 lesson from enVision Mathematics Chapter 1, students learn that a digit in one place has ten times the value of the same digit in the place to its right, exploring place value relationships across ones, tens, hundreds, thousands, and beyond. Using place-value blocks and real-world problems, students practice multiplying and dividing by 10 to understand how place values scale. The lesson builds students' ability to generalize patterns in multi-digit numbers and compare the values of repeated digits within the same number.

In this Grade 4 lesson from enVision Mathematics Chapter 1, students learn how to compare whole numbers using place value, recording comparisons with the symbols greater than, less than, or equal to. The lesson teaches a step-by-step method of aligning digits by place and comparing from left to right to find the first position where digits differ. Students apply this skill to multi-digit numbers up to the hundred-thousands place through real-world contexts such as ocean depths and country areas.

In this Grade 4 enVision Mathematics lesson, students learn how to round whole numbers to the nearest ten, hundred, thousand, and ten thousand using place value and number lines. The lesson covers identifying the rounding digit, examining the next digit to the right, and applying the rounding rules to multi-digit numbers up to the hundred thousands. Students practice with real-world contexts such as city populations and zoo attendance data from Chapter 1 on place value understanding.

In this Grade 4 enVision Mathematics lesson, students learn how to add and subtract multi-digit whole numbers using mental math strategies including Make Ten, Add On, and Compensation, along with the Associative, Commutative, and Identity Properties of Addition. Through real-world problems like combining multi-thousand dollar earnings and comparing state land areas, students practice breaking apart numbers and adjusting values to simplify calculations without pencil and paper. The lesson builds fluency with numbers up to the hundred-thousands place as part of Chapter 2's focus on adding and subtracting multi-digit whole numbers.

In this Grade 4 enVision Mathematics lesson from Chapter 2, students learn how to estimate sums and differences of multi-digit whole numbers using rounding and place value. They practice rounding to the nearest thousand, hundred, and ten-thousand to find approximate answers, and use those estimates to check whether exact calculations are reasonable. Real-world contexts, such as library checkouts and ticket sales, help students apply estimation strategies to decide when an estimate is sufficient instead of an exact answer.

In this Grade 4 enVision Mathematics lesson from Chapter 2, students learn to add multi-digit whole numbers using two key strategies: partial sums and the standard algorithm for addition, including regrouping ones and tens. The lesson connects place-value concepts to efficient addition procedures, guiding students through step-by-step regrouping when sums exceed 9 ones or 9 tens. Practice problems and real-world word problems help students build fluency with multi-digit addition.

In this Grade 4 lesson from enVision Mathematics Chapter 2, students learn how to add greater multi-digit whole numbers using the standard algorithm, applying place value concepts and regrouping across ones, tens, hundreds, thousands, and ten-thousands places. Students also practice using estimation to check whether their answers are reasonable. The lesson builds fluency with adding numbers up to the hundred-thousands place, including problems with three addends.

In this Grade 4 enVision Mathematics lesson from Chapter 2, students learn how to subtract multi-digit whole numbers using the standard algorithm, including regrouping across the ones, tens, and hundreds places. The lesson connects place-value concepts to written subtraction procedures, helping students work efficiently with problems like 358 − 172. Students also practice estimating differences to check the reasonableness of their answers.

In this Grade 4 enVision Mathematics lesson from Chapter 2, students learn to subtract greater whole numbers using the standard algorithm and place value, including regrouping across multiple digits. The lesson also covers using inverse operations (addition) to check subtraction answers and using estimation to verify whether results are reasonable. Students apply these skills to multi-step real-world problems involving numbers up to the hundred thousands.

In this Grade 4 enVision Mathematics lesson from Chapter 2, students learn how to subtract across zeros using the standard algorithm, including regrouping across multiple place values when zeros appear in the minuend. The lesson covers multi-digit subtraction problems such as 6,000 minus 4,678, where students must regroup from the thousands place through hundreds and tens before subtracting. Students also practice using estimation to verify that their differences are reasonable.

In this Grade 4 enVision Mathematics lesson, students learn how to select the most appropriate multiplication strategy — including the Distributive Property, area models, partial products, and compensation — to solve multi-digit multiplication problems. Working through real-world scenarios like calculating car repair costs and theater seating, students practice multiplying 1-digit numbers by 2-, 3-, and 4-digit numbers while explaining and justifying their chosen methods. The lesson is part of Chapter 3 and builds fluency and precision in multiplication across a variety of problem types.

In this Grade 4 enVision Mathematics lesson from Chapter 4, students learn to multiply 2-digit numbers by multiples of 10 using place-value block arrays and area models to identify partial products. By breaking apart factors and applying the Distributive Property, students solve problems such as 20 × 24 by calculating 20 × 20 and 20 × 4 separately, then adding the partial products. This lesson builds foundational multiplication fluency needed for multi-digit computation throughout the chapter.

In this Grade 4 enVision Mathematics lesson from Chapter 4, students learn how to estimate products of two-digit multiplication using two strategies: rounding factors to the nearest ten and replacing factors with compatible numbers. Students practice deciding which strategy to use, applying both methods to problems like 26 × 12, and checking whether a given answer is reasonable by comparing it to an estimate.

In this Grade 4 lesson from enVision Mathematics Chapter 4, students learn how to multiply two-digit numbers using arrays and partial products by separating each factor into tens and ones. Using grid-based array models, they break a problem like 24 × 13 into four simpler multiplication facts — 20 × 10, 20 × 3, 4 × 10, and 4 × 3 — then add the partial products to find the final answer. Place-value concepts and the Commutative Property of Addition are applied throughout to build understanding of 2-digit by 2-digit multiplication.

In this Grade 4 enVision Mathematics lesson, students learn how to use area models and the Distributive Property to multiply two 2-digit numbers by breaking apart factors into tens and ones and finding partial products. The lesson guides students through multiple strategies for problems like 25 × 15, showing how splitting factors such as 25 into 20 + 5 and 15 into 10 + 5 generates up to four simpler multiplication problems whose products are then added together. This foundational skill in Chapter 4 builds fluency with 2-digit multiplication and connects visual area models to the algebraic structure of the Distributive Property.

In this Grade 4 enVision Mathematics lesson from Chapter 5, students learn how to estimate quotients using compatible numbers and multiplication when dividing 3-digit dividends by 1-digit numbers. Students practice replacing difficult numbers with nearby compatible numbers to make mental math easier, such as replacing 700 ÷ 9 with 720 ÷ 9 because 720 is divisible by 9. The lesson builds number sense by applying basic multiplication facts to check whether estimated quotients are reasonable in real-world contexts.

In this Grade 4 enVision Mathematics lesson, students learn how to estimate quotients for 3- and 4-digit dividends using mental math strategies, including compatible numbers, multiplication patterns, place-value patterns, and rounding. Part of Chapter 5 on division by 1-digit numbers, the lesson builds on basic division facts to help students apply mental math reasoning to larger numbers like 1,320 ÷ 6 or 5,582 ÷ 7. Students practice choosing the most appropriate estimation strategy depending on the dividend and divisor.

In this Grade 4 enVision Mathematics lesson from Chapter 5, students learn how to interpret remainders in division problems by deciding whether to ignore the remainder, add 1 to the quotient, or use the remainder as the answer depending on the context of the problem. Students practice writing division equations using remainder notation (such as 27 ÷ 6 = 4 R3) and apply this skill to real-world scenarios involving equal groups.

In this Grade 4 enVision Mathematics lesson from Chapter 5, students learn how to divide by finding partial quotients, breaking a division problem into smaller, more manageable steps using estimation, multiplication, and place value. Students practice subtracting partial quotients repeatedly until no remainder is left, then adding those partial quotients to find the full quotient. The lesson also connects partial quotients to the Distributive Property, showing how dividing a number broken into parts yields the same result.

In this Grade 4 enVision Mathematics lesson from Chapter 5, students learn how to use partial quotients to divide greater dividends, including 3- and 4-digit numbers, by a 1-digit divisor. The method relies on estimation, place value, and the relationship between multiplication and division to break the problem into manageable steps until the remainder is less than the divisor. Practice problems guide students from dividing numbers like 277 ÷ 5 up to 4-digit dividends such as 1,968 ÷ 6.

In this Grade 4 lesson from enVision Mathematics Chapter 5, students learn how to select the most appropriate strategy to solve division problems, choosing among partial quotients, the Distributive Property, place value models, and mental math based on the numbers involved. The lesson guides students through breaking division into simpler calculations to find quotients for multi-digit numbers divided by 1-digit divisors. Students also practice interpreting remainders and evaluating whether quotients are reasonable.

In Grade 4 enVision Mathematics, Chapter 6, Lesson 1, students learn how to solve comparison problems using both multiplication and addition, distinguishing between "times as many" and "more than" relationships. Students write and solve equations with variables, using bar diagrams to model comparisons such as finding a quantity that is 3 times as many as or 8 more than a given value. This lesson builds foundational skills for representing real-world multiplicative and additive comparisons with whole numbers.

In this Grade 4 enVision Mathematics lesson from Chapter 6, students learn how to use multiplication and division as inverse operations to solve multiplicative comparison problems. They practice writing and solving equations such as 192 = 4 × m and m = 192 ÷ 4 to find an unknown quantity when one value is described as a multiple of another. The lesson builds skills in modeling with math using bar diagrams and comparison sentences to represent real-world situations.

In Lesson 6-3 of enVision Mathematics Grade 4, students learn how to identify hidden questions and use bar diagrams and equations to model and solve multi-step problems involving whole numbers. The lesson builds skills in writing expressions and equations with variables to represent unknown quantities across real-world contexts such as calculating totals and differences. Students practice breaking complex problems into sequential steps, combining multiplication and addition or subtraction to reach a final answer.

In this Grade 4 lesson from enVision Mathematics Chapter 6, students learn to solve multi-step problems by drawing bar diagrams and writing expressions and equations with variables. Using real-world scenarios involving ticket prices, egg cartons, and quilts, students practice identifying hidden questions and breaking complex problems into sequential steps. The lesson also introduces evaluating reasonableness by comparing calculated answers to estimates.

In this Grade 4 enVision Mathematics lesson from Chapter 7, students learn how to find factor pairs of whole numbers by building and analyzing rectangular arrays. Using grids and multiplication, students discover all the ways a number can be decomposed into two whole-number factors, practicing with numbers like 12, 16, 36, and others. The lesson connects array models to factor pair notation, building foundational skills for understanding factors and multiples.

In this Grade 4 enVision Mathematics lesson from Chapter 7 on Factors and Multiples, students learn to identify whole numbers as prime or composite by examining their factors. A prime number has exactly two factors (1 and itself), while a composite number has more than two factors, and students practice applying these definitions to numbers up to 97. The lesson also addresses the special case that 1 is neither prime nor composite.

In this Grade 4 lesson from enVision Mathematics Chapter 8, students learn to recognize and generate equivalent fractions using area models, including rectangles and circles divided into equal parts. The lesson demonstrates how fractions like 5/6 and 10/12 name the same part of a whole even when the number and size of parts differ. Students practice finding missing numerators and writing equivalent fractions to build a foundational understanding of fraction equivalence.

In this Grade 4 lesson from enVision Mathematics, students learn how to identify and name equivalent fractions by locating the same point on number lines divided into different equal parts, such as showing that 3/4, 6/8, and 9/12 all represent the same distance. Students use number lines as a tool to understand why fractions with different numerators and denominators can be equal, including fractions greater than or equal to 1. The lesson is part of Chapter 8, which extends students' understanding of fraction equivalence and ordering.

In this Grade 4 lesson from enVision Mathematics Chapter 8, students learn how to generate equivalent fractions using division by dividing both the numerator and denominator by a common factor. The lesson covers identifying common factors of two numbers and applying them to simplify fractions such as 18/24 into equivalent forms like 9/12 and 6/8. Students practice this skill across a range of problems, including real-world contexts involving time and measurement.

Grade 4 students learn how to subtract mixed numbers with like denominators using two strategies: renaming the minuend by borrowing a whole (converting it to an equivalent mixed number) and converting mixed numbers to improper fractions before subtracting. This lesson is part of Chapter 9 in enVision Mathematics Grade 4 and builds on students' understanding of equivalent fractions and the relationship between addition and subtraction.

In this Grade 4 lesson from enVision Mathematics Chapter 11, students learn how to make a line plot to represent data sets that include whole numbers and fractions such as halves, fourths, and eighths. Students practice choosing an appropriate scale, drawing a number line, and plotting data points using real-world contexts like shoe sizes and pencil lengths. The lesson also builds skills in reading and interpreting line plots to identify the most frequently occurring values.

In this Grade 4 lesson from enVision Mathematics Chapter 12, students learn how to relate fractions and decimals by writing fractions with denominators of 10 and 100 as decimals using tenths and hundredths place values. Students practice converting between forms such as 6/10 = 0.6 and 75/100 = 0.75, and explore how money amounts like $2.35 connect to fractions and decimals. Visual models including grids and place value charts help students represent and understand these equivalent representations.

In this Grade 4 lesson from enVision Mathematics Chapter 13, students learn to convert metric units of length — millimeters, centimeters, meters, and kilometers — using the relationships between units (e.g., 1 meter = 100 centimeters, 1 kilometer = 1,000 meters). Students practice multiplying to convert between units and compare measurements expressed in different units. The lesson builds fluency with the metric system through real-world contexts like measuring jumps and rainfall totals.

In this Grade 4 lesson from enVision Mathematics Chapter 14, students learn how to use multiplication and division rules to extend number patterns and complete tables. They practice identifying features of patterns, such as recognizing that one quantity is a multiple or factor of another, using real-world contexts like juice boxes, cloverleaves, and bicycle wheels. Students also apply these number rules to solve problems, including finding values for larger numbers in a pattern.

In Grade 4 math (enVision Mathematics, Chapter 14), students learn how to identify and extend repeating patterns made up of shapes or numbers, then use division to predict any specific term in the pattern, such as the 49th or 100th item. The lesson covers recognizing that positions of each shape correspond to multiples or near-multiples of the pattern's cycle length, and applying that relationship to solve problems efficiently. Students also practice constructing math arguments to justify their predictions.