Pengi Math (Grade 4)

In this Grade 4 Pengi Math lesson, students explore the base-ten system's ten-times relationship, learning how a digit in any place represents ten times the value of the same digit one place to its right. The lesson uses hands-on bundling models to show how 10 smaller units combine to form 1 larger unit, such as 10 tens equaling 1 hundred. This foundational concept prepares students to work confidently with multi-digit numbers throughout Chapter 1.

In this Grade 4 Pengi Math lesson, students learn to read and write large numbers using periods and commas to separate and name place value groups. They analyze the value of specific digits based on their position within a number and explore unbundling as a model for understanding division by 10. This lesson is part of Chapter 1: Place Value Fundamentals and Estimation.

In this Grade 4 Pengi Math lesson, students learn to read and write multi-digit whole numbers in three forms: standard form using base-ten numerals, word form using number names, and expanded form as a sum of products. Part of Chapter 1 on Place Value Fundamentals and Estimation, the lesson builds core number sense skills essential for working with large whole numbers.

In this Grade 4 lesson from Pengi Math Chapter 1, students learn to compare multi-digit numbers by analyzing the value of digits place by place, starting from the greatest place value. They practice recording comparison results using the symbols greater than, equal to, and less than.

In this Grade 4 Pengi Math lesson from Chapter 1, students learn to compare multi-digit numbers presented in different forms, such as expanded form and word form. They also practice ordering sets of multi-digit numbers from least to greatest and greatest to least. This lesson builds foundational place value skills essential for working with large numbers throughout the grade.

In this Grade 4 Pengi Math lesson, students use vertical number lines to round multi-digit whole numbers to any place value, including thousands, ten thousands, and hundred thousands, by identifying endpoints, midpoints, and applying the halfway rule. Learners develop place value understanding to explain why numbers at or above the midpoint round up, and they also work backward to determine the range of original numbers that could produce a given rounded value. This lesson is part of Chapter 1: Place Value Fundamentals and Estimation.

In this Grade 4 lesson from Pengi Math Chapter 1, students learn how to estimate sums and differences by rounding to specific place values. They practice assessing the reasonableness of answers using mental computation and apply their rounding choices to real-world contexts.

In this Grade 4 Pengi Math lesson, students learn to fluently add multi-digit whole numbers using the standard addition algorithm with a focus on proper column alignment and systematic regrouping, also known as carrying. Part of Chapter 2 on algorithms and fluency, the lesson builds the foundational skills students need to solve multi-step addition problems with confidence and accuracy.

In this Grade 4 Pengi Math lesson, students learn to fluently subtract multi-digit whole numbers using the standard subtraction algorithm. The lesson focuses on proper digit alignment and systematic decomposition, commonly known as borrowing, to solve subtraction problems accurately. Part of Chapter 2 on algorithms and fluency, this lesson builds the foundational skills needed for multi-step problem solving.

In this Grade 4 lesson from Pengi Math Chapter 2, students tackle the specific challenge of subtracting across zeros, working through multi-digit problems such as 40,005 minus 12,348 by applying regrouping strategies. Students also learn to verify their subtraction results using addition as an inverse operation, building both accuracy and number sense.

In this Grade 4 Pengi Math lesson from Chapter 2, students learn to solve addition, subtraction, and additive comparison word problems using the Read-Draw-Write (RDW) process. They use tape diagrams to model part-whole relationships and interpret comparison situations, such as finding a difference or calculating a total when a difference is known.

In this Grade 4 lesson from Pengi Math Chapter 2, students learn to deconstruct and solve multi-step word problems involving two or more operations. They practice representing problems as equations with a variable for the unknown quantity, then evaluate whether their answers are reasonable using estimation and mental computation.

In this Grade 4 lesson from Pengi Math Chapter 3, students explore division as equal groups by learning two types of division: partitive (sharing) and quotative (measurement). Students represent division problems using drawings, tables, and equations, then connect division to multiplication as its inverse operation.

In this Grade 4 lesson from Pengi Math Chapter 3, students learn to model multiplicative comparison problems using tape diagrams, bar models, and equations. They practice distinguishing multiplicative comparison from additive comparison and apply multiplication and division to solve real comparison problems.

In this Grade 4 Pengi Math lesson from Chapter 3, students learn to use rounding and compatible numbers to estimate sums, differences, and products. They practice assessing the reasonableness of answers in real-world contexts and develop judgment about when exact calculations are needed versus when estimation is sufficient.

In this Grade 4 Pengi Math lesson from Chapter 3, students learn what remainders mean in division and how to decide whether to round up, drop, or share them evenly based on the context of a problem. Students apply this understanding by solving real-world word problems involving division with remainders.

In this Grade 4 Pengi Math lesson, students learn to break down multi-step word problems by identifying the correct sequence of operations, including multiplicative comparison and division with remainders. Students represent problems using equations with a letter for the unknown quantity and apply diagrams and estimation strategies to plan and justify their answers. This lesson is part of Chapter 3: Understanding Multiplication and Division.

In this Grade 4 lesson from Pengi Math Chapter 4, students use place value understanding and the Associative and Distributive Properties to multiply by multiples of 10, 100, and 1,000. They also practice estimating products through rounding and compatible numbers, and apply compensation strategies and Unit Form to perform mental multiplication efficiently.

In this Grade 4 lesson from Pengi Math Chapter 4, students learn to multiply up to four-digit numbers by one-digit numbers using area models and place value disks to represent partial products and regrouping. They practice decomposing factors to find partial products before transitioning to the standard multiplication algorithm. The lesson connects regrouped digits in the algorithm directly to bundled place value units, building a conceptual bridge between models and procedures.

In this Grade 4 lesson from Pengi Math Chapter 4, students learn to multiply two-digit numbers by two-digit numbers using area models and partial products. They explore patterns with multiples of 10, organize four partial products in a 2x2 area model, and combine them to build toward the standard algorithm. The lesson also applies these multiplication strategies to real-world problems.

In this Grade 4 Pengi Math lesson, students learn two key division methods: the partial quotients strategy, which uses friendly multiples and place value reasoning, and the standard long division algorithm using the Divide, Multiply, Subtract, Bring Down steps. Students practice applying both approaches to solve problems with dividends up to four digits. This lesson is part of Chapter 4: Multiplication & Division Strategies and builds fluency by connecting division procedures to known multiplication facts.

In this Grade 4 Pengi Math lesson from Chapter 4, students learn how to interpret remainders in real-world contexts by deciding whether to round up, drop, or share them depending on the situation. They use tape diagrams to solve multiplicative comparison problems and tackle multi-step word problems involving all four operations. Students also practice deconstructing word problems to uncover hidden questions and determine the correct sequence of operations.

In this Grade 4 lesson from Pengi Math Chapter 5, students learn to define factors as numbers multiplied together to get a product and find all factor pairs for whole numbers from 1 to 100. They practice using division with zero remainders to check whether one number is a factor of another, and apply the Associative Property to group factors and uncover new factor pairs.

In this Grade 4 lesson from Pengi Math Chapter 5, students learn to define multiples and connect them to skip-counting, then determine whether whole numbers up to 100 are multiples of a given one-digit number. The lesson also explores the inverse relationship between factors and multiples, and teaches students to decompose larger numbers into factors as a strategy for identifying multiples without long division.

In this Grade 4 lesson from Pengi Math Chapter 5, students learn to define and distinguish prime and composite numbers based on their number of factors. They explore why 1 is neither prime nor composite, discover that all even numbers greater than 2 are composite, and apply the Sieve of Eratosthenes to systematically identify all prime numbers up to 100.

In this Grade 4 Pengi Math lesson from Chapter 5, students learn to generate number patterns by applying rules such as "Add 3" and use input-output tables to identify function rules. They explore arithmetic sequences by defining a start term and common difference, then practice recognizing implicit features of patterns, like alternating odd and even numbers, that go beyond the stated rule.

In this Grade 4 lesson from Pengi Math Chapter 6, students learn to identify and define unit fractions — fractions with a numerator of 1 that represent one equal part of a whole divided into n parts. Students also practice representing one whole as a fraction in the form n/n, building a foundational understanding of how fractions relate to equal partitioning.

In this Grade 4 Pengi Math lesson from Chapter 6, students learn to define and generate equivalent fractions using area models and number lines. They explore why a/b equals (n × a)/(n × b) through visual decomposition, and practice creating equivalent fractions by multiplying or dividing the numerator and denominator by the same common factor. By the end of the lesson, students can confidently identify and produce equivalent fractions using multiple strategies.

In this Grade 4 lesson from Pengi Math Chapter 6, students learn multiple strategies for comparing fractions, including using benchmark numbers (0, 1/2, and 1), comparing fractions with the same denominator or same numerator, and creating common denominators with area models. Students also practice ordering fractions and placing them on a number line based on their proximity to benchmarks.

In this Grade 4 lesson from Pengi Math Chapter 6, students learn how to decompose fractions into sums of unit fractions, convert between improper fractions and mixed numbers, and model these concepts using tape diagrams. Students practice multiplication strategies to rewrite mixed numbers as improper fractions and develop comparison skills by analyzing whole number and fractional parts separately.

In this Grade 4 lesson from Pengi Math Chapter 7, students learn to add and subtract fractions with like denominators by understanding joining and separating parts of a whole. Using tape diagrams, number bonds, area models, and number lines, they decompose fractions into unit fractions and apply these skills to solve word problems. An extension activity introduces adding fractions with related denominators, such as halves and fourths, by identifying common units.

In this Grade 4 lesson from Pengi Math Chapter 7, students learn to add mixed numbers by combining whole number and fractional parts separately, using strategies like "Make a Whole" and the "Arrow Way" for efficient computation. Students also practice converting between mixed numbers and improper fractions, regrouping sums when needed to express answers in standard mixed number form. The lesson builds estimation skills by rounding mixed numbers to the nearest half or whole before adding.

In this Grade 4 lesson from Pengi Math Chapter 7, students learn multiple strategies for subtracting mixed numbers, including separating wholes and fractions, regrouping by decomposing a whole into fractional parts, and converting to improper fractions. They also apply the counting up strategy on a number line to find differences. Skills are reinforced through real-world subtraction problems involving mixed numbers.

In this Grade 4 lesson from Pengi Math Chapter 7, students learn to multiply fractions and mixed numbers by whole numbers using repeated addition, area models, and the distributive and associative properties, including the core algorithm n × a/b = (n × a)/b. Students then apply these fraction multiplication skills to solve multi-step word problems involving time conversions between hours, minutes, and seconds, as well as measurement and distance scenarios.

In this Grade 4 lesson from Pengi Math Chapter 8, students learn to define decimals as fractions with denominators of 10 and 100, and express tenths and hundredths in fraction form, decimal form, and unit form. Using place value concepts, students explore the equivalence between tenths and hundredths, such as 0.3 = 0.30, and practice decomposing decimals like 2.58 into 258 hundredths.

In this Grade 4 Pengi Math lesson from Chapter 8, students learn to read, write, and model decimal numbers using place value disks, area model grids, and number lines. They practice converting between mixed numbers and decimal notation, and express decimals in expanded form using both fraction and decimal notation.

In this Grade 4 lesson from Pengi Math Chapter 8, students learn to compare and order decimals to the hundredths place using inequality symbols (<, >, =). They use area models and number lines as visual tools to justify comparisons, and practice converting between fractions and decimals to compare numbers in different forms. Students also arrange sets of decimals from least to greatest and greatest to least.

In this Grade 4 lesson from Pengi Math Chapter 8, students learn how to add fractions with denominators of 10 and 100 by converting tenths to equivalent hundredths before finding sums. The lesson covers the "Like Units" rule, adding mixed numbers with regrouping, and using visual models to represent the addition of tenths and hundredths. Students are also introduced to the standard algorithm for adding decimals.

In this Grade 4 lesson from Pengi Math Chapter 8, students connect fractions and decimals by relating coin values to fractions of a dollar and converting cents to decimal and mixed number form. They practice adding and subtracting money with regrouping, use tape diagrams to solve multi-step word problems, and express metric measurements such as meters, centimeters, kilograms, and grams as decimals.

In this Grade 4 Pengi Math lesson, students learn to construct dot plots and line plots to display measurement data in fractions (1/2, 1/4, and 1/8) and identify key statistical features including minimum, maximum, mode, and range. Students also practice calculating total values from line plots using frequency multiplication and apply their skills to solve addition and subtraction word problems using data from line plots.

In this Grade 4 Pengi Math lesson, students explore the metric system by learning how units of length (km, m, cm), mass (kg, g), and capacity (L, mL) relate to the base-ten place value system. They practice converting mixed metric units to smaller units and back, then apply regrouping strategies to add and subtract mixed metric measurements. The lesson wraps up with real-world problems involving metric distances, liquid volumes, and masses from Chapter 9.

In this Grade 4 Pengi Math lesson from Chapter 9, students learn to recognize and compare customary units of length, capacity, and weight, then build two-column conversion tables to identify patterns and conversion factors. They practice converting mixed number measurements like 1 1/2 ft to smaller units using multiplication and double number lines. The lesson also covers adding and subtracting mixed customary units through strategies such as regrouping, making the next whole unit, and compensation.

In this Grade 4 lesson from Pengi Math Chapter 9, students learn to convert units of time — hours, minutes, and seconds — using conversion tables, and practice adding and subtracting mixed units of time to solve elapsed time problems. They apply the RDW (Read, Draw, Write) process and use tape diagrams to work through complex multi-step word problems involving measurement.

In this Grade 4 lesson from Pengi Math Chapter 9, students learn to distinguish between area and perimeter, applying the formulas P = 2(l + w) and A = l × w to rectangles. They use division and algebraic thinking to find unknown side lengths and solve real-world problems involving multiplicative comparison. The lesson also covers calculating the area of composite shapes using the subtraction method.