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Mastering Array-Based Word Problems in Mathematics

In this lesson, students will explore solving word problems using arrays and tape diagrams. Anu discovers that there are 8 eggs in her carton by drawing a visual array of 2 rows with 4 eggs each. Similarly, Miss Tam arranges desks into 20 desks using the same approach. The lesson continues with examples including Yehuda’s cherry consumption and various practice problems that reinforce the concept of visual representation in problem-solving. Students will draw their solutions and write corresponding addition sentences to solidify their understanding.

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Mastering Array-Based Word Problems in Mathematics

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  1. Solving Word Problems with Array Lesson 6.9:

  2. Concept Development Problem 1 • Anu wants to know how many eggs are in the carton. She sees 4 eggs in both rows. How many eggs are there? • Read the problem aloud. • Draw to show Anu’s eggs. • What number sentence should we write to find the total? • Write your number sentence and label your answer. • What did you draw? • We can draw 2 columns of 4 eggsor 2 rows of 4 eggs. • Read your statement to your partner. • Anu has 8 eggs in the carton.

  3. Concept Development Problem 2 • Miss Tam arranges desks into 4 rows of 5. How many desks are in her classroom? • Draw a picture to solve and write a number sentence. Write a statement of your answer. • Read the problem aloud. • Draw to show Miss Tam’s desks. • How many desks are in each column, or unit? • Let’s write that unit of 4 at the bottom of each column. • What number sentence could we write to find the total? • Turn and talk, how could we represent this problem using a tape diagram?

  4. Concept Development Problem 2 • A bar that is separated into 5 fours. Since we wrote units of 4 at the bottom of each column, we can make bars with fours inside. • Let’s build our tape diagram together. • Let’s represent the first column of desks. How many units are inside? • How many in the each part? • Remind me, why are there 5 parts to our tape diagram? • We drew 5 columns. • Our tape diagram is just another way to represent the problem. It’s a great problem-solving strategy!

  5. Concept Development Problem 2 • Write a number sentence under your tape diagram and a statement of your answer. When you are writing your statement, be sure to check the original question. What is your statement? • There are 20 desks in the classroom.

  6. Concept Development Problem 3 • Let’s represent this next problem using only a tape diagram. • Yehuda ate 4 cherries each in the morning, afternoon, and evening. How many cherries did Yehuda eat altogether? • Read the problem aloud. • Draw a tape diagram to show the cherries Yehuda eats. • How did you draw your tape diagram? • We can make 3 parts, each with a 4 inside. We can make 3 groups of 4. The tape diagram shows 3 fours.

  7. Concept Development Problem 3 • What number sentence should we write to solve? • 4 + 4 + 4 = 12 • Share your statement with your partner. • Yehuda ate 12 cherries.

  8. Practice Problem • Draw an array for each word problem. Write an addition number sentence to match each array. • Jason collected some rocks. He put them in 5 rows with 3 stones in each row. How many stones did Jason have altogether? • Abby made 3 rows of 4 chairs. How many chairs did Abby use? • There are 3 wires and 5 birds sitting on each of them. How many birds in all are on the wires? • Henry’s house has 2 floors. There are four windows on each floor that face the street. How many windows face the street?

  9. Practice Problem • Draw a tape diagram for each word problem. Write an addition number sentence to match each tape diagram. • Each of Maria’s 4 friends has 5 markers. How many markers do Maria’s friends have in all? 6. Maria also has 5 markers. How many markers do Maria and her friends have in all?

  10. Practice Problem Draw a tape diagram and array. Then write an addition number sentence to match. 7. In a card game, 3 players get 4 cards each. One more player joins the game. How many total cards should be dealt now?

  11. Exit Ticket • Draw a tape diagram or an array for each word problem. Then write an addition number sentence to match. • Joshua cleans 3 cars every hour at work. He worked 4 hours on Saturday. How many cars did Joshua clean on Saturday? 2. Jason cleans 4 cars every hour at work. He worked 3 hours on Saturday. How many cars did Joshua clean on Saturday?

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