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Lesson plan Grade 3 Math

Pinegate's Pipe Yard Racks: A Grade 3 Equal Groups Lesson

Students build tile arrays to match the racks of water main pipe in a fictional utility yard, reading each product as the total held by a number of equal rows.

Objectives

  1. Students will interpret a product as the total number in a given number of equal rows.
  2. Students will build an array with tiles that matches a multiplication sentence.
  3. Students will explain why 4 rows of 7 and 7 rows of 4 hold the same total.

Vocabulary

Key words: array, row, equal groups, product, factor

Teacher overview

Pinegate Waterworks is a fictional utility that stores new water main pipe in an outdoor yard, stacked on racks in even rows so a crew can count a rack from the ground without climbing it. That stacking gives grade 3 a genuine array: the number of rows and the number of pipes in a row are both visible, and the total has to be built rather than counted one pipe at a time. The misconception this lesson corrects is adding the two numbers instead of forming equal groups, so a rack with 4 rows of 3 pipes gets recorded as 7 pipes. The formative check midway through the procedure is written to surface that error while there is still time to reteach it with tiles.

Procedure

Hook (5 min): Sketch a rack on the board holding 3 rows with 6 pipes in each row and ask students how they would tell a coworker how many pipes are on the rack without pointing at each one. Record every method offered, including counting by ones, and leave them on the board for comparison later.

Direct instruction (10 min): Build the same rack with tiles under a document camera. Say the array aloud as "3 rows of 6 pipes," write 3 × 6 = 18, and label which factor counts the rows and which counts the pipes in one row. Rebuild the array as 6 rows of 3 pipes and write 6 × 3 = 18, then ask what changed and what stayed the same. Add a second example with 5 rows of 4 pipes, this time asking a student to state the meaning of each factor before the product is written.

Guided practice (12 min): In pairs, students build four racks with tiles from teacher-called descriptions such as "7 rows of 8 pipes," then write the matching multiplication sentence on a whiteboard and hold it up. Circulate and ask individual students to point to one row and say how many pipes it holds. Run the formative check at the halfway point: display a rack of 3 rows of 6 pipes and have every student write the total on a whiteboard. If more than five students write 9, stop and rebuild the array together before continuing.

Independent practice (8 min): Students complete items 1 through 8 of the student handout, using tiles for any rack they cannot picture. Remind them that each answer is a number of pipes, not a number of rows.

Closure and exit ticket (5 min): Students answer handout item 9 on their own and hand it in. Scan the responses for students who still expect 4 rows of 7 and 7 rows of 4 to give different totals, and pull that group for a five-minute tile session the following day.

Pinegate's Pipe Yard Racks: A Grade 3 Equal Groups Lesson — Grade 3 Math
Name: ____________________________ Date: ______________

Student Handout

The pipe yard at Pinegate holds racks of new water pipe. Each rack has rows of pipe. Every row in a rack holds the same number of pipes.

  1. Rack A has 4 rows. Each row holds 3 pipes. How many pipes are on Rack A?
  2. Rack B has 6 rows. Each row holds 5 pipes. How many pipes are on Rack B?
  3. Rack C has 7 rows. Each row holds 8 pipes. How many pipes are on Rack C?
  4. Rack D has 5 rows. Each row holds 9 pipes. How many pipes are on Rack D?
  5. Rack E has 9 rows. Each row holds 9 pipes. How many pipes are on Rack E?
  6. A crew fills 8 trucks. Each truck takes 6 pipes. How many pipes does the crew load?
  7. Rack F has 4 rows. Each row holds 7 pipes. How many pipes are on Rack F?
  8. Rack G has 7 rows. Each row holds 4 pipes. How many pipes are on Rack G?
  9. Look at your answers for item 7 and item 8. What do they show about 4 rows of 7 pipes and 7 rows of 4 pipes?

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 12 pipes. The rack holds 4 equal rows of 3 pipes, so 4 × 3 = 12 pipes. A student who writes 7 added the two numbers instead of counting 4 groups of 3.
  2. Answer: 30 pipes. The rack holds 6 equal rows of 5 pipes, so 6 × 5 = 30 pipes.
  3. Answer: 56 pipes. The rack holds 7 equal rows of 8 pipes, so 7 × 8 = 56 pipes.
  4. Answer: 45 pipes. The rack holds 5 equal rows of 9 pipes, so 5 × 9 = 45 pipes.
  5. Answer: 81 pipes. The rack holds 9 equal rows of 9 pipes, so 9 × 9 = 81 pipes.
  6. Answer: 48 pipes. The 8 trucks each take 6 pipes, which is 8 equal groups of 6, so 8 × 6 = 48 pipes.
  7. Answer: 28 pipes. The rack holds 4 equal rows of 7 pipes, so 4 × 7 = 28 pipes.
  8. Answer: 28 pipes. The rack holds 7 equal rows of 4 pipes, so 7 × 4 = 28 pipes.
  9. Answer: The two racks hold the same number of pipes. Turning an array on its side changes which factor counts the rows, yet the total stays 28 pipes. Accept any answer that says the totals are equal and ties that to the same tiles arranged a different way.

Differentiation

Support

Give this group racks drawn as open grids so students can place one tile per square and count the filled rows. Limit the independent work to items 1, 2, 6, 7, and 8, and provide a multiplication chart for checking rather than for finding the first answer. Ask students to say "___ rows of ___ pipes" aloud before each written sentence.

Extension

Ask students to find every rack shape that holds exactly 36 pipes with equal rows, record each as a multiplication sentence, and then explain which shape the yard should use if the rack can be no more than 6 pipes wide. Have them predict, before building, how many such shapes exist.

ELL supports

Pre-teach "row," "rack," "each," and "in all" with tiles arranged in front of the class and a photograph of stacked pipe. Post the sentence frame "There are ___ rows with ___ pipes in each row, so there are ___ pipes." Let students build item 3 with tiles before writing, and accept an oral answer for item 9 given to a partner or the teacher.

Extensions

Have students count something in the classroom that is already stored in equal rows, such as chairs, floor tiles, or the cubby wall, then write the multiplication sentence and the total for each. Ask them to photograph or sketch one arrangement and label which factor counts the rows, building a small classroom set of arrays to revisit during division work.