Curriculum / Math / 3rd Grade / Unit 3: Multiplication and Division, Part 2 / Lesson 23
Math
Unit 3
3rd Grade
Lesson 23 of 23
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Lesson Notes
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Identify arithmetic patterns and explain them using properties of operations.
The core standards covered in this lesson
3.OA.D.9 — Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
The foundational standards covered in this lesson
2.OA.C.3 — Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
25-30 minutes
Lisa is making triangle patterns out of toothpicks of all the same length. A triangle is made from three toothpicks. Her first pattern is a single triangle.
a. Her second pattern is shown below. How many toothpicks are needed for her second pattern?
b. Her third pattern is shown below. How many toothpicks are needed for her third pattern?
c. If she continued the same pattern, how many toothpicks are needed for the fifth pattern? How many toothpicks are needed for the tenth pattern?
d. If you had 24 toothpicks, how many triangles could you make? Explain how you know.
e. Will there be a pattern in the sequence that uses exactly 37 toothpicks? Why or why not?
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Tri-Triangles from the Problems of the Month made available by Inside Mathematics under the CC BY-NC-ND 3.0 license. © Noyce Foundation. Accessed Nov. 1, 2018, 12:41 p.m..
Alex made the following pattern by adding the same number each time.
3, 10, 17, 24, 31, …
a. Find the next two numbers in the pattern.
b. Why do the values in the pattern alternate between even and odd?
15-20 minutes
Problem Set
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Which of these patterns has an odd number as its next term?
Jacqueline reads every day over the summer and records the total number of pages she has read. She notices a pattern in the total pages she has read:
4, 8, 12, 16, ______, ______, ______
If her pattern continues, how many pages will she have read the next three days? Fill in the blanks above to extend the pattern.
The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.
Extra Practice Problems
Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.
Topic A: Introduction to The Properties of Operations
Study commutativity to find known facts of 6, 7, 8, and 9.
Standards
3.OA.B.53.OA.D.9
Understand the zero and identity properties of multiplication.
3.OA.A.43.OA.B.53.OA.C.73.OA.D.9
Understand the role of parentheses and apply to solving problems.
3.OA.B.53.OA.D.8
Introduce the distributive property of multiplication.
Introduce the associative property of multiplication.
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Topic B: Multiplication and Division by 6 and 7
Build fluency with multiplication and division facts using units of 6.
3.OA.A.43.OA.C.7
Build fluency with multiplication and division facts using units of 7.
Use the associative property as a strategy to multiply by units of 6.
3.OA.B.53.OA.C.73.OA.D.9
Use the distributive property as a strategy to multiply by units of 6.
Use the distributive property as a strategy to multiply by units of 7.
Solve one- and two-step word problems involving units up to 7.
3.OA.A.33.OA.D.8
Topic C: Multiplication and Division by 8 and 9
Build fluency with multiplication and division facts using units of 8 and 9.
Use the associative property as a strategy to multiply by units of 8 and 9.
Use the distributive property as a strategy to multiply by units of 8 and 9.
Use the distributive property as a strategy to multiply by units of 8 and 9, including the subtractive use of the distributive property.
Solve one- and two-step word problems involving units up to 9.
Topic D: Multiplication and Division by Values Greater than 10
Multiply one-digit whole numbers by multiples of 10.
3.NBT.A.33.OA.A.43.OA.B.5
Multiply one-digit whole numbers by two-digit whole numbers using the associative and distributive properties.
Topic E: Two-Step Word Problems and Patterns in Arithmetic
Solve two-step word problems involving all four operations.
3.OA.D.8
Solve two-step word problems involving all four operations, including multiplying one-digit whole numbers by multiples of 10.
3.NBT.A.33.OA.D.8
Identify patterns in single or multiple rows/columns of the multiplication table.
3.OA.C.73.OA.D.9
Identify other patterns in the multiplication table.
3.OA.D.9
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