2.8 Equal Groups
Unit Goals
- Students work with equal groups of objects to gain foundations for multiplication.
Section A Goals
- Determine whether a group of objects (up to 20) has an odd or even number of members.
- Write an equation to express an even number as a sum of two equal addends.
Section B Goals
- Find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns using addition.
- Partition rectangles into rows and columns of equal-size squares, and count to find the total number of squares.
- Represent the total number of objects in an array as a sum of equal addends.
Section A: Odd and Even
Problem 1
Pre-unit
Practicing Standards: K.CC.B.5
How many dots do you see?
Solution
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Problem 2
Pre-unit
Practicing Standards: 1.OA.D.7
Select 3 correct equations.
Solution
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Problem 3
Pre-unit
Practicing Standards: 1.OA.A.2
Here are some pattern blocks.
How many corners are there all together on the pattern blocks? Explain or show your reasoning.
Solution
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Problem 4
- Noah and Lin have 13 crayons. Can they share all of the crayons equally with no leftovers? Explain or show your reasoning.
- Noah and Lin have 16 colored pencils. Can they share all of the colored pencils equally with no leftovers? Explain or show your reasoning.
Solution
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Problem 5
Mai is planning a dance and wants everyone to dance in pairs. For each number of students, decide whether everyone can dance in pairs with no one left out. Explain or show your reasoning.
- 14
- 17
- 18
Solution
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Problem 6
For each image, decide whether the number of dots is even or odd. Explain or show your reasoning.
Solution
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Problem 7
Can each number be written as a sum of two equal addends? Explain or show your reasoning.
- 12
- 15
- 18
Solution
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Problem 8
Decide if each expression represents an even number or an odd number. Explain or show your reasoning.
-
\(5 + 5\)
-
\(6 + 6 + 1\)
-
\(10 + 10\)
Solution
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Problem 9
Exploration
This classical design is called the “flower of life.”
It is made of shapes that look like this:
- Is the number of these shapes in the design even or odd? Explain or show your reasoning.
- How many of the shapes are there in the design? Explain or show your reasoning.
Solution
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Problem 10
Exploration
What are some things in the classroom that you know there are an even number of without counting them? Explain your reasoning.
Solution
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Section B: Rectangular Arrays
Problem 1
- How many counters are in each row?
- How many rows are there?
- How many counters are there in all?
Solution
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Problem 2
-
Clare described an array that she built with 16 counters. “It has only 2 columns and it's really tall.”
How many counters are in each of Clare's columns?
-
Build a different array using 16 counters. How would you describe your array?
Solution
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Problem 3
-
Circle the 2 expressions that represent the array.
\(7 + 7 + 7 + 7 + 7 + 7 + 7\)
\(7 + 7\)
\(2 + 2 + 2 + 2 + 2 + 2 + 2\)
\(2 + 2\)
-
How many counters are there in the array?
Solution
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Problem 4
-
Make an array with 15 counters.
-
Write 2 equations with equal addends to show how many counters there are.
Solution
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Problem 5
-
Draw lines so the rectangle is completely partitioned into equal-size squares.
-
How many columns of squares are there?
How many squares are in each column?
-
How many rows of squares are there?
How many squares are in each row?
- Write 2 equations that represent the number of squares in the array.
Solution
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Problem 6
-
Split the rectangle into equal-size squares.
- Write 2 equations that represent the number of squares in the array.
Solution
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Problem 7
Exploration
This large solar panel collects energy from the sun. There are different arrays of equal-size rectangles in the panel.
- Describe some arrays of equal sized rectangles that you see in the panel. How many equal-size rectangles are there in each array?
- Write an equation for the number of equal-size rectangles in each array.
Solution
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Problem 8
Exploration
- What are some things in the classroom or at home that come in arrays?
- Choose one of the arrays and find the number of rows, the number of columns, and the total number of objects.
Solution
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