Elementary Mathematics

Investigation 2 requires students to examine patterns in which a constant number is added each day. Students can contrast this situation with The Very Hungry Caterpillar, in which the Hungry Caterpillar eats one more piece of food each day. Comparing the two problem types will help students more fully understand the meaning of the various units in growing pattern problems.

***Click for Unit 7 replacement pages for Student Activity BooksSuggested Dates:

March 5- March 25

Estimated Duration: 15 Days

Investigation 1: 8 lessons

(February 12 – February 25)

Investigation 2: 7 lessons

(February 26 – March 6)

Smart Board, Promethean, and Power Point Files:

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Unit 7 Smart Board File

Unit 7 Smart Board File with Common Core Additions

Daily Weather File

End of Unit Rubrics 1st Grade

Unit 7 Vocabulary

Unit 7 Assessment

Pearson Success Net

Fuel The Brain games organized by CCSS

Interactive Math Dictionary Site

This site provides an extensive collection of

1st Grade At a Glance

1st Grade Investigations Extension Projects

1st Grade Story Problem Routine

Investigations K-2 Literature List

Progression for choosing numbers for tasks

**Suggestions for students who are struggling...**

Many students struggle to visualize what the numbers in growing patterns
represent. Create cups labeled with S, 1, 2, 3, etc. to represent the
start number and the day number. Then help students remember to transfer
the counters or pennies in the cup to the cup for the next day *before* adding the add number and counting all.

Students can practice counting on and skip counting with the support of pictures and patterns before visualizing situations that involve a start number and an add number.

Use intervention strategies in the Investigations manual. Suggestions are located throughout the chapter.

*Remember to upload files
to share with others, or locate files to use, on the wiki. Be sure to
join discussion posts with other colleagues to ask questions, answer
questions, and discuss math.

During this unit, focus on **
MP2 and MP7**.

**MP8. Look for and express regularity in repeated reasoning. **Growing patterns require students to repeatedly add a number and count on to a total. Students should use patterns to help them accomplish this task. For example, if hopping on a number line or hundreds chart to repeatedly add 3, students should notice that they skip 2 numbers and land on the third number each time. Students can also make observations about even and odd numbers. Ask, “Which numbers did you land on? What do they have in common?” This work will help students understand multiplication in the later grades.

Patterns are not specifically part of the Common Core State Standards. However, patterns can be used to encourage algebraic thinking in elementary children. Students are more likely to use algebraic reasoning to analyze the growth of a pattern when teachers as students *how* patterns are changing. Otherwise, children tend to focus on the appearance of each part in a pattern and counting all of the parts one by one. Discuss, “What questions should we ask students to encourage them to reason algebraically while working on Penny Jar and Staircase problems?”

To analyze and extend growing patterns, students must understand two variables: the start number and the grow number. Read “Teacher Note: About Number Sequences” (pgs. 125-126) and discuss, “How will we know when our students understand the two variables? How does this understanding set students up for success in the later grades?”

Read Teacher Note “The Role of Context in Visualizing Mathematical Relationships”

Read Teacher Note “About Number Sequence” Ask what are some possible numbers that fit our pattern?

**Suggestions for students who fully understand...**

Challenge students to tell if the jar will ever have _____ pennies and explain how they know using reasoning (for example, if they are adding 2 pennies each time, and they had an odd start number, they will never end up with an even total).

Students can be challenged to count on by various numbers in Counting on by twos, fives, and tens. They can compare the strategies they used to add each number.

Students can practice counting on and skip counting by finding the total number of cents represented by a collection of pennies, nickels, and dimes in Count Pennies, Nickels, and Dimes.

Have students analyze the counting sequences in Spooky Sequences to find the skip counting number and the number missing from the sequence.Use enrichment strategies in Investigations manual. Suggestions are located throughout the chapter.

Though patterns are not explicitly outlined in the Common Core, this work incorporates a number of Number Sense and Operations and Algebraic Thinking standards that are critical for the work students do in later grades. For more information, please visit the Common Core State Standards video series or the

**Extend the Counting Sequence.**

**1.NBT.1**. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

**Use place value understanding and properties of operations to add and subtract.**

**1.NBT.4**. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

**Represent and solve problems involving addition and subtraction.**

**1.OA.1**. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

**1.OA.2**. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

**Understand and apply properties of operations and the relationship between addition and subtraction.**

**1.OA.3**. Apply properties of operations as strategies to add and subtract.^{2} *Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) *

**1.OA.4**. Understand subtraction as an unknown-addend problem. *For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. Add and subtract within 20. *

**Add and subtract within 20.**

**1.OA.5**. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

**1.OA.6****.** Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

**Work with addition and subtraction equations.**

**1.OA.7**. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

**1.OA.8**. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. *For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ – 3, 6 + 6 = _.*

Repeating pattern, unit, part, whole, count on, count all

The Common Core does not specifically require students to work with patterns. However, patterns can be used to help students model with mathematics. Play a Find Your Partner game. Give half of the students a card with a unit for a repeating number, shape, or picture pattern (for example: square, square, triangle, triangle, circle). Give the other half of the students a matching equation (for example, 2 + 2 + 1 = 5). Ask students, “How did you know your pattern/equation matched your partner’s card? How many shapes would be in your pattern if the unit repeated once? Twice?” Have groups record their solutions on poster paper and present to their peers.

In this unit, students practice repeated addition through counting on. Repeated addition is the foundation of multiplication. Encourage students to practice this skill by placing them in a line. Pass out number cards in order from 1 to 20 (or however many students are in the class). Give students a growing pattern situation (For example, there is a penny jar with a start number of 1 penny and an add number of 2 pennies per day). Have students stand up if the growing pattern would end on their number on one of the days in the sequence and sit down if it would not (For example, the students holding the cards 1, 3, 5, 7, etc. would stand because there would be 1 penny at the start, 3 pennies on Day 1, 5 pennies on Day 2, etc.). Ask students to discuss, “Why are you standing/sitting? How did you figure out what to do?”

**
**This unit is related to the beginnings of multiplication. Students work with number sequences 2,4, 6, 8…3,6,9,12. Work
with the patterns is intended to give students practice in recognizing
creating and repeating patterns and then moving this concept to their
work with numbers.