# Number Line: Operations

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• Operations
• Number Line
• Integers

### Description

Explore operations with integers using an authentic context of net worth, then generalize with a number line. Experiment with adding and subtracting both positives and negatives, and make predictions about whether the total will be positive or negative.

• Represent addition and subtraction of integers on a horizontal number line
• Reason about addition and subtraction of integers in terms of number-locations
• Use logical necessity to reason that addition has the opposite effect as subtraction or that adding (or subtracting) a negative integer has the opposite effect as adding (or subtracting) a positive integer.
• Recognize and generate equivalence classes of integer sums and differences
• Show that a number and its additive inverse (opposite) have a sum of 0
• Using a net worth context, describe situations that have a positive sum or difference, negative sum or difference, and zero sum or difference
• View adding a negative as equivalent to subtracting a positive, and explain why this relationship makes sense in contexts such as net worth.
• View subtracting a negative as equivalent to adding a positive, and explain why this relationship makes sense in contexts such as net worth.
• Apply a number line model for addition and subtraction to new contexts.

### Standards Alignment

#### Common Core - Math

7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.A.1a
Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
7.NS.A.1b
Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
7.NS.A.1c
Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
7.NS.A.1d
Apply properties of operations as strategies to add and subtract rational numbers.
Version 1.0.1

### Teacher Tips Učitelská příručka (pdf) obsahuje tipy poskytnuté od členů týmu PhET. ( PDF ).

### Teacher-Submitted Activities

Integer Addition and Subtraction Assessment Gillian Walker ZŠ II.st.
Lab
Remote
Matematika
Basque All Euskara  Zenbaki-lerroa: eragiketak
Bosnian All Bosanski  Brojevna prava: Operacije
Croatian All hrvatski  Brojevna crta: Računske operacije
Danish All Dansk  Tallinje: Beregninger
Dutch All Nederlands  Getallijn: Bewerkingen
French All français  Droite numérique: opérations
German All Deutsch  Zahlenstrahl: Operationen
Greek All Ελληνικά  Αριθμογραμμή: πράξεις
Hungarian All magyar  Számegyenes - műveletek
Chinese (Taiwan) All 中文 (台灣)  Number Line: Operations_數線：數線的運算
Italian All italiano  Retta dei numeri: operazioni
Latvian All Latviešu  Skaitļu ass: Darbības
Maori All Maori  Rārangi Tau: Paheko
Polish All polski  Oś liczbowa: działania
Portuguese (Brazil) All português (Brasil)  Reta Numérica: Operações
Serbian All Српски  Бројевна права: Операције
Slovak All Slovenčina  Číselná os: Operácie
Spanish All español  Recta Numérica: Operaciones Spanish (Peru) All español (Perú)  Recta numérica: Operaciones
Turkish All Türkçe  Sayı Doğrusu: İşlemler
Vietnamese All Tiếng Việt  Đường thẳng số: Các phép toán

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