**Native Numbers Learning Objectives at Five Stars / Gold Trophy**

*Overview*

The purpose of Native Numbers is to develop a child’s Number Sense. The 25 activities in the app develop the component concepts and subskills that Number Sense depends upon. Children like to move through the curriculum in different ways. Some want to move ahead as soon as they unlock a new activity (at three stars / bronze trophy). Some prefer to complete each activity before moving on (at five stars / gold trophy). Both approaches are fine. To get the full value of the curriculum, however, parents and teachers should make sure each child goes back and completes every activity through five stars. (Note that they will need to demonstrate both accuracy and speed to earn the fourth and fifth stars in most activities.) The table below describes the learning objectives for each activity in the curriculum, assuming the child earns all five stars.

*Learning Objectives for each Native Numbers activity (at five stars / gold trophy)*

Subskill |
Activity |
Learning Objective(s) at five stars / gold trophy |

Number concepts | Rods | Connect number names (“one”, “two”) to the continuous quantities they represent for numbers 1-9 (with accuracy and fluency) |

Number concepts | Sets | For numbers 1-9, connect number names to the discrete quantities they represent and subitize the visual patterns – that is, recognize the number at a glance (with accuracy and fluency) |

Number concepts | Match Rods | Understand that the continuous and discrete representations of numbers 1-9 refer to the same underlying quantity (with accuracy and fluency) |

Number concepts | Numerals | Connect number names to their symbolic numerals 1-9 (with accuracy and fluency) |

Number concepts | Mastery | Be able to match numbers of the same quantity (from 1-9) whether represented in continuous, discrete, or symbolic form (with accuracy and fluency) |

Number relations | Rods | Connect common vocabulary for number relations (greater, less, bigger, smaller, heavier, lighter, etc.) to continuous quantities between 1 and 9 (with accuracy and fluency) |

Number relations | Sets | Connect common vocabulary for number relations to discrete quantities between 1 and 9 (with accuracy and fluency) |

Number relations | Tallies | Generalize relational concepts to a second discrete representation (tallies) |

Number relations | Numerals | Connect common vocabulary for number relations (greater, less, etc.) to symbolic numerals between 1 and 9 (with accuracy and fluency) |

Number relations | Mastery | Recognize that the numerical relations apply in the same way across all representations of numbers 1-9 (with accuracy and fluency) |

Number ordering | Rods | Understand relative position and magnitude of whole numbers 1-9 – continuous representation of quantity |

Number ordering | Sets | Understand relative position and magnitude of whole numbers 1-9 – discrete representation |

Number ordering | Tallies | Generalize relative position and magnitude of whole numbers 1-9 to a second discrete representation |

Number ordering | Numerals | Understand relative position and magnitude of whole numbers 1-9 – symbolic representation |

Number ordering | Mastery | Understand that the order of numbers applies in the same way across all representations (continuous, discrete, symbolic) |

Counting | One-to-one | Understand ordinal numbers; understand that objects can be “tagged” with numbers, that each object should get a unique number, and that the numbers used as tags should always be in standard order: 1, 2, 3, … |

Counting | Count Up | Understand cardinal numbers: Given a set of 1-9 objects, count them out and tell “how many”; relate ordinal to cardinal numbers |

Counting | Count Down | Count backwards to 1, starting from numbers up to 9 |

Counting | Count On | Given two numbers, add them together by starting with the larger number and counting up by the smaller to get the sum |

Counting | Mastery | Count out a given number of items (from 1-9) from a larger set |

Demonstrate mastery | Numbers | Be able to match numbers of the same quantity (1-9) no matter what representation is used (generalize to include tallies) |

Demonstrate mastery | Numbers+ | Be able to recognize quantities accurately and quickly no matter what representation is used (consolidate understanding of and support fluency with number concepts) |

Demonstrate mastery | Order | Be able to put numbers (1-9) in increasing or decreasing order, while being able to recognize quantities no matter what representation they are in and ignoring distractors |

Demonstrate mastery | Counting | Cardinal counting up and down: Given a number (1-9), be able to add or remove objects from a set to make that number |

Demonstrate mastery | Counting+ | Pre-addition: Given a starting amount (e.g., “2”) and a target number (e.g., “seven”), count out objects added to the starting number to make the target number |

Last updated: February 8, 2013