# PTA MS Curriculum

## Standards

**STANDARDS**

*Standard 1:* **Number and Algebra.**

*Learners understand that numbers and algebra represent and quantify our world and can be used to solve problems*

- Counting & Cardinality – Learners understand that numbers are a naming system
- Numbers Base Ten – Learners understand that the base ten place value system is used to represent and quantify our world and can be used to solve problems
- Operational Thinking & Algebra – Learners understand that numbers and algebra represent and quantify our world and can be used to solve problems
- Number & Operations – Learners understand that fractions and decimals are ways of representing whole-part relationships

*Standard 2:* **Measurement and Data.**

*Learners understand that objects and events have attributes that can be measured and compared using appropriate tools. Data analysis can help us interpret and make predictions about our world.*

*Standard 3:***Geometry.**

*Learners understand that geometry models and quantifies structures in our world and can be used to solve problems.*

** Achievement Standards examine understanding, fluency, problem-solving and reasoning at each grade level with more specific descriptors included within each curriculum document.*

## Math Workshop

At AISJ math is taught using a workshop approach rather than a whole class methodolgy. This is a way of differentiating instruction to help all students develop knowledge, skills, strategies and conceptual understanding. The workshop approach is a predictable structure that provides students with routines and time to work at their just right math level.

**FOCUS-LESSONS**

**FOCUS-LESSONS**

Each workshop has a focus lesson. This is a brief 10 – 15min whole class lesson regarding a skill, mathematical practice or concept that is relevant for all students in the class.

*PROBLEM SOLVING*

Students work independently or in small groups to practice skills and strategies, and/or develop their mathematical knowledge and conceptual understanding. Students are also challenged weekly with group problem solving tasks and/or projects.

*SMALL GROUP INSTRUCTION*

Teachers use data from pre-assessments and ongoing formative assessment to form small groups. Students then work with a teacher and engage in lessons that are geared to their needs. These groups are flexible and constantly change depending on student needs and the concepts and skills being taught.

**INDIVIDUAL CONFERENCES**

**INDIVIDUAL CONFERENCES**

Students meet one-on-one with a teacher to demonstrate new learning, and review and set mathematical goals

## KNOWLEDGE

Number knowledge describes the key items of knowledge students need to learn. It is important for students to continually increase their number knowledge to reduce the cognitive stress on the brain when solving challenging problems. The ability to solve problems accurately and efficiently is based on knowing and being able to retrieve key items of knowledge with minimal effort. Knowledge is important because using knowledge can decrease the load on working memory and enable students to solve more complex problems. Strong knowledge is essential for students to broaden their repertoire of operational strategies and for the development of more advanced strategies.

## OPERATIONAL STRATEGIES

General Text - BLUE heading- Left Aligned

Operational strategies describe the mental processes students use to estimate answers and solve operational problems with numbers. Moving through the MS grades, students build new strategies on their existing strategies and these existing strategies are not subsumed. Students frequently revert to previous strategies when presented with unfamiliar problems or when the mental load gets high.

Students learn to interpret and solve problems using the four operations using a variety of operational strategies.

THE APPLICATION OF NUMBER KNOWLEDGE AND OPERATIONAL STRATEGIES IS OFTEN DESCRIBED AS ‘NUMBER SENSE’. STRONGLY DEVELOPED NUMBER SENSE LEADS TO STRONG ALGEBRAIC THINKING.

## MATH PRACTICES

For mathematics to be relevant for the 21st century learners, it must develop knowledge and strategy (number sense) as well as mathematical practices. Mathematical knowledge, skills and content reflect new needs and goals, but are essentially unchanged. Nevertheless, because the world is changing so rapidly, more is needed. Being prepared to compete in an increasingly complicated and unpredictable world means developing stamina and disposition to struggle through totally unfamiliar, challenging problems. The confidence to approach new and unfamiliar problems and tackle them without a pre-learned solution or method is vitally important.

**THE EIGHT PREK – GR 12 MATHEMATICAL PRACTICES ARE:**

**THE EIGHT PREK – GR 12 MATHEMATICAL PRACTICES ARE:**

1. MAKE SENSE OF PROBLEMS AND PERSEVERE IN SOLVING THEM.

2. REASON ABSTRACTLY AND QUANTITATIVELY.

3. CONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE REASONING OF OTHERS.

4. MODEL WITH MATHEMATICS.

5. USE APPROPRIATE TOOLS STRATEGICALLY.

6. ATTEND TO PRECISION.

7. LOOK FOR AND MAKE USE OF STRUCTURE.

8. LOOK FOR AND EXPRESS REGULARITY IN REPEATED REASONING.

## ASSESSMENT

## Assessment

In the Elementary School, we conduct an internal standardized numeracy assessments twice a year to measure the students’ numeracy development in both mathematical knowledge and strategic thinking for students in KG – Gr 5. For PreK, this information is obtained using informal assessments such as observation, conferring and student work samples. The numeracy assessment we use are:

**JAM**

**JAM**

The Junior Assessment of Mathematics (JAM) is a one-on-one interview and assesses the achievement of a student in relation to early stages of numeracy development. This assessment is primarily used with students in K – Gr2.

**GLOSS**

**GLOSS**

The Global Strategy Stage (GloSS) one-on-one interview is used to assess the achievement of a student in relation to intermediate and advanced stages of mathematical strategic thinking. This assessment is primarily used with students in Gr 3 – 5.

**IKAN**

**IKAN**

The Individual Knowledge Assessment of Number (IKAN) is used to assess the achievement of a student in relation to intermediate and advanced stages of number knowledge. This assessment is primarily used with students in Gr 3 – 5.

**Developmental Stages and Approximation of Proficiency for the end of each grade**

Stage | End of Year | Assessment Used |
---|---|---|

0-1 Emergent | PK | Obersvation |

2-3 Counting All | Kindergarten | JAM Interview |

4 Advanced Counting | Grade 1 | JAM Interview |

5 Early Additive | Grade 2-3 | JAM/GloSS/IKAN |

6 Advanced Additive | Grade 4-5 | GloSS/IKAN |

**NUMBER PROFILE**

**NUMBER PROFILE**

We use the data from the JAM, GloSS and IKAN assessments to complete an individual number profile for students from Kindergarten through to Grade 5. A number profile (link) is also generated for students in Pre-K but this is done using observations, not the JAM interview. The number profile helps teachers and students track their growth through the stages of numeracy development. A student’s number profile is shared with parents throughout the year, so there is clear communication regarding strengths and areas for growth. Student number profiles are passed on to the following year’s teacher at the end of each academic year.

This is an example of what a completed number profile (link) for a child at the end of Grade 2 might look like.

**MAP**

**MAP**

At AISJ, we also implement the Measures of Academic Progress (MAP) achievement test in mathematics, twice a year, for all students in Grades 3 – 5.