September

As stated in the NL curriculum guide:

"The focus of instruction in this unit is on the development of flexible thinking with respect to larger whole numbers. Students should gain an understanding of the relative size (magnitude) of numbers through meaningful contexts, such as capacity for local arenas or population of the school/community. Students then begin to use personal referents to think of other large numbers. They will also use benchmarks, such as multiples of 100 and 1 000, as well as 250 and 750, as a reference point to help them develop a conceptual understanding of numbers and their size. "

Students should be able to:

• Represent and describe whole numbers to 10 000, concretely, pictorially and symbolically.

• Read a given four-digit numeral without using the word ‘and’.

• Write a given numeral, using proper spacing without commas.

• Represent a given numeral using a place value chart or other models.

• Explain the meaning of each digit in a given four-digit numeral, including numerals with all digits the same.

• Express a given numeral in expanded notation.

• Write the numeral represented by a given expanded notation.

• Write a given numeral 0 –10 000 in words.

• Create and order three different four-digit numerals.

• Identify the missing numbers in an ordered sequence or on a number line (vertical or horizontal).

• Identify incorrectly placed numbers in an ordered sequence or on a number line (vertical or horizontal).

• Order a given set of numbers in ascending or descending order, and explain the order by making references to place value

October

As stated in the NL curriculum guide:

"This unit focuses on efficiency and flexibility with both traditional algorithms and personal strategies in the addition and subtraction of larger numbers. Students worked with 3-digit addition and subtraction in Grade 3. In Grade 4, the focus will be on addition and subtraction of 4-digit numbers. Students should begin to recognize that estimation is a useful skill in their lives. To be efficient when estimating sums and differences mentally, students need a variety of strategies from which to choose and must be able to access a strategy quickly. Encourage students to estimate prior to calculating the answer. Use a variety of models, such as base-ten blocks and number lines, to assist in estimation. Students should have many opportunities to solve and create word problems for the purpose of answering meaningful questions, preferably choosing topics of interest to them."

Students should be able to:

• Describe a situation in which an estimate rather than an exact answer is sufficient.

• Estimate sums and differences, using different strategies.

• Determine the sum of two numbers using a personal strategy.

• Solve problems that involve addition and subtraction of more than two numbers.

• Determine the difference of two numbers using a personal strategy.

October/November

As stated in the NL curriculum guide:

• "Grade 4 students will extend upon previous knowledge of patterns and relations as they explore the different types of patterns, discover pattern rules, translate between concrete and pictorial representations of patterns and charts or tables, determine equalities, and investigate how patterns using symbols and variables are used mathematically to describe change. The ability to discern and utilize patterns effectively fosters the development of algebraic thinking. Students at the Grade 4 level begin to represent algebraic thinking with algebraic equations. "

Students should be able to:

• Describe the pattern found in a given table or chart.

• Determine the missing element(s) in a given table or chart.

• Identify the error(s) in a given table or chart.

• Create a concrete representation of a given pattern displayed in a table or chart.

• Create a table or chart from a given concrete representation of a pattern.

• Translate the information in a given problem into a table or chart.

• Identify and extend the patterns in a table or chart to solve a given problem.

• Explain the purpose of the symbol in a given addition, subtraction, multiplication or division equation with one unknown.

• Express a given pictorial or concrete representation of an equation in symbolic form.

• Solve a given one-step equation using manipulatives.

• Describe, orally, the meaning of a given one-step equation with one unknown.

• Solve a given equation when the unknown is on the left or right side of the equation.

• Solve a given one-step equation using “guess and test”.

• Identify the unknown in a problem, represent the problem with an equation, and solve the problem concretely, pictorially or symbolically.

• Represent and solve a given addition or subtraction problem involving a “part-part/whole” or comparison context, using a symbol to represent the unknown.

"Focus will mainly be on many-to-one correspondence and on interpreting data to see relationships. In preparation for interpreting graphs and using them as a problem-solving tool, students will gather data that is meaningful to them and learn how to construct graphs. Charts, diagrams and graphs are useful as tools to understand mathematical relationships and solve mathematical problems. Examples of such charts covered in this unit include Venn and Carroll diagrams. Although data relationships receive focus in this unit, it is important that students are given opportunities to practice what they have learned, on an ongoing basis throughout the year depending on special occasions and events that naturally occur (e.g., Halloween, sports events, seasons). "

Students should be able to:

• Collect, display and analyze data to solve problems

• Demonstrate an understanding of manyto-one correspondence.

• Construct and interpret pictographs and bar graphs involving many-to-one correspondence to draw conclusions.

• Use patterns to describe the world and solve problems.

• Identify and explain mathematical relationships, using charts and diagrams, to solve problems.

"This unit introduces students to symmetry and provides them opportunity to explore symmetry and congruency in 2-D shapes. Both of these properties are important and can be linked to the study of fractions and to the area of regular polygons. When children are learning about symmetry, they need to spend a lot of time manipulating the shapes rather than simply looking at them. Taking the time to allow students to fold, draw and work with models to fi nd properties of 2-D shapes is important, as it promotes visualization and is helpful in problem solving. During this unit, prepare an area where children have ongoing opportunities to explore and extend upon their experiences with symmetrical design. Provide geoboards, Miras™, pattern blocks, 2-D shapes, geometric dot paper, Pattern Block grid paper (Masters booklet pp.44-49), fabric, wallpaper, etc. Display symmetrical designs versus non-symmetrical designs as an exhibit in the classrooms or compile digital photographs to make a book or a bulletin board display "

Students should be able to:

• Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.

• Demonstrate an understanding of congruency, concretely and pictorially

• Describe and analyze position and motion of objects and shapes.

• Demonstrate an understanding of line symmetry by: • identifying symmetrical 2-D shapes • creating symmetrical 2-D shapes • drawing one or more lines of symmetry in a 2-D shape.

In Grade 3, students were introduced to the meaning of multiplication and division with products to 5 ´ 5. By the end of Grade 4, students will learn to describe and apply effi cient mental strategies for multiplication facts to 9 ´ 9. The meaning of multiplication and division and the connection between the operations is crucial as students develop understanding of the facts. Allow time for both strategy development and practice to ensure that students can demonstrate they know the strategies.

Students should be able to:

• Explain and apply the properties of 0 and 1 for multiplication and the property of 1 for division.

• Describe and apply mental mathematics strategies, such as:

  • skip counting from a known fact

  • using doubling or halving

  • using doubling or halving and adding or subtracting one more group

  • using patterns in the 9s facts

  • using repeated doubling to determine basic multiplication facts to 9 ´ 9 and related division facts.

"In everyday life, we often have measures that are less than one. In Grade 4, the focus is on students initially developing a fi rm understanding of these numbers. At fi rst, students will learn that fractions are one way to represent numbers less than one. They need to understand that a fraction represents one idea although it uses two numbers, with an emphasis on the relationship between these two numbers. In the second part of this unit, students will use decimals to represent numbers less than one. An introduction to decimals requires familiarity with the concept of fractional tenths. Some students will be comfortable with the concept of tenths and will be ready to move into a study of decimal hundredths fairly quickly. Students will learn that decimals allow for calculations that are consistent with whole number calculations. "

Students should be able to:

• Represent and describe decimals (tenths and hundredths), concretely, pictorially and symbolically.

• Relate decimals to fractions and fractions to decimals (to hundredths).

• Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths).

• Demonstrate an understanding of fractions less than or equal to one by using concrete, pictorial and symbolic representations to:

  • name and record fractions for the parts of a whole or a set

  • compare and order fractions

  • model and explain that for different wholes, two identical fractions may not represent the same quantity

  • provide examples of where fractions are used.

" Fluency with whole number computations is essential in everyday life. Connecting multiplication and division to measurement, area, money, etc. helps students see the usefulness of multiplication. In this unit students will use their knowledge of basic multiplication facts as well as their understanding of place value to explore patterns when multiplying by 10s and 100s to multiply 2- and 3-digit numbers by a 1-digit number. Students will also build on the strategies they learned when studying multiplication facts to enable them to develop effi cient strategies for multiplying larger numbers. As students develop the practice of estimating the product before computing, it enables them to strengthen their number sense. Being able to break apart numbers in fl exible ways is important when multiplying numbers. Students will experience greater success applying the strategies to larger numbers if they can automatically recall the multiplication facts. Knowing how to multiply 2- and 3-digit numbers by 1 digit will prepare students for developing an understanding of division and multiplying 2-digit numbers by 2-digit numbers in later grades. "

Students should be able to:

• Demonstrate an understanding of multiplication (2- or 3-digit by 1-digit) to solve problems by:

  • using personal strategies for multiplication with and without concrete materials

  • using arrays to represent multiplication

  • connecting concrete representations to symbolic representations

  • estimating products

  • applying the distributive property.

April

"Previously, students developed the concept of division through studying the division facts. In this unit they will continue to develop an understanding of division by fi nding quotients of 2-digit whole numbers divided by 1-digit numbers. They will also continue to learn the meaning of division and how it relates to multiplication. The two different meanings of division are presented as equal sharing and equal grouping. Focus is on computational fl uency with larger numbers so that students learn effi cient and accurate methods of computing. This can be developed by solving problems with larger numbers that require calculation and by recording and sharing their strategies with others. Estimation plays an important role in division because it provides a tool for judging the reasonableness of an answer. Through encounters with various problem situations, students can develop fl uency in computing division problems that will be essential in real life situations. When students can create their own division problems based on contextual situations, it strengthens their understanding of the principles of division. "

Students should be able to:

• Demonstrate an understanding of division (1-digit divisor and up to 2-digit dividend) to solve problems by:

  • using personal strategies for dividing with and without concrete materials

  • estimating quotients

  • relating division to multiplication.

• Solve one-step equations involving a symbol to represent an unknown number.

"Measurement is an essential link to many areas of the mathematics curriculum. Measurement permeates many areas of life including careers and everyday living. In its simplest form it merely attaches a number to some attribute of an object and it increases in it’s breadth and depth as students move on through the curriculum. Students must learn profi ciency in choosing and using measurement tools. Although measurement is the focus of this unit, it is also relevant in other areas of the mathematics curriculum, as well as everyday experiences "

Students should be able to:

• Read and record time, using digital and analog clocks, including 24-hour clocks

• Read and record calendar dates in a variety of formats.

• Demonstrate an understanding of area of regular and irregular 2-D shapes by:

  • recognizing that area is measured in square units

  • selecting and justifying referents for the units cm² or m²

  • estimating area, using referents for cm² or m²

  • determining and recording area (cm² or m²)

  • constructing different rectangles for a given area (cm² or m²) in order to demonstrate that many different rectangles may have the same area.

"As students develop mathematically and become more familiar with geometric attributes, they are increasingly able to identify and name a shape by examining its properties and using reasoning. Through exploration of three dimensional shapes, students develop awareness that there are certain specifi c attributes that they can use to classify the shapes. They will also be encouraged to develop and communicate mathematical arguments about geometric relationships. "

Students should be able to:

• Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.

• Describe and construct right rectangular and right triangular prisms.

Math outcomes are assessed in a variety of ways.

Daily discussions of math concepts and involvement in whole group problem solving is the most frequent form of assessment. Students are encouraged to explore their own understanding of topics discussed and demonstrate what they know.

Math journals offer students a way to practice new skills and discover challenges they may have. Each activity can be found in the Newfoundland math curriculum guide available online at https://www.gov.nl.ca/education/files/k12_curriculum_guides_mathematics_elementary_mathematics_grade_4_curriculum_guide_2014.pdf

In class worksheets are provided as independent practice and review. Students complete them after each lesson. Errors are highlighted and students are given an opportunity to correct the mistakes.

Chapter tests are given according to the schedule in the curriculum guide if topics have been covered with ample practice.

Overall assessment results (those documented in report cards) are a combination of all of the above assessments. Any particular grade awarded will not be the result of a single assessment piece. Only assessments which demonstrates the students best work will be used to evaluate a student's understanding.