{"id":28,"date":"2023-01-26T20:53:16","date_gmt":"2023-01-26T20:53:16","guid":{"rendered":"https:\/\/borenson.com\/?page_id=28"},"modified":"2023-02-21T10:28:59","modified_gmt":"2023-02-21T10:28:59","slug":"standards","status":"publish","type":"page","link":"https:\/\/borenson.com\/standards\/","title":{"rendered":"Standards"},"content":{"rendered":"[vc_row type=”full_width_background” full_screen_row_position=”middle” column_margin=”default” column_direction=”default” column_direction_tablet=”default” column_direction_phone=”default” bg_color=”#078363″ scene_position=”center” text_color=”dark” text_align=”left” row_border_radius=”none” row_border_radius_applies=”bg” overflow=”visible” overlay_strength=”0.3″ gradient_direction=”left_to_right” shape_divider_position=”bottom” bg_image_animation=”none” gradient_type=”default” shape_type=””][vc_column column_padding=”no-extra-padding” column_padding_tablet=”inherit” column_padding_phone=”inherit” column_padding_position=”all” column_element_direction_desktop=”default” column_element_spacing=”default” desktop_text_alignment=”default” tablet_text_alignment=”default” phone_text_alignment=”default” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_backdrop_filter=”none” column_shadow=”none” column_border_radius=”none” column_link_target=”_self” column_position=”default” gradient_direction=”left_to_right” overlay_strength=”0.3″ width=”1\/1″ tablet_width_inherit=”default” animation_type=”default” bg_image_animation=”none” border_type=”simple” column_border_width=”none” column_border_style=”solid”][vc_row_inner column_margin=”default” column_direction=”default” column_direction_tablet=”default” column_direction_phone=”default” text_align=”left” row_position=”default” row_position_tablet=”inherit” row_position_phone=”inherit” overflow=”visible” pointer_events=”all” css=”.vc_custom_1674774697930{margin-top: 5% !important;margin-bottom: 5% !important;background-color: #078363 !important;}”][vc_column_inner column_padding=”no-extra-padding” column_padding_tablet=”inherit” column_padding_phone=”inherit” column_padding_position=”all” column_element_direction_desktop=”default” column_element_spacing=”default” desktop_text_alignment=”default” tablet_text_alignment=”default” phone_text_alignment=”default” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_backdrop_filter=”none” column_shadow=”none” column_border_radius=”none” column_link_target=”_self” overflow=”visible” gradient_direction=”left_to_right” overlay_strength=”0.3″ width=”2\/3″ tablet_width_inherit=”default” animation_type=”default” bg_image_animation=”none” border_type=”simple” column_border_width=”none” column_border_style=”solid” column_padding_type=”default” gradient_type=”default”][vc_custom_heading text=”Math Standards” font_container=”tag:h1|text_align:left|color:%23ffffff” use_theme_fonts=”yes” css=”.vc_custom_1674774653032{margin-top: 3% !important;margin-right: 5% !important;margin-left: 5% !important;}”][vc_column_text css=”.vc_custom_1674775533679{margin-right: 5% !important;margin-left: 5% !important;}”]\n

Common Core Math Standards for Mathematical Practices<\/span><\/h3>\n[\/vc_column_text][vc_column_text css=”.vc_custom_1674774670911{margin-right: 5% !important;margin-bottom: 3% !important;margin-left: 5% !important;}”]\n
The Common Core Math Standards for Mathematical Practices seeks to have students conceptualize mathematics, rather than do mathematics by rote. Students are expected to observe mathematical structure and to reason and communicate mathematics.<\/span><\/h5>\n[\/vc_column_text][\/vc_column_inner][vc_column_inner column_padding=”no-extra-padding” column_padding_tablet=”inherit” column_padding_phone=”inherit” column_padding_position=”all” column_element_direction_desktop=”default” column_element_spacing=”default” desktop_text_alignment=”default” tablet_text_alignment=”default” phone_text_alignment=”default” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_backdrop_filter=”none” column_shadow=”none” column_border_radius=”none” column_link_target=”_self” overflow=”visible” gradient_direction=”left_to_right” overlay_strength=”0.3″ width=”1\/3″ tablet_width_inherit=”default” animation_type=”default” bg_image_animation=”none” border_type=”simple” column_border_width=”none” column_border_style=”solid” column_padding_type=”default” gradient_type=”default”][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][vc_row type=”in_container” full_screen_row_position=”middle” column_margin=”default” column_direction=”default” column_direction_tablet=”default” column_direction_phone=”default” scene_position=”center” text_color=”dark” text_align=”left” row_border_radius=”none” row_border_radius_applies=”bg” overflow=”visible” overlay_strength=”0.3″ gradient_direction=”left_to_right” shape_divider_position=”bottom” bg_image_animation=”none”][vc_column column_padding=”no-extra-padding” column_padding_tablet=”inherit” column_padding_phone=”inherit” column_padding_position=”all” column_element_direction_desktop=”default” column_element_spacing=”default” desktop_text_alignment=”default” tablet_text_alignment=”default” phone_text_alignment=”default” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_backdrop_filter=”none” column_shadow=”none” column_border_radius=”none” column_link_target=”_self” column_position=”default” gradient_direction=”left_to_right” overlay_strength=”0.3″ width=”1\/1″ tablet_width_inherit=”default” animation_type=”default” bg_image_animation=”none” border_type=”simple” column_border_width=”none” column_border_style=”solid”][vc_row_inner column_margin=”default” column_direction=”default” column_direction_tablet=”default” column_direction_phone=”default” text_align=”left” row_position=”default” row_position_tablet=”inherit” row_position_phone=”inherit” overflow=”visible” pointer_events=”all” css=”.vc_custom_1674774820918{margin-top: 5% !important;margin-bottom: 5% !important;}”][vc_column_inner column_padding=”no-extra-padding” column_padding_tablet=”inherit” column_padding_phone=”inherit” column_padding_position=”all” column_element_direction_desktop=”default” column_element_spacing=”default” desktop_text_alignment=”default” tablet_text_alignment=”default” phone_text_alignment=”default” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_backdrop_filter=”none” column_shadow=”none” column_border_radius=”none” column_link_target=”_self” overflow=”visible” gradient_direction=”left_to_right” overlay_strength=”0.3″ width=”1\/1″ tablet_width_inherit=”default” animation_type=”default” bg_image_animation=”none” border_type=”simple” column_border_width=”none” column_border_style=”solid”][vc_custom_heading text=”Math Standards” font_container=”tag:h1|text_align:center” use_theme_fonts=”yes”][vc_column_text]\n

Developing Fractions Sense<\/h3>\n[\/vc_column_text][vc_column_text]\n

Developing Fractions Sense Student Workbook A (Grade 3)<\/span><\/a><\/p>\n

Developing Fractions Sense Student Workbook B (Grade 4)<\/span><\/a><\/p>\n

Developing Fractions Sense Student Workbook C (Grade 5)<\/span><\/a><\/p>\n[\/vc_column_text][vc_custom_heading text=”Hands-On Equations Objectives” font_container=”tag:h1|text_align:center” use_theme_fonts=”yes”][vc_column_text]\n

Hands-On Equations, Level 1 and Verbal Problems Level 1<\/span><\/a><\/p>\n

Hands-On Equations Teaching Points by Lessons: Levels 1, 2 and 3<\/span><\/a><\/p>\n[\/vc_column_text][vc_custom_heading text=”NCTM Math Standards Correlation” font_container=”tag:h1|text_align:center” use_theme_fonts=”yes”][vc_column_text]\n

Grades 3 – 5<\/a>\u00a0<\/span><\/p>\n

Grandes 6 – 8<\/a>\u00a0<\/span><\/p>\n[\/vc_column_text][vc_column_text]\n

Common Core Math Standards<\/h3>\n[\/vc_column_text][vc_column_text]\n

Mathematical Practices\u00a0<\/span><\/a><\/p>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][vc_row type=”full_width_background” full_screen_row_position=”middle” column_margin=”default” column_direction=”default” column_direction_tablet=”default” column_direction_phone=”default” bg_color=”#cfe3de” scene_position=”center” text_color=”dark” text_align=”left” row_border_radius=”none” row_border_radius_applies=”bg” overflow=”visible” overlay_strength=”0.3″ gradient_direction=”left_to_right” shape_divider_position=”bottom” bg_image_animation=”none” gradient_type=”default” shape_type=””][vc_column column_padding=”no-extra-padding” column_padding_tablet=”inherit” column_padding_phone=”inherit” column_padding_position=”all” column_element_direction_desktop=”default” column_element_spacing=”default” desktop_text_alignment=”default” tablet_text_alignment=”default” phone_text_alignment=”default” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_backdrop_filter=”none” column_shadow=”none” column_border_radius=”none” column_link_target=”_self” column_position=”default” gradient_direction=”left_to_right” overlay_strength=”0.3″ width=”1\/1″ tablet_width_inherit=”default” animation_type=”default” bg_image_animation=”none” border_type=”simple” column_border_width=”none” column_border_style=”solid”][vc_row_inner column_margin=”default” column_direction=”default” column_direction_tablet=”default” column_direction_phone=”default” text_align=”left” row_position=”default” row_position_tablet=”inherit” row_position_phone=”inherit” overflow=”visible” pointer_events=”all” css=”.vc_custom_1674774851570{margin-top: 5% !important;margin-bottom: 5% !important;}”][vc_column_inner column_padding=”no-extra-padding” column_padding_tablet=”inherit” column_padding_phone=”inherit” column_padding_position=”all” column_element_direction_desktop=”default” column_element_spacing=”default” desktop_text_alignment=”default” tablet_text_alignment=”default” phone_text_alignment=”default” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_backdrop_filter=”none” column_shadow=”none” column_border_radius=”none” column_link_target=”_self” overflow=”visible” gradient_direction=”left_to_right” overlay_strength=”0.3″ width=”1\/1″ tablet_width_inherit=”default” animation_type=”default” bg_image_animation=”none” border_type=”simple” column_border_width=”none” column_border_style=”solid”][vc_custom_heading text=”Enabling Students to Make Sense of Mathematics” use_theme_fonts=”yes”][divider line_type=”No Line” custom_height=”15″][vc_column_text]More than twenty years before the Common Core Math Standards appeared on the scene, Dr. Henry Borenson, the inventor of Hands-On Equations, was already using \u201ccommon core mathematical practices\u201d in his work with students. With peer-reviewed published articles such as, \u201cTeaching the Process of Mathematical Investigation,\u201d \u201cTeaching Students to Think in Mathematics and to Make Conjectures,\u201d and \u201cPromoting Mathematical Creativity in the Classroom,\u201d Dr. Borenson emphasized the importance of students being able to understand and communicate mathematics.<\/p>\n

Since algebra deals with abstract symbols many students have difficulty conceptualizing the meaning of algebraic linear equations and the means of their solution. The visual and kinesthetic approach of Hands-On Equations enables students to grasp algebraic concepts concretely, pictorially and then abstractly. Our verbal problems books enable students to apply the Hands-On Equations strategies to the solution of verbal problems.<\/p>\n

Many students find fractions difficult since they do not understand the meaning of unit fractions or fractions. Our Developing Fractions Sense programs for grades 3, 4 and 5 enable the teacher to present the Common Core fraction standards for those grades in a sense-making approach by utilizing concrete and pictorial presentations before providing arithmetic means.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][vc_row type=”full_width_background” full_screen_row_position=”middle” column_margin=”default” column_direction=”default” column_direction_tablet=”default” column_direction_phone=”default” scene_position=”center” text_color=”dark” text_align=”left” row_border_radius=”none” row_border_radius_applies=”bg” overflow=”visible” overlay_strength=”0.3″ gradient_direction=”left_to_right” shape_divider_position=”bottom” bg_image_animation=”none” gradient_type=”default” shape_type=””][vc_column column_padding=”no-extra-padding” column_padding_tablet=”inherit” column_padding_phone=”inherit” column_padding_position=”all” column_element_direction_desktop=”default” column_element_spacing=”default” desktop_text_alignment=”default” tablet_text_alignment=”default” phone_text_alignment=”default” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_backdrop_filter=”none” column_shadow=”none” column_border_radius=”none” column_link_target=”_self” column_position=”default” gradient_direction=”left_to_right” overlay_strength=”0.3″ width=”1\/1″ tablet_width_inherit=”default” animation_type=”default” bg_image_animation=”none” border_type=”simple” column_border_width=”none” column_border_style=”solid”][vc_row_inner column_margin=”default” column_direction=”default” column_direction_tablet=”default” column_direction_phone=”default” text_align=”left” row_position=”default” row_position_tablet=”inherit” row_position_phone=”inherit” overflow=”visible” pointer_events=”all” css=”.vc_custom_1674774859372{margin-top: 5% !important;margin-bottom: 3% !important;}”][vc_column_inner column_padding=”no-extra-padding” column_padding_tablet=”inherit” column_padding_phone=”inherit” column_padding_position=”all” column_element_direction_desktop=”default” column_element_spacing=”default” desktop_text_alignment=”default” tablet_text_alignment=”default” phone_text_alignment=”default” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_backdrop_filter=”none” column_shadow=”none” column_border_radius=”none” column_link_target=”_self” overflow=”visible” gradient_direction=”left_to_right” overlay_strength=”0.3″ width=”1\/1″ tablet_width_inherit=”default” animation_type=”default” bg_image_animation=”none” border_type=”simple” column_border_width=”none” column_border_style=”solid”][vc_custom_heading text=”Common Core State Standards: Mathematical Content” use_theme_fonts=”yes”][divider line_type=”No Line” custom_height=”15″][vc_column_text]As early as the third grade the Common Core Math Standards requires students to be able to solve verbal problems and to express those as abstract equations using a letter for the unknown. Hands-On Equations enables students to experience success by first representing the problem concretely or pictorially, and only then by an abstract equation using a letter for the unknown.<\/p>\n

Hands-On Equations can enable your students to meet these Common Core Mathematical Content standards:[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_row_inner column_margin=”default” column_direction=”default” column_direction_tablet=”default” column_direction_phone=”default” text_align=”left” row_position=”default” row_position_tablet=”inherit” row_position_phone=”inherit” overflow=”visible” pointer_events=”all” css=”.vc_custom_1674774882893{margin-right: 10% !important;margin-bottom: 5% !important;margin-left: 10% !important;}”][vc_column_inner column_padding=”no-extra-padding” column_padding_tablet=”inherit” column_padding_phone=”inherit” column_padding_position=”all” column_element_direction_desktop=”default” column_element_spacing=”default” desktop_text_alignment=”default” tablet_text_alignment=”default” phone_text_alignment=”default” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_backdrop_filter=”none” column_shadow=”none” column_border_radius=”none” column_link_target=”_self” overflow=”visible” gradient_direction=”left_to_right” overlay_strength=”0.3″ width=”1\/1″ tablet_width_inherit=”default” animation_type=”default” bg_image_animation=”none” border_type=”simple” column_border_width=”none” column_border_style=”solid”]

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    \n
  • Solve two-step word problems and represent those problems using equations with a letter standing for the unknown (3.OA.8).<\/li>\n
  • Solve multistep word problems using drawing and equations with a symbol for the unknown (4.OA.2).<\/li>\n
  • Understand that positive and negative numbers have opposite values (6.NS.5).<\/li>\n
  • Solve mathematical problems using algebraic expressions and equations (7.EE.4).<\/li>\n<\/ul>\n <\/div>[\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row]\n","protected":false},"excerpt":{"rendered":"

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